3.5: Types of Rocks
IGNEOUS ROCKS
Igneous rocks form from the cooling and hardening of molten magma in many different environments. These rocks are identified by their composition and texture. More than 700 different types of igneous rocks are known.
Magma Composition
The rock beneath the Earth’s surface is sometimes heated to high enough temperatures that it melts to create magma. Different magmas have different composition and contain whatever elements were in the rock that melted. Magmas also contain gases. The main elements are the same as the elements found in the crust. Table 1 lists the abundance of elements found in the Earth’s crust and in magma. The remaining 1.5% is made up of many other elements that are present in tiny quantities.
| Table 1. Elements in Earth’s Crust and Magma | ||
|---|---|---|
| Element | Symbol | Percent |
| Oxygen | O | 46.6% |
| Silicon | Si | 27.7% |
| Aluminum | Al | 8.1% |
| Iron | Fe | 5.0% |
| Calcium | Ca | 3.6% |
| Sodium | Na | 2.8% |
| Potassium | K | 2.6% |
| Magnesium | Mg | 2.1% |
| Total | 98.5% |
Whether rock melts to create magma depends on several factors:
- Temperature: Temperature increases with depth, so melting is more likely to occur at greater depths.
- Pressure: Pressure increases with depth, but increased pressure raises the melting temperature, so melting is less likely to occur at higher pressures.
- Water: The addition of water changes the melting point of rock. As the amount of water increases, the melting point decreases.
- Rock composition: Minerals melt at different temperatures, so the temperature must be high enough to melt at least some minerals in the rock. The first mineral to melt from a rock will be quartz (if present) and the last will be olivine (if present).
The different geologic settings that produce varying conditions under which rocks melt will be discussed in the “Plate Tectonics” chapter.
As a rock heats up, the minerals that melt at the lowest temperatures will melt first. Partial melting occurs when the temperature on a rock is high enough to melt only some of the minerals in the rock. The minerals that will melt will be those that melt at lower temperatures. Fractional crystallization is the opposite of partial melting. This process describes the crystallization of different minerals as magma cools.
Bowen’s Reaction Series indicates the temperatures at which minerals melt or crystallize (figure 1). An understanding of the way atoms join together to form minerals leads to an understanding of how different igneous rocks form. Bowen’s Reaction Series also explains why some minerals are always found together and some are never found together.
Figure 1. Bowen's Reaction Series
Follow this link to see a diagram illustrating Bowen’s Reaction Series.
This excellent video that explains Bowen’s Reaction Series in detail.
If the liquid separates from the solids at any time in partial melting or fractional crystallization, the chemical composition of the liquid and solid will be different. When that liquid crystallizes, the resulting igneous rock will have a different composition from the parent rock.
Intrusive and Extrusive Igneous Rocks
Igneous rocks are called intrusive when they cool and solidify beneath the surface. Intrusive rocks form plutons and so are also called plutonic. A pluton is an igneous intrusive rock body that has cooled in the crust. When magma cools within the Earth, the cooling proceeds slowly. Slow cooling allows time for large crystals to form, so intrusive igneous rocks have visible crystals. Granite is the most common intrusive igneous rock (see figure 2 for an example).
Figure 2. Granite is made of four minerals, all visible to the naked eye: feldspar (white), quartz (translucent), hornblende (black), and biotite (black, platy).
Igneous rocks make up most of the rocks on Earth. Most igneous rocks are buried below the surface and covered with sedimentary rock, or are buried beneath the ocean water. In some places, geological processes have brought igneous rocks to the surface. Figure 3 below shows a landscape in California’s Sierra Nevada made of granite that has been raised to create mountains.
Figure 3. California's Sierra Nevada is intrusive igneous rock exposed at Earth's surface.
Igneous rocks are called extrusive when they cool and solidify above the surface. These rocks usually form from a volcano, so they are also called volcanic rocks (figure 4).
Figure 4. Extrusive igneous rocks form after lava cools above the surface.
Extrusive igneous rocks cool much more rapidly than intrusive rocks. There is little time for crystals to form, so extrusive igneous rocks have tiny crystals (figure 5).
Figure 5. Cooled lava forms basalt with no visible crystals. Why are there no visible crystals?
Some volcanic rocks have a mixed texture. A rock such as an andesite may have large crystals set within a matrix of tiny crystals. In this case, the magma cooled enough to form some crystals before erupting. Once erupted, the rest of the lava cooled rapidly. This is called porphyritic texture.
Cooling rate and gas content create other textures (see figure 6 for examples of different textures). Lavas that cool extremely rapidly may have a glassy texture. Those with many holes from gas bubbles have a vesicular texture.
Figure 6. Different cooling rate and gas content resulted in these different textures.
Igneous Rock Classification
Igneous rocks are classified by their composition, from felsic to ultramafic. The characteristics and example minerals in each type are included in table 2.
| Table 2. Properties of Igneous Rock Compositions | |||
|---|---|---|---|
| Composition | Color | Density | Minerals |
| Felsic | Light | Low | Quartz, orthoclase feldspar |
| Intermediate | Intermediate | Intermediate | Plagioclase feldspar, biotite, amphibole |
| Mafic | Dark | High | Olivine, pyroxene |
| Ultramafic | Very dark | Very high | Olivine |
| Table 3. Silica Composition and Texture of Major Igneous Rocks | |||
|---|---|---|---|
| Type | Amount of Silica | Extrusive | Intrusive |
| Ultramafic | <45% | Komatiite | Peridotite |
| Mafic | 45-52% | Basalt | Gabbro |
| Intermediate | 52-63% | Andesite | Diorite |
| Intermediate-Felsic | 63-69% | Dacite | Granodiorite |
| Felsic | >69% SiO 2 | Rhyolite | Granite |
Some of the rocks in the table 3 were pictured earlier in this chapter. Look back at them and, using what you know about the size of crystals in extrusive and intrusive rocks and the composition of felsic and mafic rocks, identify the rocks in the following photos in figure 7:
Figure 7. These are photos of A) rhyolite, B) gabbro, C) peridotite, and D) komatiite.
Uses of Igneous Rocks
Igneous rocks have a wide variety of uses. One important use is as stone for buildings and statues. Granite is used for both of these purposes and is popular for kitchen countertops (figure 8).
Figure 8. Granite is an igneous rock used commonly in statues and building materials.
Pumice is commonly used as an abrasive. Pumice is used to smooth skin or scrape up grime around the house. When pumice is placed into giant washing machines with newly manufactured jeans and tumbled, the result is “stone-washed” jeans. Ground up pumice stone is sometimes added to toothpaste to act as an abrasive material to scrub teeth.
Peridotite is sometimes mined for peridot, a type of olivine that is used in jewelry. Diorite was used extensively by ancient civilizations for vases and other decorative artwork and is still used for art today (Figure 9).
Figure 9. This diorite statue was made in approximately 2120 BC.
SEDIMENTARY ROCKS
Figure 10. The White House of the USA is made of a sedimentary rock called sandstone.
The White House (shown in the figure 10) is the official home and workplace of the President of the United States of America. Why do you think the White House is white? If you answered, “Because it is made of white rock,” you would be only partially correct. Construction for the White House began in 1792. Its outside walls are made of the sedimentary rock sandstone. This sandstone is very porous and is easily penetrated by rainwater. Water damage was common in the early days of construction for the building. To stop the water damage, workers covered the sandstone in a mixture of salt, rice, and glue, which help to give the White House its distinctive white color.
Sediments
Sandstone is one of the common types of sedimentary rocks that form from sediments. There are many other types. Sediments may include:
- fragments of other rocks that often have been worn down into small pieces, such as sand, silt, or clay.
- organic materials, or the remains of once-living organisms.
- chemical precipitates, which are materials that get left behind after the water evaporates from a solution.
Rocks at the surface undergo mechanical and chemical weathering. These physical and chemical processes break rock into smaller pieces. Physical weathering simply breaks the rocks apart. Chemical weathering dissolves the less stable minerals. These original elements of the minerals end up in solution and new minerals may form. Sediments are removed and transported by water, wind, ice, or gravity in a process called erosion (figure 11). Much more information about weathering can be found in the “Weathering and Formation of Soil” chapter. Erosion is described in detail in the “Erosion and Deposition” chapter.
Figure 11. Water erodes the land surface in Alaska’s Valley of Ten Thousand Smokes.
Streams carry huge amounts of sediment (figure 12). The more energy the water has, the larger the particle it can carry. A rushing river on a steep slope might be able to carry boulders. As this stream slows down, it no longer has the energy to carry large sediments and will drop them. A slower moving stream will only carry smaller particles.
Figure 12. A river dumps sediments along its bed and on its banks.
Sediments are deposited on beaches and deserts, at the bottom of oceans, and in lakes, ponds, rivers, marshes, and swamps. Avalanches drop large piles of sediment. Glaciers leave large piles of sediments, too. Wind can only transport sand and smaller particles. The type of sediment that is deposited will determine the type of sedimentary rock that can form. Different colors of sedimentary rock are determined by the environment where they are deposited. Red rocks form where oxygen is present. Darker sediments form when the environment is oxygen poor.
Sedimentary Rock Formation
Accumulated sediments harden into rock by lithification , as illustrated in figure 13. Two important steps are needed for sediments to lithify.
- Sediments are squeezed together by the weight of overlying sediments on top of them. This is called compaction . Cemented, non-organic sediments become clastic rocks. If organic material is included, they are bioclastic rocks.
- Fluids fill in the spaces between the loose particles of sediment and crystallize to create a rock by cementation.
Figure 13. This cliff is made of sandstone. Sands were deposited and then lithified.
The sediment size in clastic sedimentary rocks varies greatly (see table 4).
| Table 4. Sedimentary rock sizes and features | ||
|---|---|---|
| Rock | Sediment Size | Other Features |
| Conglomerate | Large | Rounded |
| Breccia | Large | Angular |
| Sandstone | Sand-sized | |
| Slitstone | Silt-sized, smaller than sand | |
| Shale | Clay-sized, smallest |
When sediments settle out of calmer water, they form horizontal layers. One layer is deposited first, and another layer is deposited on top of it. So each layer is younger than the layer beneath it. When the sediments harden, the layers are preserved. Sedimentary rocks formed by the crystallization of chemical precipitates are called chemical sedimentary rocks . As discussed in the “Earth’s Minerals” chapter, dissolved ions in fluids precipitate out of the fluid and settle out, just like the halite in figure 14.
Figure 14. The evaporite, halite, on a cobble from the Dead Sea, Israel.
Biochemical sedimentary rocks form in the ocean or a salt lake. Living creatures remove ions, such as calcium, magnesium, and potassium, from the water to make shells or soft tissue. When the organism dies, it sinks to the ocean floor to become a biochemical sediment, which may then become compacted and cemented into solid rock (figure 15).
Figure 15. Fossils in a biochemical rock, limestone, in the Carmel Formation in Utah.
