1.4: Conclusions and Review
The greatest blight affecting the modern time is the apathy associated with ignorance. We tend to strongly adhere to wrongful beliefs—all manufacturing and industrial processes are failsafe in protecting humans and the environment. The truth is that Murphy’s Law more often than not is RIGHT. Thus, the need for pre-emptive measures as embodied by the principles of green chemistry is of paramount significance. The principles as listed below will constitute a future chapter in this book:
Prevention
It is better to prevent waste than to treat or clean up waste after it has been created.
Atom Economy
Synthetic methods should be designed to maximize the incorporation of all materials used in the process into the final product.
Less Hazardous Chemical Syntheses
Wherever practicable, synthetic methods should be designed to use and generate substances that possess little or no toxicity to human health and the environment.
Designing Safer Chemicals
Chemical products should be designed to affect their desired function while minimizing their toxicity.
Safer Solvents and Auxiliaries
The use of auxiliary substances (e.g., solvents, separation agents, etc.) should be made unnecessary wherever possible and innocuous when used.
Design for Energy Efficiency
Energy requirements of chemical processes should be recognized for their environmental and economic impacts and should be minimized. If possible, synthetic methods should be conducted at ambient temperature and pressure.
Use of Renewable Feedstocks
A raw material or feedstock should be renewable rather than depleting whenever technically and economically practicable.
Reduce Derivatives
Unnecessary derivatization (use of blocking groups, protection/ deprotection, temporary modification of physical/chemical processes) should be minimized or avoided if possible, because such steps require additional reagents and can generate waste.
Catalysis
Catalytic reagents (as selective as possible) are superior to stoichiometric reagents.
Design for Degradation
Chemical products should be designed so that at the end of their function they break down into innocuous degradation products and do not persist in the environment.
Real-time analysis for Pollution Prevention
Analytical methodologies need to be further developed to allow for real-time, in- process monitoring and control prior to the formation of hazardous substances.
Inherently Safer Chemistry for Accident Prevention
Substances and the form of a substance used in a chemical process should be chosen to minimize the potential for chemical accidents, including releases, explosions, and fires.
Review Questions
\(\PageIndex{1}\) Using lysergic acid as a starting point, indicate the general type of chemistry (you can indicate in your own words what is happening) that would need to occur in order for the epimerization of lysergic and L-lysergic acid to occur shown below. https://www.wikiwand.com/en/Lysergic_acid
\(\PageIndex{2}\).How does too much salt in a human’s diet contribute to high blood pressure?
a. What are two known chemical mechanisms (reactions) that enzymes can pursue for bonding
to 4-hydroxy-2-nonenal?
b. Come up with a way to quantify the inefficiency of a reaction; that is, derive a quantitative
measure of the wastefulness of a reaction using the LeBlanc numerical process
information contained in this chapter.


7.4: Table resizing
-
- Last updated
- Save as PDF
With a good hash function, a hash table can typically contain about 70%–80% as many elements as it does table slots and still perform well. Depending on the collision resolution mechanism, performance can begin to suffer either gradually or dramatically as more elements are added. To deal with this, when the load factor exceeds some threshold, we allocate a new, larger table, and add all the contents of the original table to this new table. In Java's HashMap class, for example, the default load factor threshold is 0.75.
This can be a very expensive operation, and the necessity for it is one of the hash table's disadvantages. In fact, some naive methods for doing this, such as enlarging the table by one each time you add a new element, reduce performance so drastically as to make the hash table useless. However, if we enlarge the table by some fixed percent, such as 10% or 100%, it can be shown using amortized analysis that these resizings are so infrequent that the average time per lookup remains constant-time. To see why this is true, suppose a hash table using chaining begins at the minimum size of 1 and is doubled each time it fills above 100%. If in the end it contains n elements, then the total add operations performed for all the resizings is:
1 + 2 + 4 + ... + n = 2 n - 1.
Because the costs of the resizings form a geometric series, the total cost is O( n ). But we also perform n operations to add the n elements in the first place, so the total time to add n elements with resizing is O( n ), an amortized time of O(1) per element.
On the other hand, some hash table implementations, notably in real-time systems, cannot pay the price of enlarging the hash table all at once, because it may interrupt time-critical operations. One simple approach is to initially allocate the table with enough space for the expected number of elements and forbid the addition of too many elements. Another useful but more memory-intensive technique is to perform the resizing gradually:
- Allocate the new hash table, but leave the old hash table and check both tables during lookups.
- Each time an insertion is performed, add that element to the new table and also move k elements from the old table to the new table.
- When all elements are removed from the old table, deallocate it.
To ensure that the old table will be completely copied over before the new table itself needs to be enlarged, it's necessary to increase the size of the table by a factor of at least ( k + 1)/ k during the resizing.
Linear hashing is a hash table algorithm that permits incremental hash table expansion. It is implemented using a single hash table, but with two possible look-up functions.
Another way to decrease the cost of table resizing is to choose a hash function in such a way that the hashes of most values do not change when the table is resized. This approach, called consistent hashing, is prevalent in disk-based and distributed hashes, where resizing is prohibitively costly.


4.5: The Structure of Language
By definition, communication is behavior that affects the behavior of others by the transmission of information. Language is a series of codes made up of words and rules that allow humans to communicate. The structure of human language is complex and intricate and each language spoken in the world has different phonological systems, which is, by definition, the sounds that are used and how they are related to one another. The basic rules of language are covered here, including phonology, morphology, semantics, syntax, and how speech sounds are divided.
Phonology
Phonology is the use of sounds to encode messages within a spoken human language. Babies are born with the capacity to speak any language because they can make sounds and hear differences in sounds that adults would not be able to do. This is what parents hear as baby talk. The infant is trying out all of the different sounds they can produce. As the infant begins to learn the language from their parents, they begin to narrow the range of sounds they produce to one's common to the language they are learning, and by the age of 5, they no longer have the vocal range they had previously. For example, a common sound that is used in Indian language is /dh. To any native Indian there is a huge difference between /dh and /d, but for people like me who cannot speak Hindi, not only can we not hear the difference, but it is very difficult to even attempt to produce this sound. Another large variation between languages for phonology is where in your mouth you speak from. In English, we speak mostly from the front or middle of our mouths, but it is very common in African to speak from the glottal, which is the deepest part of one's throat. These sounds come out as deep growls, though they have great significance in African culture.
Morphology
The definition of morphology is the study of the structure of words formed together, or more simply put, the study of morphemes. Morphemes are the smallest utterances with meaning. Not all morphemes are words. Many languages use affixes, which carry specific grammatical meanings and are therefore morphemes, but are not words. For example, English-speakers do not think of the suffix “-ing” as a word, but it is a morpheme. The creation of morphemes rather than words also allowed anthropologists to more easily translate languages. For example, in the English language, the prefix -un means "the opposite, not, or lacking" which can distinguish the words "unheard" and "heard" apart from each other.
Morphology is very helpful in translating different languages, such as the language Bangla. For example, some words do not have a literal translation from Bangla to English because a word in Bangla may mean more than one word in English. Two professors from Bangladesh discovered an algorithm that could translate Bangla words, as they are generally very complex. They first search for the whole word. If this does not come up with results, they then search the first morpheme they find, in one example it was "Ma" of "Manushtir". "Ma" was a correct morpheme, however "ushtir" was not. The researchers then attempted "Man", however "ushtir" was not a correct morpheme. They next tried "Manush" and "tir", discovering that this was correct combination of morphemes. [9]
Semantics
Semantics is the study of meaning. Some anthropologists have seen linguistics as basic to a science of man because it provides a link between the biological and sociocultural levels. Modern linguistics is diffusing widely in anthropology itself among younger scholars, producing work of competence that ranges from historical and descriptive studies to problems of semantic and social variation. In the 1960's, Chomsky prompted a formal analysis of semantics and argued that grammars needed to represent all of a speaker's linguistic knowledge, including the meaning of words. Most semanticists focused attention on how words are linked to each other within a language through five different relations
- synonymy - same meaning (ex: old and aged)
- homophony - same sound, different meaning (ex: would and wood)
- antonymy - opposite meaning (ex: tall and short)
- denotation - what words refer to in the "real" world (ex: having the word pig refer to the actual animal, instead of pig meaning dirty, smelly, messy or sloppy)
- connotation - additional meanings that derive from the typical contexts in which they are used in everyday speech. (ex: calling a person a pig, not meaning the animal but meaning that they are dirty, smelly, messy or sloppy)
Formal semanticists only focused on the first four, but we have now discovered that our ability to use the same words in different ways (and different words in the same way) goes beyond the limits of formal semantics. Included in the study of semantics are metaphors which are a form of figurative or nonliteral language that links together expressions from unrelated semantic domains. A semantic domain is a set of linguistic expressions with interrelated meanings; for example, the words pig and chicken are in the same semantic domain. But when you use a metaphor to call a police officer a pig, you are combining two semantic domains to create meaning that the police officer is fat, greedy, dirty, etc. [8] [10]
Syntax
The study of the arrangement and order of words, for example if the Subject or the Object comes first in a sentence.