Table 5 shows some common types of sedimentary rocks.
| Table 5. Common Sedimentary Rocks | ||
|---|---|---|
| Picture | Rock Name | Type of Sedimentary Rock |
| Conglomerate | Clastic (fragments of non-organic sediments) | |
| Breccia | Clastic | |
| Sandstone | Clastic | |
| Siltstone | Clastic | |
| Shale | Clastic | |
| Rock Salt | Chemical precipitate | |
| Gypsum | Chemical precipitate | |
| Dolostone | Chemical precipitate | |
| Limestone | Bioclastic (sediments from organic materials, or plant or animal remains) | |
| Coal | Organic |
Uses of Sedimentary Rocks
Sedimentary rocks are used as building stones, although they are not as hard as igneous or metamorphic rocks. Sedimentary rocks are used in construction. Sand and gravel are used to make concrete; they are also used in asphalt. Many economically valuable resources come from sedimentary rocks. Iron ore and aluminum are two examples.
METAMORPHIC ROCKS
In the large outcrop of metamorphic rocks in figure 16, the rocks’ platy appearance is a result of the process metamorphism. Metamorphism is the addition of heat and/or pressure to existing rocks, which causes them to change physically and/or chemically so that they become a new rock. Metamorphic rocks may change so much that they may not resemble the original rock.
Figure 16. The platy layers in this large outcrop of metamorphic rock show the effects of pressure on rocks during metamorphism.
Metamorphism
Any type of rock—igneous, sedimentary, or metamorphic—can become a metamorphic rock. All that is needed is enough heat and/or pressure to alter the existing rock’s physical or chemical makeup without melting the rock entirely. Rocks change during metamorphism because the minerals need to be stable under the new temperature and pressure conditions. The need for stability may cause the structure of minerals to rearrange and form new minerals. Ions may move between minerals to create minerals of different chemical composition. Hornfels, with its alternating bands of dark and light crystals, is a good example of how minerals rearrange themselves during metamorphism. Hornfels is shown in table 6.
Figure 17. A foliated metamorphic rock.
Extreme pressure may also lead to foliation , the flat layers that form in rocks as the rocks are squeezed by pressure (figure 17). Foliation normally forms when pressure is exerted in only one direction. Metamorphic rocks may also be non-foliated. Quartzite and limestone, shown in table 6, are nonfoliated.
The two main types of metamorphism are both related to heat within Earth:
- Regional metamorphism: Changes in enormous quantities of rock over a wide area caused by the extreme pressure from overlying rock or from compression caused by geologic processes. Deep burial exposes the rock to high temperatures.
- Contact metamorphism: Changes in a rock that is in contact with magma because of the magma’s extreme heat.
Table 6 shows some common metamorphic rocks and their original parent rock.
| Table 6. | |||
|---|---|---|---|
| Picture | Rock Name | Type of Metamorphic Rock | Comments |
| Slate | Foliated | Metamorphism of shale | |
| Phyllite | Foliated | Metamorphism of slate, but under greater heat and pressure than slate | |
| Schist | Foliated | Often derived from metamorphism of claystone or shale; metamorphosed under more heat and pressure than phyllite | |
| Gneiss | Foliated | Metamorphism of various different rocks, under extreme conditions of heat and pressure | |
| Hornfels | Non-foliated | Contact metamorphism of various different rock types | |
| Quartzite | Non-foliated | Metamorphism of sandstone | |
| Marble | Non-foliated | Metamorphism of limestone | |
| Metaconglomerate | Non-foliated | Metamorphism of conglomerate |
Uses of Metamorphic Rocks
Quartzite and marble are commonly used for building materials and artwork. Marble is beautiful for statues and decorative items such as vases (see an example in figure 18). Ground up marble is also a component of toothpaste, plastics, and paper.
Figure 18. Marble is used for decorative items and in art.
Quartzite is very hard and is often crushed and used in building railroad tracks (see figure 19). Schist and slate are sometimes used as building and landscape materials. Graphite, the “lead” in pencils, is a mineral commonly found in metamorphic rocks.
Figure 19. Crushed quartzite is sometimes placed under railroad tracks because it is very hard and durable.
LESSON SUMMARY
- Igneous rocks form either when they cool very slowly deep within the Earth (intrusive) or when magma cools rapidly at the Earth’s surface (extrusive).
- Rock may melt to create magma if temperature increases, pressure decreases, or water is added. Different minerals melt at different temperatures.
- Igneous rocks are classified on their composition and grain size, which indicates whether they are intrusive or extrusive.
- Weathering and erosion produce sediments. Sediments are transported by water, wind, ice, or gravity.
- After sediments are deposited, they undergo compaction and/or cementation to become sedimentary rocks.
- Biochemical sedimentary rocks form when living creatures using ions in water to create shells, bones, or soft tissue die and fall to the bottom as sediments.
- Metamorphic rocks form when heat and pressure transform an existing rock into a new rock.
- Contact metamorphism occurs when hot magma transforms the rock that it contacts.
- Regional metamorphism transforms large areas of existing rocks under the tremendous heat and pressure created by geologic processes.
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Contributors and Attributions
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Original content from Kimberly Schulte (Columbia Basin College) and supplemented by Lumen Learning . The content on this page is copyrighted under a Creative Commons Attribution 4.0 International license.


9.2: Overview of the Transfer Process
Perhaps you decided to attend HACC to save some money or to explore a career before committing to a bachelor’s degree program. Now you may find that a bachelor’s degree is worth pursuing because that degree appears to be a requirement for the kind of career you want or because you will be able to boost your income opportunities. If you are thinking about transferring to a bachelor’s program, be sure to follow these steps:
- Understand the transfer process
- Select your specific transfer college as soon as possible.
- Choose a transfer curriculum.
- Work with your advisor to select required transfer courses.
- Review HACC's transfer information. This includes transfer checksheets, comprehensive transfer notebooks, course equivalencies, transfer agreements, college directories and catalogs.
2. Learn more about Dual Admission agreements. A dual-admission agreement is a cooperative partnership between HACC and a bachelor’s degree-granting college or university. Dual Admission is for students interested in pursuing a bachelor degree. This agreement will:
- facilitate your admission process;
- transfer your associate degree credits into a bachelor degree program; and
- help ensure you do not lose time or money.
HACC has over 18 colleges and universities you can choose from for a dual-admission agreement.
3. Articulation agreements are transfer agreements with the bachelor’s degree-granting colleges and universities that determine how credit is transferred.
4. Meet with your advisor regularly, at least once each semester to make sure you are on track towards meeting your academic and career goals. Your advisor can help you learn more about the transfer process and create an educational plan based on your major and transfer institution.
Once you have determined which program(s) you are interested in pursuing, then you are ready to develop your individualized student educational plan. While at HACC, you may work on multiple goals. You potentially could earn a certificate plus an associate degree plus pursue a transfer program if you select your classes wisely!


5: Decision Making Last updated Save as PDF Page ID 47564 Lumen Learning Lumen Learning 5.1: Using a Decision Tree 5.2: Introduction to Managing Group Decision Making 5.3: Managing Group Decision Making 5.4: Putting It Together- Decision Making 5.5: Assignment- Decision Making at Sun City Boards 5.6: Assignment- Your Decision-Making Process 5.7: Discussion- Improving Decision Making at Sun City Boards 5.8: Discussion- Could These Bad Decisions Have Been Avoided? 5.9: Why It Matters- Decision Making 5.10: Introduction to Barriers to Individual Decision Making and Styles of Decision Making 5.11: Barriers to Individual Decision Making 5.12: Styles of Decision Making 5.13: Introduction to Rational Decision Making vs. Other Types of Decision Making 5.14: Rational Decision Making vs. Other Types of Decision Making 5.15: Introduction to Evidence-Based Decision Making 5.16: Evidence-Based Decision Making 5.17: Introduction to Using a Decision Tree


1.5: How Do I Describe Where I Am?
Defining a location by using the geographic grid is only part of the process of describing a place. Geographers are primarily concerned with two ways of describing a place: site and situation. Site refers to the physical characteristics, such as the topography, vegetative cover, climatic conditions, and the like. Situation , on the other hand, refers to the area surrounding the place, and is sometimes referred to as relative location. In other words, where is this place relative to other places, and how is it connected to its surroundings via transportation networks? New Orleans provides an excellent example of site versus situation. The site of New Orleans is not ideal for a city, as it lies below sea level and is prone to flooding. However, the situation of New Orleans is much better in that New Orleans is connected to large portion of the Mississippi River’s network of navigable waterways while also being close to the Gulf of Mexico and convenient to coastal traffic. Hence, the situation of New Orleans is why the city has not long since been abandoned, despite catastrophic flooding such as during Hurricane Katrina in 2005. As we examine various placesaround the world, both site and situation are key considerations in determining the “why” of where a place is located.
1.5.1 Regions
While site and situation can help describe a place, a broader view of the world and the connections between places can be derived from the concept of regions. A region is an area that shares some sort of common characteristic that binds the area into a whole. Geographers use regions to help one understand the interconnections between places and simplify a complex world. Two major types of regions are formal and functional. Formal regions are characterized by homogeneity or uniformity in one or a number of different characteristics. These characteristics can be both human and physical-related, so regions could be defined by climate or vegetation types, in the sense of physical geography, or they could be defined by language or ethnicity, in the sense of human geography. One example of a map that includes formal regions would be a map of the states in the US. In this map, each state could be considered a formal region because each state is governed in a common or unique way, and hence portrays homogeneity ( Figure 1.6 ).
A functional region, which is sometimes called a nodal region, is an area that contains a central node or focal point to which other places in the region are connected by some activity. Functional regions can be seen in cities where the central area of the city might serve as the focal point for the rest of the metropolitan area ( Figure 1.7 ). At a smaller scale, a Wi-Fi hotspot could be considered the focal point of a functional region that extends to the range of the Wi-Fi signal. Even the delivery area for the local pizza restaurant would be a functional region with the restaurant as a central node.
Regions are devised and not absolute, so whether or not a particular place fits within a region is sometimes a matter of dispute. For example, scholars disagree on the exact extent of the American South as a formal region. What defines this region? It depends on what characteristics one uses to define the region, be they food, dialect, political affiliation, historical affiliation in the Civil War, or any other element the mind conjures up when one thinks of the South as a relatively homogeneous formal region. Most geographers see Texas as a part of the South, but West Texas is much different from East Texas, and Florida is likewise diverse. Extreme southern Florida is vastly different from the panhandle of Florida in ethnic make-up and political affiliation. The opinion on what constitutes the Southern region varies based on personal viewpoints ( Figure 1.8 ). The Southern region, then, may be thought of as a vernacular (or perceptual) region because theboundaries of these types of regions depend on the perspectives or mental maps of different groups of people who live both outside or inside that region. Hence, the concept of regions and their definition is not a straightforward process and involves generalities and varying opinions.


13.5: The global mercury cycle
In this lecture you will learn the following
- Mercury cycle
- Mercury toxicity.
- Mercury poisoning.
mercury
The Mercury Cycle
Mercury is 62nd in terms of natural abundance and is found everywhere, usually as the mineral cinnabar, HgS, although 30 minerals containing Hg are known. The oxidation states are Hg(0), Hg(I) and Hg(II), where Hg(I) has been shown to exist as Hg 2 2 + .
HgS - cinnabar
The three Hg species are related by the disproportionation:
Hg
2
2
+
→ Hg
0
+ Hg
2
+
E° = -0.131 V or K= 6 x 10
-3
In addition:
Hg
2
2
+
/Hg E° = 0.789 V
Hg
2
+
/Hg E° = 0.854 V
This means that to oxidise Hg to Hg
2
2
+
an oxidising agent with potential > 0.789V is required, but very importantly < 0.854 V, otherwise oxidation to Hg
2
+
will occur. There are no common oxidants that fit this arrangement so if any reaction occurs the product will be Hg
2
+
. The equilibrium constant of 6 x 10
-3
shows that when Hg(I) is formed it is moderately stable, however any agent that reduces the Hg(II) concentration automatically drives the reaction from Left → Right. Given that many Hg(II) derivatives are insoluble then this clearly restricts the range of Hg(I) compounds.
Minamata Disease
There have been several serious outbreaks of mercury poisoning. The most famous was between 1953 and 1965 at Minamata Bay in Japan when 46 people died and 120 suffered severe symptoms. As of March 2001, 2,265 victims had been officially recognised (1,784 of whom had died) and over 10,000 had received financial compensation from Chisso. By 2004, Chisso Corporation had paid $86 million in compensation, and in the same year was ordered to clean up its contamination. On March 29th, 2010, a settlement was reached to compensate as-yet uncertified victims.
The disease was first noticed in cats (who were seen throwing themselves into the sea) and was quickly traced to mercury poisoning acquired as a result of eating contaminated fish (5-10 ppm Hg). The investigations that followed showed that the fish had acquired the high mercury due to the dumping of inorganic mercury salts and methylmercury from the Chisso Co. plastics factory upstream.
Analysis of fish exhibits from museums, some over 90 years old, has shown that mercury levels for ocean fish are similar but that river fish levels have risen as a result of man-made contamination. The forms of mercury occuring in the environment are Hg 2 + and methylmercury, either MeHg + or Me 2 Hg. Interconversion can be affected by microorganisms.
Aerobes can solubilize Hg 2 + from cinnabar (K sp ~10 -53 ) which in sediments was considered safe since the solubility product was so small. The conversion of S 2- → SO 3 2 - → SO 4 2 - allows the insoluble sulfide to breakdown and in the process other Hg(II) salts are formed or the mercury may get reduced to Hg(0) enzymatically.
\[\ce{Hg^{2+} + NADH + H^{+} → Hg^{0} + NAD^{+} + 2 H^{+}}\]
where NADH = reduced form of nicotinamideadeninedinucleotide. This conversion can be considered as a detoxification process since Hg 0 is more easily eliminated.
In the environment, sulfate-reducing bacteria take up mercury in its inorganic form and through metabolic processes convert it to methylmercury. Sulfate-reducing bacteria are found in anaerobic conditions, typical of the well-buried muddy sediments of rivers, lakes, and oceans where methylmercury concentrations tend to be highest. Sulfate-reducing bacteria use sulfur rather than oxygen as their cellular energy-driving system. One hypothesis is that the uptake of inorganic mercury by sulfate-reducing bacteria occurs via passive diffusion of the dissolved complex HgS. Once the bacterium has taken up this complex, it utilizes detoxification enzymes to strip the sulfur group from the complex and replaces it with a methyl group:
\[\ce{HgS → CH3Hg(II)X + H2S }\]
Upon methylation, the sulfate-reducing bacteria transport the new mercury complex back to the aquatic environment, where it is taken up by other microorganisms. Bacteria eliminate Hg by methylating it first to MeHg + and Me 2 Hg. The detoxification process for them is the reverse for us unfortunately! The conversion probably involves vitamin B12 a methyl-cobalt organometallic compound so this is another example of synthesis involving transmetallation.
The major source of methylmercury exposure in humans is consumption of fish, marine mammals, and crustaceans. Once inside the human body, roughly 95% of the fish-derived methylmercury is absorbed from the gastrointestinal tract and distributed throughout the body. Uptake and accumulation of methylmercury is rapid due to the formation of methylmercury-cysteine complexes. Methylmercury is believed to cause toxicity by binding the sulfhydryl groups at the active centers of critical enzymes and structural proteins. Binding of methylmercury to these moieties constitutively alters the structure of the protein, inactivating or significantly lowering its functional capabilities.
Once the Me 2 Hg is formed it is volatile and when released into the atmosphere it is readily photolysed by UV light
\[\ce{Me2Hg → Hg^{0} + 2 CH3^{\cdot} → CH4 \,text{ or } C2H6}\]
Other microorganisms can convert MeHg + to Hg 0 + CH 4 that is make the mercury considerably less toxic to humans.
Mercury Toxicity
The toxicity of mercury arises from the very high affinity of the soft Hg atom for sulfhydryl (—SH) groups in enzymes. Simple mercury-sulfur compounds have been studied as potential analogs of natural systems. The Hg atoms are most commonly four-coordinated, as in [Hg 2 (SMe) 6 ] 2- .
Mercury poisoning was a serious concern even from early days. Issac Newton, Alfred Stock worked in the early 20 th century. Later in 60s awareness came following the incidence of brain damage and death it caused among the inhabitants in Minamata, Japan. Mercury from a plastic company was allowed to escape into a bay where it found its way into fish that were later eaten. Research has shown that bacteria found in sediments are capable of methylating mercury, and that species such HgMe 2 and [HgCH 3 ] + enter the food chain because they readily penetrate cell walls. The bacteria appear to produce HgMe 2 as a means of eliminating toxic mercury ions through their cell walls and into the environment.
References
- Inorganic Chemistry, Principles of structure and reactivity, 4 th edition; 1993, J. E. Huheey, E. A. Keiter, R. L. Keiter, Addison-Wesley Publishing Co, New York.
- Advanced Inorganic Chemistry, 6 th edition, 1999, F. A. Cotton, G. Wilkinson, C. A. Murillo, M. Bochmann, John Wiley and Sons, New York.
- Organometallics, A Concise Introduction, 2 nd edition (revised), 1992, Ch. Elschenbroich, A. Salzer, Weinheim, Germany.
- Inorganic Chemistry, 3 rd Edition, 1999, D. F. Shriver, P. W. Atkins, Oxford University Press, Oxford.
- Inorganic Chemistry, 2 nd Edition, 2005, C.C. Housecroft and A. G. Sharpe, Pearson, Prentice Hall, England.
Methylmercury
The usual method of ingestion of a metal into the body is:
a) Orally - the Gastrointestinal Tract
b) via the lungs - the Respiratory Tract
a) Orally - (mouth, stomach, small intestine): Food digestion begins in the mouth where saliva containing the enzyme amylase beaks down starch to lower sugars. Most digestion occurs in the stomach in the presence of HCl (pH ~1.6 ie. 0.17M HCl). In the case of mercury it is quite readily absorbed through the stomach since reaction of mercury salts with HCl produces HgCl
2
. This neutral covalent molecule (solubility in H
2
O 0.5 g/100 mL but 8g/100 mL in ethanol) is absorbed far better than most inorganic ions and this no doubt contributes to its high toxicity.
b) Respiratory tract (nose, lungs): This is usually unimportant for most metals but in some cases it can be more efficient that via the gastrointestinal tract. For example, lead where 50% of Pb in air can be absorbed but only 5-10% via the gastrointestinal tract. Volatile dimethyl mercury is another case for concern.
dimethyl
Summary
Organic mercury tends to increase up the food chain, particularly in lakes. The mud at the bottom of a lake may have 100 or 1000 times the amount of mercury than is in the water. Bacteria, worms and insects in the mud extract and concentrate the organic mercury. Small fish that eat them further concentrate the mercury in their bodies. This concentration process, known as "bioaccumulation", continues as larger fish eat smaller fish until the top predator fish in the lake may have methylmercury levels in their tissues that are up to 1,000,000 times the level in the water in which they live. We then eat the fish....
To consume a human being would be extremely unhealthy for any animal. Humans carry the highest concentration of toxic chemicals of all creatures on the planet. Their livers, hearts, kidneys and brains are so heavily contaminated with hundreds of different synthetic chemicals that if humans were slaughtered as a meat source, they'd never pass USDA food safety standards.
Table \(\PageIndex{1}\): Properties of Me
2
Hg
| Molecular formula | C 2 H 6 Hg |
| Molar mass | 230.66 g mol -1 |
| Appearance | Colourless liquid |
| Density | 2.96 g/mL |
| Melting point | -43 °C |
| Boiling point | 87-97 °C |
| Solubility in water | Insoluble |


5.1: Agency Report
The Agency Organizational Report has four parts:
GENERAL AGENCY INFORMATION
- Provide Agency name and address
- Identify the purpose of the organization. Include a copy of the mission statement and the vision statement if these exist
- Identify the funding source[s] for the organization
- Present a brief history of the organization – who, when, why etc. Who founded the agency? When was it founded and why? Upon what is the agency founded (e.g. a law, charter, judicial decision, and executive order)?
INTERNAL STRUCTURE OF THE AGENCY
1. How is the agency structured? Identify all the components (e.g. units, departments) which make up the agency.
Typically, agencies have an organizational chart which identifies all of the organization’s segments. It is NOT sufficient for the student to merely place this chart into his/her report. The student may, however, include this chart as long as he/she explains each part. If the student is working in a program which fits into a larger organization (e.g. a mental health center which is part of a county-wide system or a larger corporation), the student need only briefly describe the structure of the “parent “organization, while going into more detail regarding the portion in which the student is placed).
2. Within every organization a variety of decisions are made. Clearly identify where the following decisions are made:
a. policy decisions
b. program decisions
c. budget decisions
d. hiring and firing decisions
e. treatment (for clients) decisions
3. Identify the variety of services offered by the agency and show how these are designed to meet the agency’s stated purpose
EXTERNAL RELATIONS OF AGENCY AND ACCOUNTABILITY
- Briefly identify the major agencies your organization has relationships with, and the nature of these relationships (e.g., referral, legislative, etc.). It may be helpful to identify the agency and/or the other major agencies affiliated with your agency, i.e., provide a chart that shows the type of agency and relationship to the student’s agency.
- How does your agency demonstrate that it is doing the job it claims to be doing? (i.e., what is its evaluation model?) To whom is your agency ultimately accountable? (e.g. a board of directors, a funding source, the tax payer, government or legislative bodies, the clients). Determine the cost per client (total budget and total number of clients served)
AGENCY STRUCTURE AND CLIENT SERVICES
How does your agency’s structure (see Part II) impact upon the delivery of services to clients? For example, if an agency’s administrative tone is democratic and personally warm, one may find this style has increased morale among the workers. The outcome may be more effective and personalized services by workers to clients. A student is expected to demonstrate that he/she understands that an organization’s structure affects the delivery of services to clients by citing examples like the one above.