Syntax is the study of rules and principles for constructing sentences in natural languages. Syntax studies the patterns of forming sentences and phrases as well. It comes from ancient Greek (“syn”- means together and “taxis” means arrangement.) Outside of linguistics, syntax is also used to refer to the rules of mathematical systems, such as logic, artificial formal languages, and computer programming language. There are many theoretical approaches to the study of syntax. Noam Chomsky, a linguist, sees syntax as a branch of biology, since they view syntax as the study of linguistic knowledge as the human mind sees it. Other linguists take a Platonistic view, in that they regard syntax to be the study of an abstract formal system.
Major Approaches to Syntax
Generative Grammar: Noam Chomsky pioneered the generative approach to syntax. The hypothesis is that syntax is a structure of the human mind. The goal is to make a complete model of this inner language, and the model could be used to describe all human language and to predict if any utterance would sound correct to a native speaker of the language. It focuses mostly on the form of the sentence rather than the communicative function of it. The majority of generative theories assume that syntax is based on the constituent structure of sentences.
Categorial Grammar: An approach that attributes the syntactic structure to the properties of the syntactic categories, rather than to the rules of grammar.
Dependency Grammar: Structure is determined by the relations between a word and its dependents rather than being based on constituent structure.
Computational Analysis of Syntax of ancient Indus symbols
One recent case of computational analysis of the syntax of an unknown language comes form the work of Rajesh P. N. Rao (2009[11]) at the Dept. of Computer Science & Engineering, University of Washington. His team's computational analysis decoding patterns in the ancient Indus script has shown that it is in fact patterned like spoken language. Like spoken language, the Indus symbols follow a degree of ordering that is intermediate between highly patterned systems such a computer programming languages and highly variable systems such as the DNA code. Further analysis of the pattern of symbols with unknown meaning has linked it to the ancient Sumerian language of Mesopotamia and Old Tamil from India.
Speech Sounds
Human Speech sounds are traditionally divided between vowels and consonants, but scientific distinctions are much more precise. An important distinction between sounds in many languages is the vibration of the glottis, which is referred to as voicing. It distinguishes such sounds as /s/ (voiceless;no vibrating) and /z/ (voiced;vibrating). The chart below mentions pulmonic consonants, which are produced by releasing air from the lungs and somehow obstructing it on its way out the mouth. The non-pulmonic Consonants are clicks, implosives (similar to the 'glug-glug' sound sometimes made to imitate a liquid being poured or being drunk), and explosives. Co-articulation refers to sounds that are produced in two areas at once (like /W/).
Phoneme
A phoneme is the smallest phonetic unit in a language that is capable of conveying a distinction in meaning.[8] For example, in English we can tell that pail and tail are different words, so /p/ and /t/ are phonemes. Two words differing in only one sound, like pail and tail are called a minimal pair. The International Phonetic Association created the International Phonetic Alphabet (IPA), a collection of standardized representations of the sounds of spoken language. [9]
When a native speaker does not recognize different sounds as being distinct they are called allophones. For example, in the English language we consider the p in pin and the p in spin to have the same phoneme, which makes them allophones. In Chinese, however, these two similar phones are treated separately and both have a separate symbol in their alphabet. The minimum bits of meaning that native speakers recognize are known as phonemes. It is any small set of units, usually about 20 to 60 in number, and different for each language, considered to be the basic distinctive units of speech sound by which morphemes, words, and sentences are represented.[12]
Morpheme
Morphemes are "the smallest unit grammatical of language" that has semantic meaning. In spoken language, morphemes are composed of phonemes(the smallest unit of spoken language), but in written language morphemes are composed of graphemes(the smallest unit of written language). A morpheme can stand alone, meaning in forms a word by itself, or be a bound morpheme, where it has to attach to another bound morpheme or a stand alone morpheme in order to form a word. Prefixes and suffixes are the simplest form of bound morphemes. For example, the word "bookkeeper" has three morphemes: "book", "keep", and "-er". This example illustrates the key difference between a word and a morpheme; although a morpheme can be a standalone word, it can also need to be associated with other units in order to make sense. Meaning that one would not go around saying "-er" interdependently, it must be bound to one or more other morphemes.


Skip to main content
-
-
5.1: Ensembles of N-molecule Systems
-
Imagine collecting n N-molecule, constant-volume, constant-temperature systems. An aggregate of many multi-molecule systems is called an ensemble. Just as we assume that no forces act among the non-interacting molecules we consider earlier, we assume that no forces act among the systems of the ensemble. However, as we emphasize above, our model for the systems of an ensemble recognizes that intermolecular forces among the molecules of an individual system can be important
-
-
5.2: The Ensemble Entropy and the Value of ß
-
-
-
5.3: The Thermodynamic Functions of the N-molecule System
-
We can find the other thermodynamic functions for the N -molecule system from the equations for Z and P^i by the arguments we used previously.


9.2: Hubble Space Telescope
Hubble Space Telescope
Perhaps the best known unmanned spacecraft is the Hubble Space Telescope, HST, launched in 1991 and still fully operational. Even though the HST was not the first space telescope, it is by far the most famous and productive to date. The images returned by the HST are often beyond words. They give astronomers and stargazers a look at the Universe in detail never seen before.
The idea of a space telescope was first mentioned in writings in 1923 by German rocket pioneer Hermann Oberth. The direct link to what is now known as the Hubble Space telescope can be traced directly to Lyman Spitzer, an astronomer, who wrote in 1946 of the advantages such a space-based telescope would have. Being above Earth’s atmosphere would allow such a telescope to “see” without any atmospheric interference. And, the telescope could observe in the ultraviolet and infrared ranges of the spectrum; these wavelengths are mostly blocked by the Earth’s atmosphere; a good thing for humans but a bad thing when one is trying to study and understand the Universe.
Progress was made in the 1960’s towards the development and launch of a large space-based telescope. First, NASA launched a space telescope 1962 specifically to study the Sun, the Orbiting Solar Observatory. And in 1966, NASA launched the first telescope, the Orbiting Astronomical Observatory.
With the experience and knowledge from the OSO and OAO missions, NASA began planning for a larger, longer term space telescope. The concept for the Large Space Telescope was that it features a 3 meter-diameter primary mirror (about 118 inches) and be placed into orbit by the under-development Space Shuttle as early as 1979.
As is often the case, funding became an issue, so the Large Space Telescope’s primary mirror was reduced in size from 3 meters to 2.4 meters (about 94 1 / 2 inches). Additionally, the European Space Agency was brought on as a partner of the Large Space Telescope. The proposed launch was pushed way back from the original 1979 target, due to both Space Shuttle and Large Space Telescope developmental issues.
In 1983, the Large Space Telescope was renamed the Hubble Space Telescope, to honor Edwin Hubble for his work in astronomy and specifically Hubble’s discovery that the Universe is expanding. One of the key objectives for the HST was to determine the rate at which the Universe is expanding.
Development and construction of the HST took longer than planned, yet finally a launch date was set: October 1986. With the Challenger tragedy January 28, 1986, all shuttle launches were stopped until the Space Shuttle could undergo major modifications. Finally, on April 24, 1990, the HST was flown into orbit aboard Space Shuttle Discovery and successfully deployed on orbit.


14.11: Exercises
Write equations that show NH 3 as both a conjugate acid and a conjugate base.
Write equations that show acting both as an acid and as a base.
Show by suitable net ionic equations that each of the following species can act as a Brønsted-Lowry acid:
- (f)
Show by suitable net ionic equations that each of the following species can act as a Brønsted-Lowry acid:
- (f) HS −
Show by suitable net ionic equations that each of the following species can act as a Brønsted-Lowry base:
- (f)
Show by suitable net ionic equations that each of the following species can act as a Brønsted-Lowry base:
- (f)
What is the conjugate acid of each of the following? What is the conjugate base of each?
- OH −
- H 2 O
- NH 3
- H 2 O 2
- HS −
What is the conjugate acid of each of the following? What is the conjugate base of each?
- H 2 S
- PH 3
- HS −
- H 4 N 2
- CH 3 OH
Identify and label the Brønsted-Lowry acid, its conjugate base, the Brønsted-Lowry base, and its conjugate acid in each of the following equations:
- (f)
Identify and label the Brønsted-Lowry acid, its conjugate base, the Brønsted-Lowry base, and its conjugate acid in each of the following equations:
- (f)
What are amphiprotic species? Illustrate with suitable equations.
State which of the following species are amphiprotic and write chemical equations illustrating the amphiprotic character of these species:
- H 2 O
- S 2−
State which of the following species are amphiprotic and write chemical equations illustrating the amphiprotic character of these species.
- NH 3
- Br −
Is the self-ionization of water endothermic or exothermic? The ionization constant for water ( K w ) is 2.9 \times 10^{−14} at 40 °C and 9.3 \times 10^{−14} at 60 °C.
Explain why a sample of pure water at 40 °C is neutral even though [H 3 O + ] = 1.7 \times 10^{−7} M . K w is 2.9 \times 10^{−14} at 40 °C.
The ionization constant for water ( K w ) is 2.9 \times 10^{−14} at 40 °C. Calculate [H 3 O + ], [OH − ], pH, and pOH for pure water at 40 °C.
The ionization constant for water ( K w ) is 9.311 \times 10^{−14} at 60 °C. Calculate [H 3 O + ], [OH − ], pH, and pOH for pure water at 60 °C.