2.5: Correlation and Causation, Scatter Plots
The label on a can of Planters Cocktail Peanuts says, “Scientific evidence suggest but does not prove that eating 1.5 ounces per day of most nuts, such as peanuts, as part of a diet low in saturated fat and cholesterol & not resulting in increased caloric intake may reduce the risk of heart disease. See nutritional information for fat content (1.5 oz. is about 53 pieces).” Why is it written this way and what does this statement mean? There are many studies that exist that show that two variables are related to one another. The strength of a relationship between two variables is called correlation . Variables that are strongly related to each other have strong correlation. However, if two variables are correlated it does not mean that one variable caused the other variable to occur. The above example from the Planters Cocktail Peanuts label is an example of this. There is a strong correlation between eating a diet that is low in saturated fat and cholesterol and heart disease. But that correlation does not mean that eating a diet that is low in saturated fat and cholesterol will cause your risk of heart disease to go down. There could be many different variables that could cause both variables in question to go down or up. One example is that a person’s genetic makeup could make them not want to eat fatty food and also not develop heart disease. No matter how strong a correlation is between two variables, you can never know for sure if one variable causes the other variable to occur without conducting experimentation. The only way to find out if eating a diet low in saturated fat and cholesterol actually lowers the risk of heart disease is to do an experiment.  You cannot morally do this experiment, so there is no way to prove the statement. That is why the word “may” is in the statement. We see many correlations like this one. Always be sure not to make a correlation statement into a causation statement.
Example \(\PageIndex{1}\): Correlation vs Causation
For each of the following scenarios answer the question and give an example of another variable that could explain the correlation.
- There is a negative correlation between number of children a woman has and her life expectancy.
A correlation between two variables does not mean that one causes the other. A possible cause for both variables could be better health care. If there is better health care, then life expectancy goes up, and also with better health care birth control is more readily available.
- There is a positive correlation between ice cream sales and the number of drownings at the beach. Does that mean that eating ice cream can cause a person to drown?
A correlation between two variables does not mean that one causes the other. The cause for both could be that the temperature is going up. The higher the temperature, the more likely someone will buy ice cream and the more people at the beach.
- There is a correlation between waist measures and wrist measures. Does this mean that your waist measurement causes your wrist measurement to change?
A correlation between two variables does not mean that one causes the other. The cause of both could be a person’s genetics, eating habits, exercise habits, etc.
How do we tell if there is a correlation between two variables? The easiest way is to graph the two variables together as ordered pairs on a graph called a scatter plot . To create a scatter plot, consider that one variable is the independent variable and the other is the dependent variable. This means that the dependent variable depends on the independent variable. We usually set up these two variables as ordered pairs where the independent variable is first and the dependent variable is second. Thus, when graphed, the independent variable is graphed along the horizontal axis and the dependent variable is graphed along the vertical axis. You do not connect the dots after plotting these ordered pairs. Instead look to see if there is a pattern, such as a line, that fits the data well. Here are some examples of scatter plots and how strong the linear correlation is between the two variables.
Creating a scatter plot is not difficult. Just make sure that you set up your axes with scaling before you start to plot the ordered pairs.
Example \(\PageIndex{2}\): Creating a Scatter Plot
Data has been collected on the life expectancy and the fertility rate in different countries ("World health rankings," 2013). A random sample of 10 countries was taken, and the data is:
| Country | Life Expectancy (years) | Fertility Rate (number of children per mother) |
| SINGAPORE | 82.3 | 1.1 |
| MONACO | 81.9 | 1.8 |
| CANADA | 81.5 | 1.6 |
| ECUADOR | 76 | 2.5 |
| MALAYSIA | 73.9 | 3 |
| LITHUANIA | 73.8 | 1.2 |
| BELIZE | 73.6 | 3.4 |
| ALGERIA | 73 | 1.8 |
| TRINIDAD/TOB. | 70.8 | 1.7 |
| TAJIKISTAN | 67.9 | 3 |
To make the scatter plot, you have to decide which variable is the independent variable and which one is the dependent variable. Sometimes it is obvious which variable is which, and in some case it does not seem to be obvious. In this case, it seems to make more sense to predict what the life expectancy is doing based on fertility rate, so choose life expectancy to be the dependent variable and fertility rate to be the independent variable. The horizontal axis needs to encompass 1.1 to 3.4, so have it range from zero to four, with tick marks every one unit. The vertical axis needs to encompass the numbers 70.8 to 81.9, so have it range from zero to 90, and have tick marks every 10 units.
Note: Always start the vertical axis at zero to avoid exaggeration of the data.
Graph 2.5.3: Scatter Plot of Life Expectancy versus Fertility Rate
From the graph, you can see that there is somewhat of a downward trend, but it is not prominent. What this says is that as fertility rate increases, life expectancy decreases. The trend is not strong which could be due to not having enough data or this could represent the actual relationship between these two variables. Let’s see what the scatter plot looks like with data from all countries in 2013 ("World health rankings," 2013).
Graph 2.5.4: Scatter Plot of Life Expectancy versus Fertility Rate for All Countries in 2013
Again, there is a downward trend. It looks a little stronger than the previous scatter plot and the trend looks more obvious. This correlation would probably be considered moderate negative correlation. It appears that there is a trend that the higher the fertility rate, the lower the life expectancy. Caution: just because there is a correlation between higher fertility rate and lower life expectancy, do not assume that having fewer children will mean that a person lives longer. The fertility rate does not necessarily cause the life expectancy to change. There are many other factors that could influence both, such as medical care and education. Remember a correlation does not imply causation.


4.4: Reading- Mechanical Weathering
Mechanical weathering (also called physical weathering) breaks rock into smaller pieces. These smaller pieces are just like the bigger rock, just smaller. That means the rock has changed physically without changing its composition. The smaller pieces have the same minerals, in just the same proportions as the original rock.
There are many ways that rocks can be broken apart into smaller pieces. Ice wedging is the main form of mechanical weathering in any climate that regularly cycles above and below the freezing point (figure 2). Ice wedging works quickly, breaking apart rocks in areas with temperatures that cycle above and below freezing in the day and night, and also that cycle above and below freezing with the seasons.
Ice wedging breaks apart so much rock that large piles of broken rock are seen at the base of a hillside, as rock fragments separate and tumble down. Ice wedging is common in Earth’s polar regions and mid latitudes, and also at higher elevations, such as in the mountains. Abrasion is another form of mechanical weathering. In abrasion, one rock bumps against another rock.
- Gravity causes abrasion as a rock tumbles down a mountainside or cliff.
- Moving water causes abrasion as particles in the water collide and bump against one another.
- Strong winds carrying pieces of sand can sandblast surfaces.
- Ice in glaciers carries many bits and pieces of rock. Rocks embedded at the bottom of the glacier scrape against the rocks below.
Abrasion makes rocks with sharp or jagged edges smooth and round. If you have ever collected beach glass or cobbles from a stream, you have witnessed the work of abrasion (figure 3).
Now that you know what mechanical weathering is, can you think of other ways it could happen? Plants and animals can do the work of mechanical weathering (figure 4). This could happen slowly as a plant’s roots grow into a crack or fracture in rock and gradually grow larger, wedging open the crack. Burrowing animals can also break apart rock as they dig for food or to make living spaces for themselves.
Mechanical weathering increases the rate of chemical weathering. As rock breaks into smaller pieces, the surface area of the pieces increases figure 5. With more surfaces exposed, there are more surfaces on which chemical weathering can occur.
Contributors and Attributions
- 9.1: Weathering. Provided by : CK-12. Located at : http://www.ck12.org/book/CK-12-Earth-Science-For-High-School/section/9.1/ . License : CC BY-NC: Attribution-NonCommercial


Titrations
Skills to Develop
- Perform and interpret titration calculations
A titration is a laboratory technique used to precisely measure molar concentration of an unknown solution using a known solution. The basic process involves adding a standard solution of one reagent to a known amount of the unknown solution of a different reagent. For instance, you might add a standard base solution to an mystery acid solution. As the addition takes place, the two reagents in the solutions, in this the acid and base, react. You also add an indicator , which is a molecule that changes color when the original reagent (the acid in the mystery solution, say) is completely consumed by reaction with the standard solution reagent. If you know exactly how much standard was added before the color change, you can calculate how many moles of the unknown were present at the beginning, and thus the concentration of the unknown.
Many of the standard reagents you might use in the lab, especially HCl and NaOH, which are very common and important, are hard to prepare at precise concentration without titration. The reason is that HCl is purchased as a concentrated solution, which can vary a little in concentration because both the HCl and the water can evaporate. NaOH can be purchased as a solid, but it is hygroscopic which means that it absorbs water from the air. It can absorb so much water that it actually dissolves. For this reason, even if you buy it dry, once you open the bottle, it might start to absorb water, and it would be difficult to know when you measure it what % water it is. Thus, if you work in a biochemistry lab, for instance, you might want to control the pH of your solutions by adding a little bit of dilute HCl or NaOH, because chloride and sodium ions are very common and probably are already included in the solution, but you might want to know how concentrated your solutions are. To determine this, you would use a standard solution made of some easier-to-mass acid or base to titrate the solution you actually want to use. Once titrated, you could dilute it precisely to the concentration you want. Some other reagents you might want standard solutions of react with air; these you might also titrate if they have been waiting a long time so you know what the current concentration is.
Titrations might seem a little old-fashioned. Actually, the number of automated titration machines available (try a google search!) suggest that titrations are still very important in industry. One reason might be that titrations can be good for studying newly discovered molecules, for instance to measure the molecular weight and other properties that we will study more later.
Traditionally, you take a known mass or volume of the unknown solution and put it in a flask with the indicator. Then you add the standard solution in a buret, which is a special tube for adding solution slowly and measuring the volume added at the end. These days, it might be easier to use a plastic squeeze bottle instead of a buret. You put the standard solution in the squeeze bottle, get the mass of the bottle, do the titration, and then mass the bottle again. Now you know exactly how much standard was added!
Example \(\PageIndex{1}\)
We have a solution of HCl whose concentration is known imprecisely (~2.5 M). (We made this solution in the previous section on molarity.) We want to determine the concentration more precisely. We have a solution of NaOH that is known to be 5.1079 M. We place 100.00 ml of the HCl solution in a flask with a drop of an indicator that will change color when the solution is no longer acidic. Then we add NaOH slowly until the indicator color changes. At this point, we have added 46.67 ml NaOH. Calculate the precise concentration of the HCl.
Solution
To answer, we need to know that the reaction is
\[HCl + NaOH \rightarrow NaCl + H_{2}O\]
So the ratio is 1 HCl:1 NaOH. We calculate the number of moles of NaOH added:
\[(5.1079\; mol/L)(46.67\; mL)= 238.4\; mmol\]
This is also the number of moles of HCl in the original 100.00 mL of solution, because the reaction ratio is 1:1. To calculate the concentration of the HCl solution, we just divide the number of moles of HCl by the volume.
\[(238.4\; mmol)/(100.00\; mL) = 2.384\; M\]
We could do this in one step using dimensional analysis:
\[(46.67\; \cancel{mL\; NaOH}) \left(\dfrac{5.1079\; \cancel{mol\; NaOH}}{1000\; \cancel{mL}}\right) \left(\dfrac{1\; mol\; HCl}{1\; \cancel{mol\; NaOH}}\right) \left(\dfrac{1}{100.00\; mL}\right)=2.384\; M\]
Now, we diluted 250 mL of the original stock solution to 1.00 L to make this solution. What is the concentration of the 10 M HCl, precisely? First we calculate the moles of HCl in the whole "2.5 M" solution, which is equal to the number of moles of HCl in quantity of stock solution ("10 M") that was used to make it (250ml).
\[(1.00\; \cancel{L\; of\; diluted\; solution}) \left(\dfrac{2.384\; mol\; HCl}{1\; \cancel{L\; of\; diluted\; solution}}\right) \left(\dfrac{1}{0.250\; L\; of\; conc.\; solution}\right)=9.536\; M\]
Why so low? HCl is a gas, and can evaporate out of solution. The stock solution must have been pretty old.