Calculate the pH and the pOH of each of the following solutions at 25 °C for which the substances ionize completely:
- 0.200 M HCl
- 0.0143 M NaOH
- 3.0 M HNO 3
- 0.0031 M Ca(OH) 2
Calculate the pH and the pOH of each of the following solutions at 25 °C for which the substances ionize completely:
- 0.000259 M HClO 4
- 0.21 M NaOH
- 0.000071 M Ba(OH) 2
- 2.5 M KOH
What are the pH and pOH of a solution of 2.0 M HCl, which ionizes completely?
What are the hydronium and hydroxide ion concentrations in a solution whose pH is 6.52?
Calculate the hydrogen ion concentration and the hydroxide ion concentration in wine from its pH. See Figure 14.2 for useful information.
Calculate the hydronium ion concentration and the hydroxide ion concentration in lime juice from its pH. See Figure 14.2 for useful information.
The hydronium ion concentration in a sample of rainwater is found to be 1.7 \times 10^{−6} M at 25 °C. What is the concentration of hydroxide ions in the rainwater?
The hydroxide ion concentration in household ammonia is 3.2 \times 10^{−3} M at 25 °C. What is the concentration of hydronium ions in the solution?
Explain why the neutralization reaction of a strong acid and a weak base gives a weakly acidic solution.
Explain why the neutralization reaction of a weak acid and a strong base gives a weakly basic solution.
Use this list of important industrial compounds (and Figure 14.8) to answer the following questions regarding: Ca(OH) 2 , CH 3 CO 2 H, HCl, H 2 CO 3 , HF, HNO 2 , HNO 3 , H 3 PO 4 , H 2 SO 4 , NH 3 , NaOH, Na 2 CO 3 .
- Identify the strong Brønsted-Lowry acids and strong Brønsted-Lowry bases.
- Identify the compounds that can behave as Brønsted-Lowry acids with strengths lying between those of H 3 O + and H 2 O.
- Identify the compounds that can behave as Brønsted-Lowry bases with strengths lying between those of H 2 O and OH − .
The odor of vinegar is due to the presence of acetic acid, CH 3 CO 2 H, a weak acid. List, in order of descending concentration, all of the ionic and molecular species present in a 1- M aqueous solution of this acid.
Household ammonia is a solution of the weak base NH 3 in water. List, in order of descending concentration, all of the ionic and molecular species present in a 1- M aqueous solution of this base.
Explain why the ionization constant, K a , for H 2 SO 4 is larger than the ionization constant for H 2 SO 3 .
Explain why the ionization constant, K a , for HI is larger than the ionization constant for HF.
Gastric juice, the digestive fluid produced in the stomach, contains hydrochloric acid, HCl. Milk of Magnesia, a suspension of solid Mg(OH) 2 in an aqueous medium, is sometimes used to neutralize excess stomach acid. Write a complete balanced equation for the neutralization reaction, and identify the conjugate acid-base pairs.
Nitric acid reacts with insoluble copper(II) oxide to form soluble copper(II) nitrate, Cu(NO 3 ) 2 , a compound that has been used to prevent the growth of algae in swimming pools. Write the balanced chemical equation for the reaction of an aqueous solution of HNO 3 with CuO.
What is the ionization constant at 25 °C for the weak acid the conjugate acid of the weak base CH 3 NH 2 , K b = 4.4 \times 10^{−4}.
What is the ionization constant at 25 °C for the weak acid the conjugate acid of the weak base (CH 3 ) 2 NH, K b = 5.9 \times 10^{−4}?
Which base, CH 3 NH 2 or (CH 3 ) 2 NH, is the stronger base? Which conjugate acid, or , is the stronger acid?
Which is the stronger acid, or HBrO?
Which is the stronger base, (CH 3 ) 3 N or
Predict which acid in each of the following pairs is the stronger and explain your reasoning for each.
- H 2 O or HF
- B(OH) 3 or Al(OH) 3
- or
- NH 3 or H 2 S
- H 2 O or H 2 Te
Predict which compound in each of the following pairs of compounds is more acidic and explain your reasoning for each.
- or
- NH 3 or H 2 O
- PH 3 or HI
- NH 3 or PH 3
- H 2 S or HBr
Rank the compounds in each of the following groups in order of increasing acidity or basicity, as indicated, and explain the order you assign.
- acidity: HCl, HBr, HI
- basicity: H 2 O, OH − , H − , Cl −
- basicity: Mg(OH) 2 , Si(OH) 4 , ClO 3 (OH) (Hint: Formula could also be written as HClO 4 .)
- acidity: HF, H 2 O, NH 3 , CH 4
Rank the compounds in each of the following groups in order of increasing acidity or basicity, as indicated, and explain the order you assign.
- (f) basicity: BrO − ,
Both HF and HCN ionize in water to a limited extent. Which of the conjugate bases, F − or CN − , is the stronger base?
The active ingredient formed by aspirin in the body is salicylic acid, C 6 H 4 OH(CO 2 H). The carboxyl group (−CO 2 H) acts as a weak acid. The phenol group (an OH group bonded to an aromatic ring) also acts as an acid but a much weaker acid. List, in order of descending concentration, all of the ionic and molecular species present in a 0.001- M aqueous solution of C 6 H 4 OH(CO 2 H).
Are the concentrations of hydronium ion and hydroxide ion in a solution of an acid or a base in water directly proportional or inversely proportional? Explain your answer.
What two common assumptions can simplify calculation of equilibrium concentrations in a solution of a weak acid or base?
Which of the following will increase the percent of NH 3 that is converted to the ammonium ion in water?
- addition of NaOH
- addition of HCl
- addition of NH 4 Cl
Which of the following will increase the percentage of HF that is converted to the fluoride ion in water?
- addition of NaOH
- addition of HCl
- addition of NaF
What is the effect on the concentrations of HNO 2 , and OH − when the following are added to a solution of KNO 2 in water:
- HCl
- HNO 2
- NaOH
- NaCl
- KNO
What is the effect on the concentration of hydrofluoric acid, hydronium ion, and fluoride ion when the following are added to separate solutions of hydrofluoric acid?
- HCl
- KF
- NaCl
- KOH
- HF
Why is the hydronium ion concentration in a solution that is 0.10 M in HCl and 0.10 M in HCOOH determined by the concentration of HCl?
From the equilibrium concentrations given, calculate K a for each of the weak acids and K b for each of the weak bases.
(a) CH
3
CO
2
H: = 1.34 \times 10^{−3}
M
;
= 1.34 \times 10^{−3}
M
;
[CH 3 CO 2 H] = 9.866 \times 10^{−2} M ;
(b) ClO − : [OH − ] = 4.0 \times 10^{−4} M ;
[HClO] = 2.38 \times 10^{−4} M ;
[ClO − ] = 0.273 M ;
(c) HCO
2
H: [HCO
2
H] = 0.524
M
;
= 9.8 \times 10^{−3}
M
;
= 9.8 \times 10^{−3}
M
;
(d) = 0.233 M ;
[C
6
H
5
NH
2
] = 2.3 \times 10^{−3}
M
;
= 2.3 \times 10^{−3}
M
From the equilibrium concentrations given, calculate K a for each of the weak acids and K b for each of the weak bases.
(a) NH
3
: [OH
−
] = 3.1 \times 10^{−3}
M
;
= 3.1 \times 10^{−3}
M
;
[NH 3 ] = 0.533 M ;
(b) HNO
2
: = 0.011
M
;
= 0.0438
M
;
[HNO 2 ] = 1.07 M ;
(c) (CH
3
)
3
N: [(CH
3
)
3
N] = 0.25
M
;
[(CH
3
)
3
NH
+
] = 4.3 \times 10^{−3}
M
;
[OH − ] = 3.7 \times 10^{−3} M ;
(d) = 0.100 M ;
[NH
3
] = 7.5 \times 10^{−6}
M
;
[H
3
O
+
] = 7.5 \times 10^{−6}
M
Determine K b for the nitrite ion, In a 0.10- M solution this base is 0.0015% ionized.
Determine K a for hydrogen sulfate ion, In a 0.10- M solution the acid is 29% ionized.
Calculate the ionization constant for each of the following acids or bases from the ionization constant of its conjugate base or conjugate acid:
- (f) (as a base)
Calculate the ionization constant for each of the following acids or bases from the ionization constant of its conjugate base or conjugate acid:
- (f) (as a base)
Using the K a value of 1.4
Calculate the concentration of all solute species in each of the following solutions of acids or bases. Assume that the ionization of water can be neglected, and show that the change in the initial concentrations can be neglected.
- 0.0092 M HClO, a weak acid
- 0.0784 M C 6 H 5 NH 2 , a weak base
- 0.0810 M HCN, a weak acid
- 0.11 M (CH 3 ) 3 N, a weak base
- 0.120 M a weak acid, K a = 1.6 \times 10^{−7}
Propionic acid, C 2 H 5 CO 2 H ( K a = 1.34 \times 10^{−5}), is used in the manufacture of calcium propionate, a food preservative. What is the pH of a 0.698- M solution of C 2 H 5 CO 2 H?
White vinegar is a 5.0% by mass solution of acetic acid in water. If the density of white vinegar is 1.007 g/cm 3 , what is the pH?