4.10: Coral Reefs
It may seem odd to be discussing coral reefs in a section about geology, but due to the stony calcium carbonate skeletons secreted by many coral species, coral reefs are as interesting as geological features as they are biological ones. Corals grow best in warm, clear, tropical water, that is close enough to the surface for light to support photosynthesis by the algae living in the coral tissues. Because of this need for light, new coral will often grown on top of the stony skeletons of older corals.
In the 1830s Charles Darwin made some observations about different types of coral reefs, and hypothesized that they represent a progression from one form to the next. The types of reefs he examined were fringing reefs, barrier reefs, and atolls, which are associated with oceanic islands (Figure \(\PageIndex{1}\)). Fringing reefs are reefs that are close to or are connected to shore. Barrier reefs are offshore reefs that are separated from the land by an expanse of water, such as a lagoon. Atolls are circular or oval reefs surrounding a lagoon, without any central land mass in the lagoon. Darwin speculated that reefs progressed from fringing, to barrier, to atolls as the land mass subsided. However, he had no explanation for how volcanic islands could sink. Today we know that Darwin was correct, and that islands can sink as oceanic crust subsides as it moves away from a spreading center, or as sea level rises as glaciers melt.
The progression starts with a fringing reef built against the shores of island (Figure \(\PageIndex{2}\)). If sea level doesn’t change or the land doesn’t sink, many reefs will not progress beyond this stage. But if the land does subside, the corals would eventually sink too deep for light penetration (see section 6.5) and they would die. So as the reef gets deeper, the corals continue to grow upwards, at a rate of about 3-5 m per 1000 years, and eventually a lagoon develops between the reef and the island; the reef is now a barrier reef. If the land continues to subside until it is completely submerged, all that is left is a ring of coral that has been growing upwards around the central lagoon; an atoll.*”Physical Geology” by Steven Earle used under a CC-BY 4.0 international license. Download this book for free at http://open.bccampus.ca


2.2: Partial Derivatives
Now that we have an idea of what functions of several variables are, and what a limit of such a function is, we can start to develop an idea of a derivative of a function of two or more variables. We will start with the notion of a partial derivative.
Definition 2.3
Let \(f (x, y)\) be a real-valued function with domain \(D\) in \(\mathbb{R}^2\), and let \((a,b)\) be a point in \(D\). Then the partial derivative of \(\textbf{f}\) at \((a,b)\) with respect to \(x\) , denoted by \(\dfrac{∂f}{∂x}(a,b)\), is defined as
\[\dfrac{∂f}{∂x}(a,b)=\lim \limits_{h \to 0}\dfrac{f(a+h,b)-f(a,b)}{h} \label{Eq2.2}\]
and the partial derivative of \(f\) at \((a,b)\) with respect to \(y\) , denoted by \(\dfrac{∂f}{∂y}(a,b)\), is defined as
\[\dfrac{∂f}{∂x}(a,b) = \lim \limits_{h \to 0}\dfrac{f(a+h,b)-f(a,b)}{h}\label{Eq2.3}\]
Note: The symbol \(∂\) is pronounced “del”.
Recall that the derivative of a function \(f (x)\) can be interpreted as the rate of change of that function in the (positive) \(x\) direction. From the definitions above, we can see that the partial derivative of a function \(f (x, y)\) with respect to \(x\) or \(y\) is the rate of change of \(f (x, y)\) in the (positive) \(x\) or \(y\) direction, respectively. What this means is that the partial derivative of a function \(f (x, y)\) with respect to \(x\) can be calculated by treating the \(y\) variable as a constant , and then simply differentiating \(f (x, y)\) as if it were a function of \(x\) alone, using the usual rules from single-variable calculus. Likewise, the partial derivative of \(f (x, y)\) with respect to \(y\) is obtained by treating the \(x\) variable as a constant and then differentiating \(f (x, y)\) as if it were a function of \(y\) alone.
Example 2.10
Find \(\dfrac{∂f}{∂x} (x, y)\) and \(\dfrac{∂f}{∂y} (x, y)\) for the function \(f (x, y) = x^2y+ y^3\).
Solution
Treating \(y\) as a constant and differentiating \(f (x, y)\) with respect to \(x\) gives
\[\nonumber \dfrac{∂f}{∂x}(x,y)=2xy\]
and treating \(x\) as a constant and differentiating \(f (x, y)\) with respect to \(y\) gives
\[\nonumber \dfrac{∂f}{∂y}(x,y)=x^2+3y^2\]
We will often simply write \(\dfrac{∂f}{∂x}\) and \(\dfrac{∂f}{∂y}\) instead of \(\dfrac{∂f}{∂x} (x, y)\) and \(\dfrac{∂f}{∂y} (x, y)\).
Example 2.11
Find \(\dfrac{∂f}{∂x}\) and \(\dfrac{∂f}{∂y}\) for the function \(f (x, y) = \dfrac{\sin{(xy^2)}}{ x^2 +1}\).
Solution
Treating \(y\) as a constant and differentiating \(f (x, y)\) with respect to \(x\) gives
\[\nonumber \dfrac{∂f}{∂x}=\dfrac{(x^2+1)(y^2\cos{(xy^2)})-(2x)\sin{(xy^2)}}{(x^2+1)^2}\]
and treating \(x\) as a constant and differentiating \(f (x, y)\) with respect to \(y\) gives
\[\nonumber \dfrac{∂f}{∂y}=\dfrac{2xy\cos{(xy^2)}}{x^2+1}\]
Since both \(\dfrac{∂f}{∂x}\) and \(\dfrac{∂f}{∂y}\) are themselves functions of \(x\) and \(y\), we can take their partial derivatives with respect to \(x\) and \(y\). This yields the higher-order partial derivatives :
\[\nonumber \dfrac{∂^2f}{∂x^2}=\dfrac{∂}{∂x}\left ( \dfrac{∂f}{∂x}\right) \quad \dfrac{∂^2f}{∂y^2}=\dfrac{∂}{∂y}\left ( \dfrac{∂f}{∂y}\right )\]
\[\nonumber \dfrac{∂^2f}{∂y∂x}=\dfrac{∂}{∂y}\left ( \dfrac{∂f}{∂x}\right) \quad \dfrac{∂^2f}{∂x∂y}=\dfrac{∂}{∂x}\left ( \dfrac{∂f}{∂y}\right )\]
\[\nonumber \dfrac{∂^3f}{∂x^3}=\dfrac{∂}{∂x}\left ( \dfrac{∂^2f}{∂x^2}\right) \quad \dfrac{∂^3f}{∂y^3}=\dfrac{∂}{∂y}\left ( \dfrac{∂^2f}{∂y^2}\right )\]
\[\nonumber \dfrac{∂^3f}{∂y∂x^2}=\dfrac{∂}{∂y}\left ( \dfrac{∂^2f}{∂x^2}\right) \quad \dfrac{∂^3f}{∂x∂y^2}=\dfrac{∂}{∂x}\left ( \dfrac{∂^2f}{∂y^2}\right )\]
\[\nonumber \dfrac{∂^3f}{∂y^2∂x}=\dfrac{∂}{∂y}\left ( \dfrac{∂^2f}{∂y∂x}\right) \quad \dfrac{∂^3f}{∂x^2∂y}=\dfrac{∂}{∂x}\left ( \dfrac{∂^2f}{∂x∂y}\right )\]
\[\nonumber \dfrac{∂^3f}{∂x∂y∂x}=\dfrac{∂}{∂x}\left ( \dfrac{∂^2f}{∂y∂x}\right) \quad \dfrac{∂^3f}{∂y∂x∂y}=\dfrac{∂}{∂y}\left ( \dfrac{∂^2f}{∂x∂y}\right )\]
\[\nonumber \vdots\]
Example 2.12
Find the partial derivatives \(\dfrac{∂f}{∂x}\), \(\dfrac{∂f}{∂y}\), \(\dfrac{∂^2f}{∂x^2}\), \(\dfrac{∂^2f}{∂y^2}\), \(\dfrac{∂^2f}{∂y∂x}\) and \(\dfrac{∂^2f}{∂x∂y}\) for the function \(f (x, y) = e^{x^2y} + xy^3\).
Solution
Proceeding as before, we have
\[\nonumber \begin{split}\dfrac{∂f}{∂x}&=2xye^{x^2y}+y^3 \\ \nonumber \dfrac{∂^2f}{∂x^2}&=\dfrac{∂}{∂x}(2xye^{x^2y}+y^3) \\ \nonumber &=2ye^{x^2y}+4x^2y^2e^{x^2y}\\ \nonumber \dfrac{∂^2f}{∂y∂x}&=\dfrac{∂}{∂y}(2xye^{x^2y}+y^3) \\ \nonumber &=2xe^{x^2y}+2x^3ye^{x^2y}+3y^2 \\ \nonumber \end{split} \qquad \begin{split}\dfrac{∂f}{∂y}&=x^2e^{x^2y}+3xy^2 \\ \nonumber \dfrac{∂^2f}{ ∂y^2}&=\dfrac{∂}{∂y}(x^2e^{x^2y}+3xy^2) \\ \nonumber &=x^4e^{x^2y}+6xy \\ \nonumber \dfrac{∂^2f}{∂x∂y}&=\dfrac{∂}{∂x}(x^2e^{x^2y}+3xy^2) \\ \nonumber &= 2xe^{x^2y}+2x^3ye^{x^2y}+3y^2 \\ \end{split}\]
Higher-order partial derivatives that are taken with respect to different variables, such as \(\dfrac{∂^2f}{∂y∂x}\) and \(\dfrac{∂^2f}{∂x∂y}\), are called mixed partial derivatives . Notice in the above example that \(\dfrac{∂^2f}{∂y∂x} = \dfrac{∂^2f}{∂x∂y}\). It turns that this will usually be the case. Specifically, whenever both \(\dfrac{∂^2f}{∂y∂x}\) and \(\dfrac{∂^2f}{∂x∂y}\) are continuous at a point \((a,b)\), then they are equal at that point. All the functions we will deal with will have continuous partial derivatives of all orders, so you can assume in the remainder of the text that
\[\nonumber \dfrac{∂^2f}{∂y∂x}=\dfrac{∂^2f}{∂x∂y}\text{ for all }(x,y)\text{ in the domain of }f\]
In other words, it doesn’t matter in which order you take partial derivatives. This applies even to mixed partial derivatives of order 3 or higher.