The ionization constant of lactic acid, CH 3 CH(OH)CO 2 H, an acid found in the blood after strenuous exercise, is 1.36 \times 10^{−4}. If 20.0 g of lactic acid is used to make a solution with a volume of 1.00 L, what is the concentration of hydronium ion in the solution?
Nicotine, C 10 H 14 N 2 , is a base that will accept two protons ( K b1 = 7 \times 10^{−7}, K b2 = 1.4 \times 10^{−11}). What is the concentration of each species present in a 0.050- M solution of nicotine?
The pH of a 0.23- M solution of HF is 1.92. Determine K a for HF from these data.
The pH of a 0.15- M solution of is 1.43. Determine K a for from these data.
The pH of a 0.10-
M
solution of caffeine is 11.70. Determine
K
b
for caffeine from these data:
The pH of a solution of household ammonia, a 0.950 M solution of NH 3, is 11.612. Determine K b for NH 3 from these data.
Determine whether aqueous solutions of the following salts are acidic, basic, or neutral:
- Al(NO 3 ) 3
- RbI
- KHCO 2
- CH 3 NH 3 Br
Determine whether aqueous solutions of the following salts are acidic, basic, or neutral:
- FeCl 3
- K 2 CO 3
- NH 4 Br
- KClO 4
Novocaine, C 13 H 21 O 2 N 2 Cl, is the salt of the base procaine and hydrochloric acid. The ionization constant for procaine is 7 \times 10^{−6}. Is a solution of novocaine acidic or basic? What are [H 3 O + ], [OH − ], and pH of a 2.0% solution by mass of novocaine, assuming that the density of the solution is 1.0 g/mL.
Which of the following concentrations would be practically equal in a calculation of the equilibrium concentrations in a 0.134- M solution of H 2 CO 3 , a diprotic acid: [OH − ], [H 2 CO 3 ], No calculations are needed to answer this question.
Calculate the concentration of each species present in a 0.050- M solution of H 2 S.
Calculate the concentration of each species present in a 0.010-
M
solution of phthalic acid, C
6
H
4
(CO
2
H)
2
.
Salicylic acid, HOC 6 H 4 CO 2 H, and its derivatives have been used as pain relievers for a long time. Salicylic acid occurs in small amounts in the leaves, bark, and roots of some vegetation (most notably historically in the bark of the willow tree). Extracts of these plants have been used as medications for centuries. The acid was first isolated in the laboratory in 1838.
- Both functional groups of salicylic acid ionize in water, with K a = 1.0 \times 10^{−3} for the—CO 2 H group and 4.2 \times 10^{−13} for the −OH group. What is the pH of a saturated solution of the acid (solubility = 1.8 g/L).
- Aspirin was discovered as a result of efforts to produce a derivative of salicylic acid that would not be irritating to the stomach lining. Aspirin is acetylsalicylic acid, CH 3 CO 2 C 6 H 4 CO 2 H. The −CO 2 H functional group is still present, but its acidity is reduced, K a = 3.0 \times 10^{−4}. What is the pH of a solution of aspirin with the same concentration as a saturated solution of salicylic acid (See Part a).
The ion HTe − is an amphiprotic species; it can act as either an acid or a base.
- What is K a for the acid reaction of HTe − with H 2 O?
- What is K b for the reaction in which HTe − functions as a base in water?
- Demonstrate whether or not the second ionization of H 2 Te can be neglected in the calculation of [HTe − ] in a 0.10 M solution of H 2 Te.
Explain why a buffer can be prepared from a mixture of NH 4 Cl and NaOH but not from NH 3 and NaOH.
Explain why the pH does not change significantly when a small amount of an acid or a base is added to a solution that contains equal amounts of the acid H 3 PO 4 and a salt of its conjugate base NaH 2 PO 4 .
Explain why the pH does not change significantly when a small amount of an acid or a base is added to a solution that contains equal amounts of the base NH 3 and a salt of its conjugate acid NH 4 Cl.
What is [H
3
O
+
] in a solution of 0.25
M
CH
3
CO
2
H and 0.030
M
NaCH
3
CO
2
?
What is [H
3
O
+
] in a solution of 0.075
M
HNO
2
and 0.030
M
NaNO
2
?
What is [OH
−
] in a solution of 0.125
M
CH
3
NH
2
and 0.130
M
CH
3
NH
3
Cl?
What is [OH
−
] in a solution of 1.25
M
NH
3
and 0.78
M
NH
4
NO
3
?
What is the effect on the concentration of acetic acid, hydronium ion, and acetate ion when the following are added to an acidic buffer solution of equal concentrations of acetic acid and sodium acetate:
- HCl
- KCH 3 CO 2
- NaCl
- KOH
- CH 3 CO 2 H
What is the effect on the concentration of ammonia, hydroxide ion, and ammonium ion when the following are added to a basic buffer solution of equal concentrations of ammonia and ammonium nitrate:
- KI
- NH 3
- HI
- NaOH
- NH 4 Cl
What will be the pH of a buffer solution prepared from 0.20 mol NH 3 , 0.40 mol NH 4 NO 3 , and just enough water to give 1.00 L of solution?
Calculate the pH of a buffer solution prepared from 0.155 mol of phosphoric acid, 0.250 mole of KH 2 PO 4 , and enough water to make 0.500 L of solution.
How much solid NaCH 3 CO 2 •3H 2 O must be added to 0.300 L of a 0.50- M acetic acid solution to give a buffer with a pH of 5.00? (Hint: Assume a negligible change in volume as the solid is added.)
What mass of NH 4 Cl must be added to 0.750 L of a 0.100- M solution of NH 3 to give a buffer solution with a pH of 9.26? (Hint: Assume a negligible change in volume as the solid is added.)
A buffer solution is prepared from equal volumes of 0.200 M acetic acid and 0.600 M sodium acetate. Use 1.80 \times 10^{−5} as K a for acetic acid.
- What is the pH of the solution?
- Is the solution acidic or basic?
- What is the pH of a solution that results when 3.00 mL of 0.034 M HCl is added to 0.200 L of the original buffer?
A 5.36–g sample of NH 4 Cl was added to 25.0 mL of 1.00 M NaOH and the resulting solution
diluted to 0.100 L.
- What is the pH of this buffer solution?
- Is the solution acidic or basic?
- What is the pH of a solution that results when 3.00 mL of 0.034 M HCl is added to the solution?
Explain how to choose the appropriate acid-base indicator for the titration of a weak base with a strong acid.
Explain why an acid-base indicator changes color over a range of pH values rather than at a specific pH.
Calculate the pH at the following points in a titration of 40 mL (0.040 L) of 0.100 M barbituric acid ( K a = 9.8 \times 10^{−5}) with 0.100 M KOH.
- no KOH added
- 20 mL of KOH solution added
- 39 mL of KOH solution added
- 40 mL of KOH solution added
- 41 mL of KOH solution added
The indicator dinitrophenol is an acid with a K a of 1.1 \times 10^{−4}. In a 1.0 \times 10^{−4}- M solution, it is colorless in acid and yellow in base. Calculate the pH range over which it goes from 10% ionized (colorless) to 90% ionized (yellow).


2.2.3: Internal Root Structure
-
- Last updated
- Save as PDF
- Tom Buckley
- University of California, Davis
Learning Objectives
- Describe the different structures and zones of a root.
- Compare and contrast a monocot root to a eudicot root.
- Describe secondary root growth and the function of vascular and cork cambium.
Root Anatomy
Root growth begins with seed germination. When the plant embryo emerges from the seed, the radicle of the embryo begins to grow downward and forms the root system. As the root system grows, various structures begin to appear.
Longitudinal Section
If you were to cut a root down longitudinally, you would see the various layers inside. The tip of the root is protected by the root cap , a structure exclusive to roots and unlike any other plant structure. The root cap is continuously replaced because it gets damaged easily as the root pushes through soil. The root tip can be divided into three zones: a zone of cell division , a zone of elongation , and a zone of maturation and differentiation (Figure \(\PageIndex{1}\)). The zone of cell division is a continuation of the root cap; it is made up of the actively dividing cells of the root meristem. The zone of elongation is where the newly formed cells begin to increase in length, thereby lengthening the root. They are older than cells at the zone of cell division. Beginning at the first root hair is the zone of cell maturation where the root cells begin to differentiate into special cell types. The root has an outer layer of cells called the epidermis, which surrounds areas of ground tissue and vascular tissue. The epidermis provides protection and helps in absorption. Root hairs , which are extensions of root epidermal cells, increase the surface area of the root, greatly contributing to the absorption of water and minerals. All three zones are in the first centimeter or so of the root tip.
Cross Section
If you were to cut a cross section of the leaf, you could see other features that are not as obvious in the longitudinal section. Inside the root, the ground tissue may form two regions: the cortex and the pith (Figure \(\PageIndex{2}\)). When comparing roots to stems, roots have much more cortex and very little pith. Whereas eudicot roots have no central pith, monocots have a small pith. Both cortex and pith include cells that store photosynthetic products. The cortex is between the epidermis and the vascular tissue, whereas the pith lies between the vascular tissue and the center of the root.