The notation for partial derivatives varies. All of the following are equivalent:
\[\nonumber \dfrac{∂f}{∂x} : f_x(x,y),\quad f_1(x,y),\quad D_x(x,y),\quad D_1(x,y)\]
\[\nonumber \dfrac{∂f}{∂y} : f_y(x,y),\quad f_2(x,y),\quad D_y(x,y),\quad D_2(x,y)\]
\[\nonumber \dfrac{∂^2f}{∂x^2} : f_{xx}(x,y),\quad f_{11}(x,y),\quad D_{xx}(x,y),\quad D_{11}(x,y)\]
\[\nonumber \dfrac{∂^2f}{∂y^2} : f_{yy}(x,y),\quad f_{22}(x,y),\quad D_{yy}(x,y),\quad D_{22}(x,y)\]
\[\nonumber \dfrac{∂^2f}{∂y∂x} : f_{xy}(x,y),\quad f_{12}(x,y),\quad D_{xy}(x,y),\quad D_{12}(x,y)\]
\[\nonumber \dfrac{∂^2f}{∂x∂y} : f_{yx}(x,y),\quad f_{21}(x,y),\quad D_{yx}(x,y),\quad D_{21}(x,y)\]


1.8: Spinning Wheel
|
Spinning Wheel
Norwegian Maker unknown, c.1840 Wood, metal Little Norway Collection, Gift of Scott & Jennifer Winner MHAHS 2014.050.0081 |
Spinning wheels were vital, if ordinary, objects that a family often brought from Norway to America. Spinning thread to make yarn was an important way that women contributed to family life during early immigrant days. Like the mangle board on display, these items were utilitarian. But by adding traditional Norwegian motifs and decorations, like the acanthus leaf carving seen here, another level of meaning is bestowed on these pieces that would become heirlooms for Norwegian-American families. Of unknown origin, this spinning wheel was acquired by Little Norway creator Isaak Dahle and displayed in the museum’s Norway Building for more than 80 years.
Museum records are silent regarding the identity of the original owner of this spinning wheel. However, the carved acanthus ornamentation and particular configuration of the spinning wheel’s components signal its Norwegian origins. The most likely scenario is that it belonged to a Norwegian woman who selected it as one of the handful of possessions she brought with her when she emigrated. Other possibilities are that a woman, likely a Norwegian immigrant, purchased the spinning wheel from a Norwegian craftsman in the United States or even from a company that imported spinning wheels from Norway. The piece probably dates to the mid nineteenth century.
Though infrequently used for decorating spinning wheels, the acanthus carving establishes the Norwegian character of this piece. Acanthus is a spinney-leafed plant that grows around the Mediterranean Sea. Since Antiquity, motifs based on acanthus leaves have been popular throughout Europe. The Norwegian tradition of acanthus carving has its roots in the Baroque and Rococo styles. These styles, emphasizing curvilinear design and heavily carved surfaces, came to prominence in England and France in the seventeenth and eighteenth centuries. In the first half of the eighteenth century these styles spread to Norway through port cities like Oslo and Bergen. Furniture in the Baroque and Rococo styles became popular among Norway’s noble and merchant classes. From the affluent port cities, these designs spread to the rest of the country through decoration adorning parish churches. Rural craftsmen incorporated the acanthus designs when making furniture and other wooden items.
As the acanthus style spread and was reproduced throughout Norway’s isolated valleys, it took on new attributes distinct from its Continental counterparts. Norwegian acanthus carving tends to have rounder shapes departing from the more naturalistic sharpness of the leaves that continued in European design. This gives Norwegian acanthus design softer appearance. Norwegian carvers also incorporated flowers into their interpretation of the acanthus mode. Examples of this can be seen on the fineals of the turned sections of this spinning wheel which are carved into blossoms. While the carvings on this spinning wheel are unpainted, Norwegian acanthus carvings were often painted in bold colors. Examples exist with leaves painted in a combination of sky blue, maroon, and gilt gold; this effect is unlike any use of the motif in other parts of Europe.
While decoration on the level of acanthus carving was rare for spinning wheels, it’s presence on this piece illustrates the importance of this object to the woman who owned it. Spinning wheels stand apart from most other domestic items as the objects of exclusively women’s use. During the nineteenth century, women in rural Norway produced the majority of textiles and garments used by the household. Women not only spun yarn and wove it into fabric, they also were involved in both tending and shearing the sheep, producing the fibers to be transformed into yarn. Textile production was essential to home economy and a fundamental part of feminine gender roles in Norwegian culture.
When Norwegians immigrated to America, spinning and weaving continued to be critical to the family livelihood. Letters immigrants sent back to friends and family in Norway who were considering immigrating themselves often advised women to bring their spinning wheels with them. While factory-made yarns and textiles were available in much of the United States, they were still often less available on the frontier. Additionally, many Norwegian women considered the mass-produced yarn to be of inferior quality and not capable of keeping their families warm. By producing their own thread and textiles, immigrant women were able to contribute financially to their households. By continuing Norwegian gender roles in caring for their own sheep, Norwegian immigrant women possessed a greater degree of financial autonomy than their Anglo-American counterparts.
References
Bergland, Betty A. and Lori Ann Lahlum. Norwegian American Women: Migration, Communities, and Identities. St.Paul: Minnesota Historical Society, 2011. https://books.google.com/books/about...d=1SjAmgqmG6YC
Hagen, Håvard. “Cartilage Baroque.” Store norske leksikon. https://snl.no/bruskbarokk (accessed May 23, 2017).


21.9: Chemistry of Thioesters and Acyl Phosphates - Biological Carboxylic Acid Derivatives
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Objectives
After completing this section, you should be able to
- discuss, briefly, the role played in nature by acetylating agents, such as acetyl coenzyme A, and explain what is happening in reactions such as the acetylation in biological systems, without necessarily being able to write a detailed equation.
- rank the reactivity of thioesters and acyl phosphates towards nucleophiles compared with other carboxylic acid derivatives.
Introduction to thioesters and Coenzyme A
Acyl phosphates and acyl adenosine phosphates are not the only activated forms of carboxylate groups in biochemical reactions. Slightly lower on the reactivity scale are thioesters. In the metabolism of lipids (fats and oils), thioesters are the principal form of activated carboxylate groups. They are employed as acyl carriers, assisting with the transfer of acyl groups such as fatty acids from one acyl X substrate to another.
The ‘acyl X group’ in a thioester is a thiol. The most important thiol compound used to make thioesters is called coenzyme A, which has the following structure:
Coenzyme A is often abbreviated HSCoA, in order to emphasize that it is the thiol sulfur that provides the critical thioester linkage to acyl groups. When fuel (carbohydrate and fat) is broken down in your body, it is eventually converted to a simple two-carbon unit called acetyl CoA, which is essentially a thioester derivative of acetic acid:
Activation of fatty acids by coenzyme A: a thioesterification reaction
In the biologically active form of fatty acids, the carboxylate groups have been converted to thioesters using coenzyme A. For example, the activated form of the C 16 fatty acid palmitate is:
Let’s take a look at how this activation takes place, in a reaction catalyzed by an enzyme called acyl CoA synthetase. You already know that carboxylates are not themselves good substrates for acyl substitution reactions, and must be activated. Thus, you might predict that the first step of this reaction requires ATP to make a high-energy acyl phosphate intermediate. In fact, the activated carboxylate in this case is an acyl-AMP, formed in the same way as the acyl-AMP intermediate in the asparagine synthetase reaction ( section 12.2B ).
The activated acyl-AMP intermediate is then attacked by the thiol sulfur of coenzyme A, and the AMP group is expelled to form the fatty acyl CoA.
Transfer of fatty acyl groups to glycerol: a thioester to ester substitution
The -SCoA thioester form of the fatty acid is a good substrate for a number of metabolic transformations. This is the form of fatty acid, for example, that is oxidized and broken down for energy in the mitochondria of your cells.  Recall ( section 12.1B ) that triacylglycerol is composed of a glycerol ‘backbone’ connected to three fatty acid groups through ester linkages.
The reaction in which a fatty acid acyl group is linked to glycerol represents the conversion of a thioester (fatty acyl CoA) to an ester. First, however, a transthioesterification reaction occurs. A transthioesterification is merely the conversion of one thioester to another. In the case of monoacylglycerolacyltransferase, the fatty acyl group first trades its thioester link to coenzyme A for another thioester link to a cysteine residue in the active site of the enzyme. It is a common strategy for enzymes to first form a covalent link to one substrate before catalyzing the principle chemical reaction.
The fatty acyl group is now ready to be transferred to glycerol, trading its thioester linkage to the cysteine for a new ester linkage to one of the alcohol groups on glycerol. The attacking nucelophile in this reaction is of course the alcohol oxygen of monoacylglycerol.
Because esters are more stable than thioesters, this is an energetically downhill reaction.
Transthioesterification reactions
In the previous section we saw one example of a transthioesterification. Another important transthioesterification reaction involves acetyl CoA, the activated form of acetic acid and the basic two-carbon building block for fats and oils. Before it can be incorporated into a growing fatty acid molecule, acetyl CoA must first be linked to a so-called ‘acyl carrier protein’ (ACP). The acetyl group is linked to the acyl carrier protein via a thiol group on a carrier molecule that is covalently attached to the protein.
Notice that the structure of this carrier group (called phosphopantetheine) is identical to the region of coenzyme A (structure shown earlier in this section) near the thiol group. Once attached to the ACP, the two-carbon acetyl group condenses with another acyl group (which is also attached to its own ACP), and the fatty acid chain begins to grow. We will study these important carbon-carbon bond forming reactions in section 13.4.
Finally, a transthioesterification is the final step in one of the most important and well-studied reactions in animal metabolism: the conversion of pyruvate to acetyl CoA by a cluster of enzymes called the pyruvate dehydrogenase complex.
The overall reaction looks simple, but is actually quite complex and involves several intermediate species. The final step in the process is a transthioesterification, involving a dithiol molecule called lipoamide:
We will look more closely at the complete biochemical transformation catalyzed by the pyruvate dehydrogenase complex in section 16.12B .
Hydrolysis of thioesters
The acyl group of a thioester can be transferred to a water molecule in a hydrolysis reaction, resulting in a carboxylate. An example of thioester hydrolysis is the conversion of (S)-citryl CoA to citrate in the citric acid cycle (also known as the Krebs cycle).
Reactivity of thioesters and acyl phosphates
Recall from Section 21.2 that thioesters and acyl phosphates are the most reactive among the biologically relevant acyl groups. However, neither is as reactive as an acid chloride or acid anhydride.
Relative reactivity of biologically relevant acyl groups


9.6: Wave Polarization
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Polarization refers to the orientation of the electric field vector. For waves, the term “polarization” refers specifically to the orientation of this vector with increasing distance along the direction of propagation, or, equivalently, the orientation of this vector with increasing time at a fixed point in space. The relevant concepts are readily demonstrated for uniform plane waves, as shown in this section. A review of Section 9.5 (“Uniform Plane Waves: Characteristics”) is recommended before reading further.
To begin, consider the following uniform plane wave, described in terms of the phasor representation of its electric field intensity:
\[\widetilde{\bf E}_x = \hat{\bf x}E_x e^{-j\beta z} \nonumber \]
Here \(E_x\) is a complex-valued constant representing the magnitude and phase of the wave, and \(\beta\) is the positive real-valued propagation constant. Therefore, this wave is propagating in the \(+\hat{\bf z}\) direction in lossless media. This wave is said to exhibit linear polarization (and “linearly polarized”) because the electric field always points in the same direction, namely \(+\hat{\bf x}\). Now consider the wave
\[\widetilde{\bf E}_y = \hat{\bf y}E_y e^{-j\beta z} \nonumber \]
Note that \(\widetilde{\bf E}_y\) is identical to \(\widetilde{\bf E}_x\) except that the electric field vector now points in the \(+\hat{\bf y}\) direction and has magnitude and phase that is different by the factor \(E_y/E_x\). This wave too is said to exhibit linear polarization, because, again, the direction of the electric field is constant with both time and position. In fact, all linearly-polarized uniform plane waves propagating in the \(+\hat{\bf z}\) direction in lossless media can be described as follows: \[\widetilde{\bf E} = \hat{\bf \rho}E_{\rho} e^{-j\beta z} \nonumber \] This is so because \(\hat{\bf \rho}\) could be \(\hat{\bf x}\), \(\hat{\bf y}\), or any other direction that is perpendicular to \(\hat{\bf z}\). If one is determined to use Cartesian coordinates, the above expression may be rewritten using (Section 4.3)
\[\hat{\bf \rho} = \hat{\bf x}\cos\phi + \hat{\bf y}\cos\phi \nonumber \] yielding \[\widetilde{\bf E} = \left( \hat{\bf x}\cos\phi + \hat{\bf y}\cos\phi \right) E_{\rho} e^{-j\beta z} \label{m0131_eLinAI} \]
When written in this form, \(\phi=0\) corresponds to \(\widetilde{\bf E}=\widetilde{\bf E}_x\), \(\phi=\pi/2\) corresponds to \(\widetilde{\bf E}=\widetilde{\bf E}_y\), and any other value of \(\phi\) corresponds to some other constant orientation of the electric field vector; see Figure \(\PageIndex{1}\) for an example.
Figure \(\PageIndex{1}\): Linear polarization. Here \(\bf{E}_x\) is shown in blue, \(\bf{E}_y\) is shown in green, and \(bf{E}\) is shown in red with black vector symbols. In this example the phases of \(E_x\) and \(E_y\) are zero and \(\phi = - \pi / 4\). (Modified; RJB1)A wave is said to exhibit linear polarization if the direction of the electric field vector does not vary with either time or position.
Linear polarization arises when the source of the wave is linearly polarized. A common example is the wave radiated by a straight wire antenna, such as a dipole or a monopole. Linear polarization may also be created by passing a plane wave through a polarizer ; this is particularly common at optical frequencies (see “Additional Reading” at the end of this section).
A commonly-encountered alternative to linear polarization is circular polarization . For an explanation, let us return to the linearly-polarized plane waves \(\widetilde{\bf E}_x\) and \(\widetilde{\bf E}_y\) defined earlier. If both of these waves exist simultaneously, then the total electric field intensity is simply the sum:
\begin{align}
\tilde{\mathbf{E}} &=\tilde{\mathbf{E}}_{x}+\tilde{\mathbf{E}}_{y} \nonumber \\
&=\left(\hat{\mathbf{x}} E_{x}+\hat{\mathbf{y}} E_{y}\right) e^{-j \beta z} \label{m0131_eCirc1}
\end{align}
If the phase of \(E_x\) and \(E_y\) is the same, then \(E_x = E_{\rho}\cos\phi\), \(E_y = E_{\rho}\sin\phi\), and the above expression is essentially the same as Equation \ref{m0131_eLinAI}. In this case, \(\widetilde{\bf E}\) is linearly polarized. But what if the phases of \(E_x\) and \(E_y\) are different? In particular, let’s consider the following case. Let \(E_x = E_0\), some complex-valued constant, and let \(E_y = +jE_0\), which is \(E_0\) phase-shifted by \(+\pi/2\) radians. With no further math, it is apparent that \(\widetilde{\bf E}_x\) and \(\widetilde{\bf E}_y\) are different only in that one is phase-shifted by \(\pi/2\) radians relative to the other. For the physical (real-valued) fields, this means that \({\bf E}_x\) has maximum magnitude when \({\bf E}_y\) is zero and vice versa. As a result, the direction of \({\bf E}={\bf E}_x+{\bf E}_y\) will rotate in the \(x-y\) plane, as shown in Figure \(\PageIndex{2}\).
Figure \(\PageIndex{2}\): A circularly-polarized wave (in red, with black vector symbols) resulting from the addition of orthogonal linearly-polarized waves (shown in green and blue) that are phase-shifted by \(\pi / 2\) radians.The rotation of the electric field vector can also be identified mathematically. When \(E_x = E_0\) and \(E_y = +jE_0\), Equation \ref{m0131_eCirc1} can be written:
\[\widetilde{\bf E} = \left( \hat{\bf x} + j\hat{\bf y} \right) E_0 e^{-j\beta z} \nonumber \]
Now reverting from phasor notation to the physical field:
\begin{align}
\mathbf{E} &=\operatorname{Re}\left\{\widetilde{\mathbf{E}} e^{j \omega t}\right\} \nonumber \\
&=\operatorname{Re}\left\{(\hat{\mathbf{x}}+j \hat{\mathbf{y}}) E_{0} e^{-j \beta z} e^{j \omega t}\right\} \nonumber \\
&=\hat{\mathbf{x}}E_{0} \cos (\omega t-\beta z)+\hat{\mathbf{y}}E_{0} \cos \left(\omega t-\beta z+\frac{\pi}{2}\right)
\end{align}
As anticipated, we see that both \({\bf E}_x\) and \({\bf E}_y\) vary sinusoidally, but are \(\pi/2\) radians out of phase resulting in rotation in the plane perpendicular to the direction of propagation.
In the example above, the electric field vector rotates either clockwise or counter-clockwise relative to the direction of propagation. The direction of this rotation can be identified by pointing the thumb of the left hand in the direction of propagation; in this case, the fingers of the left hand curl in the direction of rotation. For this reason, this particular form of circular polarization is known as left circular (or ”left-hand” circular) polarization (LCP). If we instead had chosen \(E_y = -jE_0 = -jE_x\), then the direction of \({\bf E}\) rotates in the opposite direction, giving rise to right circular (or “right-hand” circular) polarization (RCP). These two conditions are illustrated in Figure \(\PageIndex{3}\).
Figure \(\PageIndex{3}\): Left-circular polarization (LCP; top) and right-circular polarization (RCP; bottom)
A wave is said to exhibit circular polarization if the electric field vector rotates with constant magnitude. Left- and right-circular polarizations may be identified by the direction of rotation with respect to the direction of propagation.
In engineering applications, circular polarization is useful when the relative orientations of transmit and receive equipment is variable and/or when the medium is able rotate the electric field vector. For example, radio communications involving satellites in non-geosynchronous orbits typically employ circular polarization. In particular, satellites of the U.S. Global Positioning System (GPS) transmit circular polarization because of the variable geometry of the space-to-earth radio link and the tendency of the Earth’s ionosphere to rotate the electric field vector through a mechanism known Faraday rotation (sometimes called the “Faraday effect”). If GPS were instead to transmit using a linear polarization, then a receiver would need to continuously adjust the orientation of its antenna in order to optimally receive the signal. Circularly-polarized radio waves can be generated (or received) using pairs of perpendicularly-oriented dipoles that are fed the same signal but with a \(90^{\circ}\) phase shift, or alternatively by using an antenna that is intrinsically circularly-polarized, such as a helical antenna (see “Additional Reading” at the end of this section).
Linear and circular polarization are certainly not the only possibilities. Elliptical polarization results when \(E_x\) and \(E_y\) do not have equal magnitude. Elliptical polarization is typically not an intended condition, but rather is most commonly observed as a degradation in a system that is nominally linearly- or circularly-polarized. For example, most antennas that are said to be “circularly polarized” instead produce circular polarization only in one direction and various degrees of elliptical polarization in all other directions.


5.1: Tips for the Listening Exam
As on the last test, the question you should ask yourself when you are listening to a piece is “What am I hearing?” Specifically listen for the musical characteristics that would enable you to recognize the genre (concerto, fugue, etc.) or individual movement (1st–4th movements of a symphony). Unlike the last test, there are very few pieces of vocal music so the “vocal vs. instrumental” question won’t really narrow things down much. We’ll need to be able to hear more specific characteristics within the music.
I Hear Singing
If you hear a singer or ensemble of singers, then the only two possible answers are “Notte e giorno fatticar” and “La ci darem la mano,” from Mozart’s Don Giovanni . These should be fairly easy to distinguish by the performance forces. In other words, the number and type of singers you hear will provide the most obvious clue as to which piece you’re hearing. Both pieces contain a great deal of stylistic and variation as well. Understanding the order of the styles (e.g. recitative, ensemble, aria) in each piece will also be a key to identification. First, a quick primer on operatic voice parts: male voices (from lowest to highest)—bass, baritone, tenor; female voices (from lowest to highest)—contralto, mezzo-soprano, soprano. In “Notte e giorno fatticar,” we begin with a lively, comical bass aria, followed by a very frantic ensemble consisting of three voices (soprano, baritone, bass). A duel is fought, and then our recording ends with a somber ensemble (two basses and a baritone). Our exam excerpt of course will not be long enough for you to hear all of that, but you will certainly hear some of the dramatic emotional changes for which Mozart is so well known. In “La ci darem la mano,” you hear only two characters (soprano and baritone). First they sing a simple recitative, listen for the speech-like delivery of the recitative accompanied by harpsichord, and then they sing a lyrical duet (essentially an aria for two). Again, if you understand the performance forces and styles found in each piece, you’ll be in good shape on these two pieces.
I Hear Instruments Only
On this test you not only need to be able to recognize the various genres (serenade, symphony, concerto, sonata) but, in certain cases, the individual movements of a piece (Mozart’s Eine Kleine Nachtmusik and Beethoven’s Symphony No. 5 in C minor). Let’s start with the pieces that don’t involve individual movements as separate listening examples.
I Hear Solo Piano
This has to be Beethoven’s Pathetique Sonata , 1st mvmt.. The first movement is the only one on your CD, though you should remember that this work, like all sonatas, consists of 3 movements. Remember that in the Classical period a sonata was played by either a piano/violin or piano/cello duet, or by a solo piano. Also remember that the solo piano sonatas are considered the “New Testament” for piano players (Bach’s Well-Tempered Clavier being the “Old Testament”) so his solo sonatas are very significant. Don’t get this confused with the concerto by Mozart. A concerto must have an orchestra. Although the instrumentation of this piece gives it away, it is worth remembering that the 1st movement of any multi-movement instrumental work in this period is going to have a fast tempo and sonata-allegro form. Beethoven likes to bend the rules so he starts off with a slow introduction followed by the first (very fast) theme.