The inner portion of the root contains the vascular tissue (xylem and phloem). This area is called the stele . A layer of cells known as the endodermis borders the stele (Figure \(\PageIndex{2}\)) and is considered the innermost layer of the cortex. The endodermis is exclusive to roots, and serves as a checkpoint for materials entering the root’s vascular system. A waxy substance called suberin is present on the walls of the endodermal cells. This waxy region, known as the Casparian strip , forces water and solutes to cross the plasma membranes of endodermal cells instead of slipping between the cells. This ensures that only materials required by the root pass through the endodermis, while toxic substances and pathogens are generally excluded. The outermost cell layer of the root’s vascular tissue is the pericycle , an area that can give rise to lateral roots.
Monocots
Note that the size of the stele in the monocot cross section is large (everything inside the green ring (Figure \(\PageIndex{3}\)). The vascular tissue is arranged in a ring around the pith. This arrangement is called a siphonostele . The cortex surrounds the stele. The endodermis is the innermost layer of the cortex, and the exodermis is the outermost layer of the cortex. The exodermis controls the flow of water, ions, and nutrients. The outermost layer of the root (external to the cortex) is the epidermis, which covers the root and aids in absorption.
Eudicots
In eudicot roots, the vascular tissue fills the center of the root, and there is no pith. This arrangment is called a protostele . The xylem and phloem of the stele are arranged alternately in an X shape (Figure \(\PageIndex{4}\)). Most of the root is composed of cortex tissue, and the endodermis , the innermost layer of the cortex, borders the stele. The outer layer of the root (external to the cortex) is the epidermis.
Secondary Root Growth
Many roots have secondary growth as well as primary growth (figures \(\PageIndex{5-6}\)). This occurs by the production of two types of meristemic tissue, the vascular cambium and the cork cambium . The cork cambium is responsible for the girth or growth in the diameter of the root. This occurs by the cork cambium adding vascular tissue to the root. Cells of the pericycle and procambium (the meristematic tissue between the primary phloem and xylem) begin division, and form a vascular cambium around the primary xylem. The vascular cambium then divides to form secondary xylem on the inside and secondary phloem on the outside.
Some roots with secondary growth may form a periderm (a protective layer, replacing the epidermis). This occurs by the formation of a cork cambium which originate from the pericycle. The cork cambium produces parenchyma tissues called phelloderm to the inside of the root and the cork on the outside of the root. Cork cells (phellem) are dead at maturity. They are hollow and the addition of air space in the tissue functions as a protective layer. They also produce a waxy substance called
suberin
. This wax functions to aid in water loss. It also makes the root more resistant to bacterial and fungal infections. The three layers 1. phelloderm 2. cork cambium and 3. cork cells are collectively known as the periderm.
Attributions
Curated and authored by Kammy Algiers and Melissa Ha from the following sources
- 11.2 Secondary Growth from A Photographic Atlas for Botany by Maria Morrow ( CC-BY-NC ).
- 30.3 Roots from General Biology by OpenStax ( CC-BY ).


7.13: Editing Grammatical Errors
- Edit for common grammatical errors
Grammatically, writers tend to make their most obvious errors in the areas below.
Subject/Verb Agreement
This can usually be addressed by identifying each subject and verb in a sentence, ignoring the other words mentally, and making certain subjects/verbs match in number and sound.
- The word “and” linking two subjects makes them plural so you need to use the plural verb. For example, “Grammar and mechanics are related.”
- When subjects are connected by “or,” the subject closer to the verb determines the verb’s number, as in, “Either the punctuation marks or the usage is flawed.”
Pronoun Reference
Pronoun reference errors also make the list because pronouns seem to give a lot of beginning writers some trouble. A pronoun reference error occurs when you use a pronoun like he or she , and it’s not clear what that pronoun refers to. Here is an example:
- When Darth Vader and Luke Skywalker were battling with their light sabers, he became angry .
Who does he refer to? It isn’t clear. A pronoun should clearly refer to its antecedent (the word it replaces), so if the antecedent is not clear, you need to revise. Here’s an example of how you might correct the pronoun reference error:
- When Darth Vader and Luke Skywalker were battling with their light sabers, Luke became angry .
Verb Tense
You want to be sure that you are always consistent with your verb tense . When you shift verb tenses for no reason, and this is an easy mistake to make, you can really confuse your readers.
If you’re writing in the present tense, be sure you stay in the present tense. If you’re writing in the past tense, be sure you stay in the past tense. The exception would be if you need to shift tenses to tell a story, but that would be purposeful shifting. It’s the random, accidental shifting that causes the problems, as illustrated in this example:
- She grabs my hand then flipped me like I weighed nothing. This showed what a good self-defense course has done.
Here is what a corrected version of the sentence looks like:
- She grabbed my hand then flipped me like I weighed nothing. This showed what a good self-defense course has done.
It’s important to check verbs both for consistency and context.
Sentence Structure
Have you ever had a teacher say, “That sentence starts one way and ends another”? If you have, don’t feel badly. Others make this same mistake all the time. Sometimes, we simply lose our train of thought when we write, and we literally start a sentence one way and end it another, as illustrated in the following example:
- I occasionally get the urge to study late at night for instance my exams are going to take me longer than usual to study for because this works.
It’s tough to make sense of this sentence, right?
Of course, this is not the only faulty sentence structure error you might make. It’s important to pay close attention to your sentence structure to make sure you have both a subject and a verb. And, if you are listing items or phrases in a sentence, make sure you keep the items in your list in the same form. Doing so keeps your sentences “parallel,” which is a good thing.
Here is an example of a sentence without parallel structure:
- I start my day with breakfast, exercising, and checking out the latest blogs.
In the sentence above, breakfast is a noun, and exercising and checking begin verb phrases. The items in the list are not in the same form. Here is a correction where the items listed are in the same form:
- I start my day by eating breakfast, exercising, and checking out the latest blogs.
Run-ons and Fragments
You can address run-ons and fragments by identifying subjects and verbs. Sentence length can sometimes be a clue in helping you identify sentences that are too long.
Apostrophe Errors
Apostrophes give many writers a lot of trouble. Sometimes, you might be tempted to put an apostrophe where it does not belong, such as when you are simply making a word plural. Other times, you need to make a word possessive, but you might forget to use the apostrophe.
Then, of course, there is that whole its / it’s thing that confuses most everyone. Remember, the rule is to use an apostrophe when you need to show possession or ownership. The exception is with its .
Its shows ownership because it’s means it is . So, it’s like it’s is already taken, so its gets to be an ownership exception. To make sure you are using It’s correctly, just say it is when you read it. If it makes sense, you’re fine. However, if you’re trying to show ownership, and it is would not work in the sentence, you need to make the change to its . Otherwise, you might end up with a sentence like this:
- Its abundantly clear, to me, that creature’s of the night are just misunderstood and misguided beings who sometimes err in judgment and eat their neighbors’ as well as their neighbors families.
And, you would want a sentence like this:
- It’s abundantly clear, to me, that creatures of the night are just misunderstood and misguided beings who sometimes err in judgment and eat their neighbors as well as their neighbors’ families.
Commonly Confused Terms
Writers often also have trouble with some commonly confused terms. The chart below briefly describes a few.
| affect vs. effect | “Affect” is usually a verb meaning “to influence,” while “effect” is usually a noun meaning “outcome” or “result.” |
| it’s vs. its | “It’s” always means “it is,” while “its” always shows possession. |
| e.g. vs. i.e. | The abbreviation “e.g.” is Latin for exempli gratia and means “for example,” while “i.e.” is Latin for id est and means “that is.” |
| imply vs. infer | The word “imply” means “to suggest” or “to indicate,” while “infer” involves a person actively applying deduction. |
| that vs. which | The word “that” is used to define and limit a noun’s meaning, while “which” is used to provide descriptive information not central to the noun’s definition. |
Active and Passive Voice
Readers prefer sentences constructed with the active voice because they are more concise and direct. Consider the following revisions:
Passive
: Listeners are encouraged by the lyrics to cast aside their fear and be themselves.
Active
: The lyrics encourage listeners to cast aside their fears and be themselves.
Passive
: Alana’s toes were crushed by the garage door.
Active
: The garage door crushed Alana’s toes.
In both cases, the writer was able to eliminate the “be” verb (is, are, was, were), and the active sentences are less wordy.
Below is an accessible version of the above activity.
This draft contains 5 grammatical errors. Identify each one in the text box and check your answers:
Sports reporters and the media in general treat professional female athletes unfairly, as can be seen in the recent controversy over Serena Williams’ catsuit. Returning to tennis soon after giving birth to her daughter, Serena was advised by her doctors to wear something that would effect the blood flow in her legs due to her history of blood clots. To go along with her doctors’ request, Serena wore a black Nike catsuit to the French Open (Friedman). This suit, that Serena Williams tried to wear for her health, caused so much commotion that new rules about dress for women at the French Open are set in place. Elle magazine reporter Megan Friedman explains, “The rules won’t be as strict as Wimbledon … but they will be asking designers to give them an advance look at designs for players and will impose certain limits.” The fact that Serena Williams, someone who has won four Olympic medals, cannot wear something needed for health reasons is ridiculous. Not only have sportswriters stated their views on this issue, but now the people running these events are making rules against what female athletes can wear while performing their sport, inferring that female sports are more about fashion than athletics. Whether it is for health reasons or not. Women should be able to wear whatever makes them feel comfortable while they perform the sport they are good at.
[practice-area rows=”8″][/practice-area]
[reveal-answer q=”557120″]Show Answer[/reveal-answer]
[hidden-answer a=”557120″]1. Affect should replace effect in the second sentence. 2. Which should replace that in the fourth sentence. 3. The verb (are) should be in the past tense (were) in the fourth sentence. 4. Implying should replace inferring in the seventh sentence. 5. The second to last sentence is a fragment; it should be combined with the last sentence. [/hidden-answer]
Contributors and Attributions
- Obvious Grammatical Errors. Authored by : Karen Forgette. Provided by : University of Mississippi. License : CC BY: Attribution
- Image of the word grammar. Authored by : PDPics. Provided by : Pixabay. Located at : pixabay.com/photos/grammar-magnifier-magnifying-glass-389907/. License : Other . License Terms : pixabay.com/service/terms/#license
- Active and Passive Voice. Provided by : Lumen Learning. Located at : https://courses.lumenlearning.com/styleguide/wp-admin/post.php?post=821&action=edit . License : CC BY: Attribution
- 20 Most Common Grammar Errors. Provided by : Excelsior OWL. Located at : https://owl.excelsior.edu/grammar-essentials/common-errors/ . License : CC BY: Attribution


2: Derivative Introduction Last updated Save as PDF Page ID 88616 Tyler Seacrest University of Montana Western 2.1: Ball Toss Project 2.2: Position to Velocity 2.3: Homework- Position to Velocity 2.4: Algebra Tips and Tricks Part II (Piecewise Defined Functions) 2.5: Limits 2.6: Homework- Limits 2.7: Algebra Tips and Tricks Part III (Factoring) 2.8: Algebraic Limits 2.9: Homework- Algebraic Limits 2.10: Instantaneous Velocity 2.11: Homework- Instantaneous Velocity 2.12: Algebra Tips and Tricks IV (Tips for dealing with fractions) 2.13: Definition of Derivative Examples 2.14: Project- Hard Definition of Derivative Problems 2.15: Homework- Examples of the Definition of the Derivative 2.16: Project- Killdeer Migration Speed


4.3: Green’s Theorem
We will now see a way of evaluating the line integral of a smooth vector field around a simple closed curve. A vector field \(\textbf{f}(x, y) = P(x, y)\textbf{i} + Q(x, y)\textbf{j}\) is smooth if its component functions \(P(x, y)\) and \(Q(x, y)\) are smooth. We will use Green’s Theorem (sometimes called Green’s Theorem in the plane ) to relate the line integral around a closed curve with a double integral over the region inside the curve:
Theorem 4.7: Green's Theorem
Let \(R\) be a region in \(\mathbb{R}^2\) whose boundary is a simple closed curve \(C\) which is piecewise smooth. Let \(\textbf{f}(x, y) = P(x, y)\textbf{i}+Q(x, y)\textbf{j}\) be a smooth vector field defined on both \(R\) and \(C\). Then
\[\oint_C \textbf{f}\cdot d\textbf{r} = \iint\limits_R \left ( \dfrac{∂Q}{ ∂x} - \dfrac{∂P}{ ∂y} \right )\,dA, \label{Eq4.21}\]
where \(C\) is traversed so that \(R\) is always on the left side of \(C\).
Proof: We will prove the theorem in the case for a simple region \(R\), that is, where the boundary curve \(C\) can be written as \(C = C_1 \cup C_2\) in two distinct ways:
\[\begin{align} C_1 &= \text{ the curve }y = y_1(x)\text{ from the point }X_1 \text{ to the point }X_2 \label{Eq4.22} \\[4pt] C_2 &=\text{ the curve }y = y_2(x) \text{ from the point }X_2 \text{ to the point } X_1 , \label{Eq4.23} \\[4pt] \end{align}\]
where \(X_1\) and \(X_2\) are the points on \(C\) farthest to the left and right, respectively; and
\[\begin{align} C_1 &= \text{ the curve }x = x_1(y)\text{ from the point }Y_2 \text{ to the point } Y_1 \label{Eq4.24} \\[4pt] C_2 &= \text{ the curve } x = x_2(y)\text{ from the point } Y_1 \text{ to the point }Y_2,\label{Eq4.25} \\[4pt] \end{align}\]
where \(Y_1\) and \(Y_2\) are the lowest and highest points, respectively, on \(C\). See Figure 4.3.1.
Integrate \(P(x, y)\) around \(C\) using the representation \(C = C_1 \cup C_2\) given by Equation \ref{Eq4.23} and Equation \ref{Eq4.24}.
Since \(y = y_1(x) \text{ along }C_1\) (as \(x\) goes from \(a \text{ to }b)\) and \(y = y_2(x) \text{ along }C_2\) (as \(x\) goes from \(b \text{ to }a)\), as we see from Figure 4.3.1, then we have
\[\nonumber \begin{align} \oint_C P(x, y)\,dx&=\int_{C_1}P(x, y)\,dx+\int_{C_2}P(x, y)\,dx \\[4pt] \nonumber &=\int_a^b P(x, y_1(x))\,dx+\int_b^a P(x, y_2(x))\,dx \\[4pt] \nonumber &=\int_a^b P(x, y_1(x))\,dx - \int_a^b P(x, y_2(x))\,dx \\[4pt] \nonumber &=-\int_a^b (P(x, y_2(x)) - P(x, y_1(x)))\, dx \\[4pt] \nonumber &=-\int_a^b \left ( P(x, y) \Big |_{y=y_1(x)}^{y=y_2(x)} \right )\,dx \\[4pt] \nonumber &=-\int_a^b \int_{y_1(x)}^{y_2(x)} \dfrac{∂P(x, y)}{ ∂y}\,dy\,dx \text{ (by the Fundamental Theorem of Calculus)} \\[4pt] &=-\iint\limits_R \dfrac{∂P}{ ∂y}\,dA. \\[4pt] \label{Eq4.26} \end{align}\]
Likewise, integrate \(Q(x, y)\) around \(C\) using the representation \(C = C_1 \cup C_2\) given by Equation \ref{Eq4.25} and Equation \ref{Eq4.26}. Since \(x = x_1(y) \text{ along }C_1\) (as \(y\) goes from \(d\) to \(c\)) and \(x = x_2(y) \text{ along }C_2\) (as \(y\) goes from \(c\) to \(d\)), as we see from Figure 4.3.1, then we have
\[\nonumber \begin{align} \oint_C Q(x, y)\,dy&=\int_{C_1}Q(x, y)\,dy+\int_{C_2}Q(x, y)\,dy \\[4pt] \nonumber &=\int_d^c Q(x_1(y), y)\,dy+\int_c^d Q(x_2(y), y)\,dy \\[4pt] \nonumber &=-\int_c^d Q(x_1(y), y)\,dy + \int_c^d Q(x_2(y), y)\,dy \\[4pt] \nonumber &=\int_c^d (Q(x_2(y), y) - Q(x_1(y), y))\, dy \\[4pt] \nonumber &=\int_c^d \left ( Q(x, y) \Big |_{x=x_1(y)}^{x=x_2(y)} \right )\,dy \\[4pt] \nonumber &=\int_c^d \int_{x_1(y)}^{x_2(y)} \dfrac{∂Q(x, y)}{ ∂x}\,dx\,dy \text{ (by the Fundamental Theorem of Calculus)} \\[4pt] \nonumber &=\iint\limits_R \dfrac{∂Q}{ ∂x}\,dA,\text{ and so} \\[4pt] \end{align}\]
\[\nonumber \begin{align} \oint_C \textbf{f}\cdot d\textbf{r} &= \oint_C P(x, y)\,dx + \oint_C Q(x, y)\,d y \\[4pt] \nonumber &= -\iint_R \dfrac{∂P}{ ∂y}\,dA + \iint_R \dfrac{∂Q}{∂x}\,dA \\[4pt] \nonumber &= \iint_R \left ( \dfrac{∂Q}{ ∂x}-\dfrac{∂P}{ ∂y} \right ) \,dA. \\[4pt] \end{align}\]
\(\tag{\(\textbf{QED}\)}\)
Though we proved Green’s Theorem only for a simple region \(R\), the theorem can also be proved for more general regions (say, a union of simple regions).
Example 4.7
Evaluate \(\oint_C (x^2 + y^2 )\,dx+2x y\, d y\), where \(C\) is the boundary (traversed counterclockwise) of the region \(R = {(x, y) : 0 ≤ x ≤ 1, 2x^2 ≤ y ≤ 2x}\).
\(R\) is the shaded region in Figure 4.3.2. By Green’s Theorem, for \(P(x, y) = x^2 + y^2 \text{ and }Q(x, y) = 2x y\), we have
\[\nonumber \begin{align} \oint_C (x^2+y^2)\,dx+2x y \,d y &=\iint_R \left ( \dfrac{∂Q}{ ∂x}-\dfrac{∂P}{ ∂y} \right ) \, dA \\[4pt] \nonumber &=\iint_R (2y−2y)\,d A = \iint_R 0\,dA = 0. \\[4pt] \end{align}\]
We actually already knew that the answer was zero. Recall from Example 4.5 in Section 4.2 that the vector field \(\textbf{f}(x, y) = (x^2 + y^2 )\textbf{i}+2x y\textbf{j}\) has a potential function \(F(x, y) = \dfrac{1}{3} x^3 + x y^2\), and so \(\oint_C \textbf{f}\cdot d\textbf{r} = 0\) by Corollary 4.6.