I Hear Orchestra and Solo Piano
This has to be Mozart’s Piano Concerto in A major, 1st mvmt. A concerto features the contrast between a solo instrument and full orchestra and we definitely hear that contrast in this piece. Remember that in the Classical era the term concerto refers to a solo concerto as the concerto grosso falls out of favor at the end of the Baroque. If you were to hear this piece from the beginning you might think it was a symphony as the orchestra plays the first exposition (the first movement of any multi-movement instrumental work is going to be in sonata-allegro form) and the piano doesn’t enter until the repeat of the exposition. Once you hear those solo piano passages though, the genre becomes clear. Solo piano and orchestra must be the piano concerto by Mozart. Again the instrumentation of this piece gives it away, but it is worth remembering that along with the sonata-allegro form, the 1st movement of any multi-movement instrumental work is going to have a fast tempo and duple meter.
I Hear Orchestra and Solo French Horn
This has to be Mozart’s Horn Concerto in E flat major, 3rd mvmt. As a concerto, this piece is based on the same solo vs. orchestra contrast as in the piano concerto. While the alternation between the orchestra and the horn should give this piece away, it’s also worth noting that the form of this movement is a rondo. That means that the opening theme heard in the horn will return over and over throughout the piece.
I Hear a Chamber Ensemble that Features Only Stringed Instruments
Okay, now we have to listen a bit more carefully. There are three pieces for chamber strings: movements 1 and 3 of Mozart’s Eine Kleine Nachtmusik , and Haydn’s Emperor Quartet , 2nd movement. These pieces feature only strings, namely violins, violas, and cellos, so if you hear any other instruments, such as piano, woodwinds, or brass, it must be another piece. The size of the ensembles will help you distinguish between Haydn and Mozart. The Emperor is a string quartet—two violins, a viola, and a cello. It will have a very delicate, intimate sound compared to the larger string ensemble that plays the Mozart movements. So even though the same instruments are in use, being able to hear the difference between the large group and the small group will be a big help to you. However, the best way to tell these three examples apart is to listen for tempo and meter. Those distinctions are as follows:
- I hear a fast tempo and a familiar theme. This is the 1st movement Eine Kleine Nachtmusik . It is faster than the 3rd movement and a lot faster than the Haydn quartet. The opening theme should also be a big clue. It’s very catchy and most of us have heard that tune before. If you haven’t, consider committing the tune or theme to memory so that you can easily recognize the 1st movement. No matter where the excerpt is taken from, you’re bound to hear that theme.
- I hear a triple meter and moderate tempo. The triple meter gives away the 3rd movement of Eine Kleine Nachtmusik . This movement is a minuet and trio, two dances with a 1-2-3 beat. Minuets are typically stately and crisp, while trios are more flowing and lyrical. The moderate or medium tempo is also a good clue that you’re hearing the 3rd movement.
- I hear a slow tempo. Slow tempo has to be the Emperor Quartet , 2nd movement by Haydn. 2nd movements are always slow and lyrical so the tempo, along with the small size of the ensemble, should be a pretty strong clue for you.
I Hear an Orchestra
A full orchestra without soloists indicates a symphony or an overture. This category will probably present the biggest challenge for the identification questions as you’ll need to hear the difference between a larger number of pieces or movements: Symphony No. 40 in G minor by Mozart, the Overture to Don Giovanni by Mozart, and the four individual movements of Symphony No. 5 in C minor by Beethoven. Remember that a full orchestra will feature instruments from all four orchestral families: strings, woodwinds, brass, and percussion. If all you hear are the strings, you aren’t hearing a symphony – you’re hearing chamber music, such as Eine Kleine Nachtmusik. It should be easy to tell when you’re hearing the Beethoven symphony as it features the largest orchestra and makes much greater use of brass and percussion, along with the strings and woodwinds, than the other pieces. The challenge with the Beethoven symphony is to correctly ID the movements. Knowing the characteristics of the multi-movement cycle work will be vital to your success so be sure to study those slides carefully as you listen to the CD. Let’s start with the movements of Beethoven’s Symphony No. 5 in C minor.
- I hear a fast tempo and a familiar theme. This is the first movement of Beethoven’s 5th symphony. As in the Mozart serenade, the first movement should be easily recognizable by its fast tempo and first theme. Most of us have heard the “da-da-da-dum” tune before. If you haven’t, I suspect you’ll have it memorized quickly after listening to the symphony a few times. It’s a very memorable, powerful theme. Remember that this is in sonata-allegro form you’ll hear all the themes in the exposition, some of the themes being modified in the development, and then all the themes again (along with an oboe mini-cadenza) in the recapitulation. Sometimes it’s helpful to think of characteristics that would rule this movement out. If you hear a slow tempo or a triple meter, it can’t be the first movement.
- I hear a slow tempo. If you know you’re hearing Beethoven’s symphony and it’s slow, it must be the 2nd movement. 2nd movements are always slow and lyrical. Unlike most second movements, this one is in triple meter. The form of this movement is theme and variations. That means you’re going to hear theme 1 (the lush, lyric opening theme) coming back with changes in its rhythm, instrumentation, and mode (major vs. minor). Furthermore, theme 2 is very majestic. While it doesn’t get varied, it is quite heroic. I like to say that Beethoven’s music often seems to depict a struggle of good against evil. In that context, the 1 st movement is the theme music for the villain, while the 2nd movement is the theme music for the hero.
- I hear a lot of activity in the low strings. This is the 3rd movement. While this movement features a triple meter, this characteristic can be a little tough to pick out. Most 3rd movements feature a moderate (medium) tempo, but this movement is marked Allegro, or “fast,” and that makes the triple meter harder to hear or feel. It should be said that the trio section seems faster than the opening scherzo, but they’re both pretty fast for a 3rd movement—not to mention the fact that Ludwig throws us a curve ball by putting the 2nd movement in a triple meter. What can I say—Beethoven was a rule-breaker. Instead of tempo and meter, I suggest listening for an emphasis on certain instruments, namely the low strings. They start off the scherzo (this is a scherzo and trio, not a minuet and trio) with a rocket theme in the low strings (cellos and basses). Then when the trio begins, the trio theme is treated fugally.  The trio theme really gives those bass players a workout so if you find yourself imagining low string players breaking a sweat, you are hearing the trio. If you hear the pitch run from low to high in the low strings, you’re hearing a rocket and that means scherzo.
- I hear a fast tempo with heroic quality. The 4th movement is the most heroic sounding of all four movements. While I can’t confirm this, I’m 99.9% sure that the transition theme was copied by the composer of the film score for the old (the real) Superman movie with Christopher Reeves. It must sound heroic if they’re copying it for Superman, right? Remember that fourth movements are essentially the finale, and in Beethoven’s hands there is usually a very strong sense of triumph. Remember our struggle of good against evil analogy? The fourth movement is the hero beating the villain, getting the girl, and then coming home to a ticker tape parade. Now let’s get down to some musical specifics. Often the 4th movement of a work like this is the fastest. That really isn’t the case here. The 1st movement has a tempo marking of Allegro con brio, which means “fast with brilliance.” The 4th movement is just Allegro, or “fast.” For this reason, tempo by itself isn’t going to give this movement away, though it certainly can eliminate the 2nd and to some extent 3rd movements as possibilities. However, tempo combined with mode is another story. Mode refers to whether we are hearing a major, which often seems happy or joyful, or minor, which often seems sad or foreboding, tonality in the music. The symphony begins, as the title indicates, in C minor. Remember how dark and foreboding the 1st movement seemed? The symphony ends with a triumphant C major. So if you hear a fast tempo in a minor mode, chances are it’s the 1st movement. Fast tempo and a triumphant major mode would indicate the 4th movement.
Now there are two other works for orchestra besides the Beethoven symphony. Both of these works are by Mozart, the Symphony No. 40 in G minor and the Overture to Don Giovanni, which means that there will generally be a more elegant, understated, even delicate quality to these pieces. They are no less masterful than the Beethoven symphony, it’s just that these two geniuses each spoke their own expressive language. To oversimplify, Mozart’s music has grace and class, while Beethoven’s music has raw emotive power. To oversimplify even more, Mozart wore a powdered wig and Beethoven did not. So as I said before, I think you should be able to, once you’ve determined that you’re hearing an orchestral work with no soloists, easily determine whether you’re hearing Mozart or Beethoven. If the determination is Mozart, then here are some suggestions for distinguishing Symphony No. 40 from the Overture to Don Giovanni.
- I hear a change in tempo (slow to fast). If you hear a slow, solemn tempo suddenly change to a fast, lively tempo, you are definitely listening to the Overture to Don Giovanni. This Overture is in sonata-allegro form but he does not immediately start with the first theme. He leads into the faster music with a kind of dark musical premonition of the Don’s ultimate end. The slow, writhing string passages of this introduction are incredibly moving. To then shift gears to the sprightly acrobatics of the first theme is a kind of contrast that in the hands of a lesser composer would just seem jarring and overdone. Mozart carries it off with ease. In case the excerpt comes from later in the piece it’s also worth noting that Mozart makes use of occasional brass and percussion in the Overture. There is no percussion in the 1st movement of his Symphony No. 40, and he makes such subtle use of the horns that you almost don’t notice the brass. One last thing: the genre for this piece is listed as opera. This overture is often performed as a stand-alone piece so I could have listed the genre as overture. I just felt that since Mozart has integrated the overture so seamlessly into the larger work, it would be best to give it the same designation as the two vocal works, namely opera.
- I hear an insistent, urgent theme in the violins. The first theme of Symphony No. 40 in G minor is so captivating in its urgency that it’s the best way to pick out this piece. It appears in all the sections of the movement, exposition, development, and recapitulation, so it would be nearly impossible to have an excerpt that didn’t include it. I’ve also mentioned that this piece doesn’t have any of the percussion that the overture has so instrumentation will provide a significant clue.
Titles, Composers, & Genres for Exam 3
| Title | Composer | Genre |
|---|---|---|
| Eine Kleine Nachtmusik , 1st mvmt. | Wolfgang Amadeus Mozart | Serenade |
| Eine Kleine Nachtmusik , 3rd mvmt. | Wolfgang Amadeus Mozart | Serenade |
| Horn Concerto in E flat major, 3rd mvmt. | Wolfgang Amadeus Mozart | Concerto |
| Symphony No. 40 in G minor, 1st mvmt. | Wolfgang Amadeus Mozart | Symphony |
| Emperor Quartet, 2nd mvmt. | Franz Joseph Haydn | String Quartet |
| Piano Concerto in A major, 1st mvmt. | Wolfgang Amadeus Mozart | Concerto |
| Overture to Don Giovanni | Wolfgang Amadeus Mozart | Opera |
| “Notte e giorno fatticar,” Don Giovanni | Wolfgang Amadeus Mozart | Opera |
| “La ci darem la mano,” Don Giovanni | Wolfgang Amadeus Mozart | Opera |
| Pathetique Sonata, 1st mvmt. | Ludwig van Beethoven | Sonata |
| Symphony No. 5 in C minor, 1st mvmt. | Ludwig van Beethoven | Symphony |
| Symphony No. 5 in C minor, 2nd mvmt. | Ludwig van Beethoven | Symphony |
| Symphony No. 5 in C minor, 3rd mvmt. | Ludwig van Beethoven | Symphony |
| Symphony No. 5 in C minor, 4th mvmt. | Ludwig van Beethoven | Symphony |
Contributors and Attributions
- Authored by : Elliott Jones. Provided by : Santa Ana College. Located at : http://www.sac.edu . License : CC BY: Attribution