Example 4.8
Let \(\textbf{f}(x, y) = P(x, y)\textbf{i}+Q(x, y)\textbf{j}\), where
\[\nonumber P(x, y) =\dfrac{-y}{x^2+y^2} \text{ and }Q(x, y) =\dfrac{x}{x^2+y^2},\]
and let \(R = {(x, y) : 0 < x^2 + y^2 ≤ 1}\). For the boundary curve \(C : x^2 + y^2 = 1\), traversed counterclockwise, it was shown in Exercise 9(b) in Section 4.2 that \(\oint_C \textbf{f}\cdot d\textbf{r} = 2π\). But
\[\nonumber \dfrac{∂Q }{∂x} = \dfrac{y^2+x^2}{(x^2+y^2)^2} = \dfrac{∂P }{∂y} \Rightarrow \iint\limits_R \left ( \dfrac{∂Q}{ ∂x} - \dfrac{ ∂P}{ ∂y} \right )\,dA= \iint\limits_R 0\,dA = 0\]
This would seem to contradict Green’s Theorem. However, note that \(R\) is not the entire region enclosed by \(C\), since the point \((0,0)\) is not contained in \(R\). That is, \(R\) has a “hole” at the origin, so Green’s Theorem does not apply.
If we modify the region \(R\) to be the annulus \(R = {(x, y) : 1/4 ≤ x^2 + y^2 ≤ 1}\) (see Figure 4.3.3), and take the “boundary” \(C \text{ of }R \text{ to be }C = C_1 \cup C_2\), where \(C_1\) is the unit circle \(x^2 + y^2 = 1\) traversed counterclockwise and \(C_2\) is the circle \(x^2 + y^2 = 1/4\) traversed clockwise , then it can be shown (see Exercise 8) that
\[\nonumber \oint_C \textbf{f} \cdot d\textbf{r} = 0 \]
We would still have \(\iint\limits_R \left ( \dfrac{∂Q}{∂x} − \dfrac{∂P}{ ∂y } \right )\,d A = 0\), so for this \(R\) we would have
\[\nonumber \oint_C \textbf{f}\cdot d\textbf{r} = \iint\limits_R \left ( \dfrac{∂Q}{ ∂x} - \dfrac{∂P}{ ∂y} \right ) \, dA,\]
which shows that Green’s Theorem holds for the annular region \(R\).
It turns out that Green’s Theorem can be extended to multiply connected regions , that is, regions like the annulus in Example 4.8, which have one or more regions cut out from the interior, as opposed to discrete points being cut out. For such regions, the “outer” boundary and the “inner” boundaries are traversed so that \(R\) is always on the left side.
The intuitive idea for why Green’s Theorem holds for multiply connected regions is shown in Figure 4.3.4 above. The idea is to cut “slits” between the boundaries of a multiply connected region \(R\) so that \(R\) is divided into subregions which do not have any “holes”. For example, in Figure 4.3.4(a) the region \(R\) is the union of the regions \(R_1 \text{ and }R_2\), which are divided by the slits indicated by the dashed lines. Those slits are part of the boundary of both \(R_1 \text{ and }R_2\), and we traverse then in the manner indicated by the arrows. Notice that along each slit the boundary of \(R_1\) is traversed in the opposite direction as that of \(R_2\), which means that the line integrals of \textbf{f} along those slits cancel each other out. Since \(R_1 \text{ and }R_2\) do not have holes in them, then Green’s Theorem holds in each subregion, so that
\[\nonumber \oint_{bdy\,of\,R_1}\textbf{f} \cdot d\textbf{r} = \iint\limits_{R_1}\left (\dfrac{ ∂Q }{∂x} - \dfrac{∂P }{∂y} \right )\,dA \text{ and }\oint_{bdy\,of\,R_2}\textbf{f}\cdot d\textbf{r} = \iint\limits{R_2} \left ( \dfrac{∂Q }{∂x} - \dfrac{∂P}{ ∂y} \right )\,dA.\]
But since the line integrals along the slits cancel out, we have
\[\nonumber \oint_{C_1 \cup C_2} \textbf{f}\cdot d\textbf{r} = \oint_{bdy\,of\,R_1} \textbf{f} \cdot d\textbf{r} +\oint_{bdy\,of\,R_2}\textbf{f}\cdot d\textbf{r},\]
and so
\[\nonumber \oint_{C_1 \cup C_2} \textbf{f}\cdot d\textbf{r} = \iint\limits_{R_1} \left ( \dfrac{∂Q}{ ∂x} − \dfrac{∂P}{ ∂y} \right ) \,dA + \iint\limits_{R_2} \left ( \dfrac{∂Q}{ ∂x} − \dfrac{∂P}{ ∂y} \right ) \,dA = \iint\limits_R \left ( \dfrac{∂Q}{ ∂x} - \dfrac{∂P }{∂y} \right ) \,dA,\]
which shows that Green’s Theorem holds in the region \(R\). A similar argument shows that the theorem holds in the region with two holes shown in Figure 4.3.4(b).
We know from Corollary 4.6 that when a smooth vector field \(\textbf{f}(x, y) = P(x, y)\textbf{i}+Q(x, y)\textbf{j}\) on a region \(R\) (whose boundary is a piecewise smooth, simple closed curve \(C\)) has a potential in \(R\), then \(\oint_C \textbf{f}\cdot d\textbf{r} = 0\). And if the potential \(F(x, y)\) is smooth in \(R\), then \(\dfrac{∂F}{ ∂x} = P \text{ and }\dfrac{∂F}{ ∂y} = Q\), and so we know that
\[\nonumber \dfrac{∂^2F }{∂y∂x} = \dfrac{∂^2F}{ ∂x∂y} \Rightarrow \dfrac{∂P}{ ∂y} = \dfrac{∂Q }{∂x}\text{ in }R\]
Conversely, if \(\dfrac{∂P}{ ∂y} = \dfrac{∂Q}{ ∂x}\) in \(R\) then
\[\nonumber \oint_C \textbf{f} \cdot d\textbf{r} = \iint\limits_R \left ( \dfrac{∂Q }{∂x}-\dfrac{∂P }{∂y} \right ) \,dA \iint\limits_R 0\,dA = 0 \]
For a simply connected region \(R\)(i.e. a region with no holes), the following can be shown:
The following statements are equivalent for a simply connected region \(R\) in \(\mathbb{R}^2\) :
- \(\textbf{f}(x, y) = P(x, y)\textbf{i}+Q(x, y)\textbf{j} \) has a smooth potential \(F(x, y)\) in \(R\)
- \(\int_C \textbf{f}\cdot d\textbf{r}\) is independent of the path for any curve \(C\) in \(R\)
- \(\oint_C \textbf{f} \cdot d\textbf{r} = 0\) for every simple closed curve \(C\) in \(R\)
- \(\dfrac{ ∂P}{ ∂y} = \dfrac{∂Q }{∂x} \) in \(R\) (in this case, the differential form \(P dx+Q d y\) is exact)


5.5: Creating Forms in Google Docs
By the end of this section, you will be able to:
- Create a fillable form using a template
- Create a fillable form from scratch
- Distribute the form and view responses
Google released Google Forms in 2008 as a feature of Google Sheets. It became a stand-alone product in 2016 and became its own program, which enabled Google to add more features to it. Forms helps you create an online form that tabulates responses and analyzes information gathered from the form. This is the main advantage of using Forms over creating a fillable form in Word. Forms not only collects the responses, but can also summarize the responses for you. You just need to plan the questionnaire, write and design the questions, and email the form link to respondents. It has an easy-to-use interface, like other Google products, and includes additional features to help you sort through and understand the form responses. Because you are collecting the responses electronically through the Forms app rather than having the responses saved in a document file, you have many more options for how to view and summarize your responses. In the Forms app, you have options to view individual responses, download the responses to Sheets, and view graphs that summarize all of the responses collected.
In the marketing department at WorldCorp, there are many uses for Forms. Forms might be more useful to the marketing department at WorldCorp because it is much easier to create a form and collect information in Google as compared with creating the form in Word. The process to create a form in Google is much more direct and Forms also summarizes the information collected right in the application. As the Google programs are web-based, we will use the web browser to construct the questionnaire, and the clients will receive an email with a link. After respondents answer the questions, Forms can automatically create graphs to summarize the responses, which you can import into other documents or programs if needed.
Form Templates
Creating a Form is like creating any other Google file. Begin in your Google Drive, select the New drop-down menu, and find Google Forms, as seen in Figure 5.49. From here, you have the choice of creating a survey from a Blank form or From a template. For this walk-through, we will choose From a template, but we will review how to create one from scratch in Creating a New Form. The advantage to using a template is that you can choose a form that is already similar to the one you might have in mind. Using a template from the Template Gallery (Figure 5.50) will help save you time, as all you will need to do is modify the questions and answers, and then add some new questions as needed.
Some of the templates in the Template Gallery are designed with specific purposes in mind: event invitations, contact information requests, order forms, work requests, and customer feedback surveys. As Figure 5.51 shows, most templates just have a few questions, and are meant to be modified and added to.
Creating a New Form
If you want to create a form from scratch, select Blank form from the drop-down menu. The form will start with a blank document that says “Untitled form.” As in Docs, rename this file by clicking on the title bar to type the new name of the form. All new forms also have a blank space for a description, just below the form’s title. The respondent will see the description, so it needs to be informative to them, as Figure 5.52 shows. It is important to name the form; otherwise, you are not going to be able to find it easily in your Drive later.
Now, you can begin typing the questionnaire. Use the first sample item in the blank form—a multiple-choice item—or choose a different type of question using the drop-down menu on the right. There are eleven types of questions, as Figure 5.53 shows. Table 5.1 explains each type of question and what it is used for.
| Type | Description |
|---|---|
| Short Answer | These are open questions (the answer can be anything). Similar to the “plain text” controls in Word. |
| Paragraph | These are open questions. Similar to the “plain text” controls, but you can answer with a lot of text and paragraphs. There is no Rich Text Format control in Forms. |
| Multiple Choice | The multiple choice question is like the “combo box” in Word. You can include an “Other” option. The “Other” option can be typed. |
| Checkboxes | The checkboxes are the same as in Word controls, but in Forms, you can have an “Other” open answer as well. |
| Drop-down | The drop-down is like the “drop-down list” control in Word. The survey taker has to choose one option. There is no “Other” option. |
| File Upload | The survey taker can upload a document or a picture file (or any other file extension). |
| Linear Scale | It is a scaling question that can be configured to start from “0” and end at “10.” |
| Multiple-Choice Grid |
This is a kind of multiple choice, which the survey taker has to choose one per row or column. There are many rows/columns.
Can be used for Likert scales. |
| Tick Box Grid | This is a kind of checkbox, which the survey taker has to choose one per row or column. There are many rows/columns. Can be used for Likert scales. |
| Date | This makes the user choose a date, like the “date picker” control. |
| Time | This makes the user choose a time. It can be 24h or AM/PM format. |
You should learn the various question types, as there are many interesting options for how to set up your form. There is a sidebar that lets you add a new question, as well as several additional commands, as seen in Figure 5.54. The additional commands on that sidebar are importing a list, adding a text description (similar to the Design Mode instructive text in Word), and inserting an image or video for the question. Lastly, there is a command for making different section breaks; this can be used as a way to divide up the form, which can be useful if the form is chunked into different topics or if it is several pages long. For example, the demographic questions could all be in one section, and the TV viewing questions could be in another.
There are two toolbars in Forms. The top toolbar is used for themes. The bottom toolbar (Figure 5.55) gives the writer more question-level configuration options. It contains the Duplicate question command, the Delete command (the trash icon), and the Required toggle . If you select the Duplicate icon, Forms will repeat the previous question, so that all you need to do is edit the question instead of writing it again from scratch. The Delete command is for removing the question from the list. The Required toggle allows the form creator to make the question mandatory; in other words, the respondent must provide an answer for this question before sending their final responses. In the form, the mandatory question will be followed by a red “*” to indicate that the question is required. The last item is the three-dots menu drop-down menu that contains a few more question-level settings, like letting you add a description to the question, manage the list of questions, and change the order of the questions.
Importing Questions
Importing questions means adding questions from another form or form template to your current form. You can do this by choosing the Import button on the sidebar (as seen in Figure 5.56). This will take you to the gallery of form templates (Forms) or your archive of saved forms (Recent) that you have created. Select any one of these, and you will be taken to that form, where you will see the questions on a sidebar, as Figure 5.57 shows. In this example, we selected the Customer Feedback Form Template. Select the questions you want to import by ticking the checkboxes. When you are finished making your selections, select Import questions from the bottom of the sidebar. If you want to add questions from multiple forms, you will have to do the same steps over again for each form.
If you want to import questions from a form that you wrote in Word, the easiest route is to create a new question using the type you need, then copy and paste the text from the other file. This is the most direct approach. Forms will not automatically recognize the type of question you want (such as drop-down list or checkbox), but if you create the question first, then you can paste the specific text into that question. There are add-ons that you can download to help facilitate importing questions from other file types, but using a copy/paste method can be a simple, easy way to get the information from one file into Forms because it involves fewer steps and is often less complicated than using an add-on.
Let’s use the fillable form that we created in Word and copy the information from a couple of the questions into Forms using this approach. First, create a blank form in Docs and open the fillable form you created in Word. Recall that the first line on the office supply order form is “Date.” In the blank form, you can set the first question to use the date question format type. We can then copy and paste the text from the Word fillable form into the question we just created. This approach is not necessarily importing the questions from the Word fillable form, but it provides a simple way to get the information from one file type into Forms.
Customizing the Form Settings and Theme
Although you cannot change the font or text formatting within the form questions, you can change the form theme, which applies some formatting changes globally throughout the form. In the top toolbar in Forms, you will find commands for document formatting and applying themes, as Figure 5.58 shows.
The first command, the painter’s palette icon, is for changing the overall survey form theme. When you select this, a sidebar, Theme options, will appear, with theme and background color configurations (see Figure 5.59). From here, you can choose an image for the header, such as a custom design or a company logo, as well as change the color scheme of the document or change the font type of the whole document. There are only four font types available.
The second command, the eye icon, is for previewing, and it displays the survey how the survey taker would see it. This can be a handy tool for previewing the form before it is sent to the survey takers.
The third command, the gear icon, is the Form Settings . When you access the Form Settings, you will see three tabs. The General tab gives you configurations for the survey takers, such as letting you collect the emails of survey takers, sending the survey takers an email receipt, limiting the takers to only do one survey response, and other configurations, as shown in Figure 5.60. In the Presentation tab, you can change some of the appearance options for your survey, such as the confirmation message, the order of questions (e.g., shuffled or in the same order each time), and other options. The third tab is Quizzes, which contains configuration settings for survey types and is used more commonly in the education industry.
 Build out the rest of the questions from the form that we created in Word. We can use some of the tools now to customize the theme to make it more visually appealing and professional in appearance. Figure 5.61 shows an example of some customizations that you might choose to include in the form.
Distributing the Form
The last command of the top toolbar is the Send button, which lets you start the actual surveying process. After you press Send, you’ll have four options of how to distribute the survey: you can type your clients’ email addresses and send it to them directly; get a public link, which you can paste into an email; embed the survey into a website; or post the survey to a social media account (Figure 5.62).
If you choose to send it by email, you will need to copy and paste or manually type in all of the recipients’ email addresses. You’ll be able to write the body and subject of the message, but there are limitations to the length and style of the message. You cannot do any text formatting or add graphics in this interface like you would if you constructed the email in your email program and included the form link. Note that the recipients will not see the other recipients’ email addresses in the list. Also, there is no way to use the email addresses in your Google Contacts or other contact list. This approach is best for a small number of recipients. If you expect to send the form to a large number of people, it is better to use your email program to send the form with the link.
The second option is to send the form via a public link. You can copy this link and paste it anywhere. For example, you can save it for later use, and send it to clients after a business activity has passed (e.g., after a successful purchase). You could also paste it into an email and send it to your recipients that way.
The third option is embedding, which will give you the .html code so that you can insert the form link on the company website. When you choose this option, the HTML code will be displayed. You can then copy that code and use it to embed the form on a website. This option can be used when you want the responders to go to your company’s website to answer the questions.
Lastly, you can send the form via social media. Forms has Facebook and Twitter (now X) icons on the right side of the Send form dialog box. Selecting one of these will allow you to embed the form directly onto your social media page or feed for others to access.
Viewing Responses
Once you send the survey, you may want to wait a few days for individuals to respond. You can consult the response statistics by going to your form and looking at the top of the form screen. By default, you are viewing the Questions tab, as seen in Figure 5.63.
If you choose the Responses tab, you’ll be taken to the responses report page, as shown in Figure 5.64. At the top of the Responses report, there is a Google Sheets icon command; if you choose this, all the report output will be exported to your Sheets app, and from there you can download the file as an Excel file or CSV. Forms provides some basic visualizations for the response. If you want more in-depth analysis, you might use other programs more suited for statistical analysis.
When you want to close the form to new responses, you can toggle the Accepting responses lever on the right side of Responses tab. This means that no one can submit any more responses to your form.
Forms is not just used to create surveys. Read this article on creative ways to use Google Forms in the workplace to learn more. Forms can also be used in your personal life. Read this article on some very unique uses of Forms to learn more.


8.6: Key Terms Defined
Boundary – an invisible, vertical plane that separates one state from another, which includes both the airspace above the line on the surface and the ground below.
Centripetal force – a force that tends to bind a state together.
Centrifugal force – a force that tends to break a state apart.
Compact state – a state where the distance from the center to any border does not vary significantly; roughly circular.
Ethnic boundary – a boundary that encompasses a particular ethnic group.
Fragmented state – a state whose territory is not contiguous, but consists of isolated parts such as islands.
Geometric boundary – a boundary that follows a straight line and may coincide with a line of latitude or longitude.
Gerrymandering – the process of redrawing legislative districts in order to benefit the party in power and ensure victory in elections.
Irredentism – an effort to expand the political influence of a state on a group of people in a neighboring state.
Multi-national state – state that has more than one nation within their borders.
Nation – group of people bonded by cultural attributes such as language, ethnicity and religion.
Nation-state – state in which the territorial boundaries encompass a group of people with a shared ethnicity.
Physical boundary – a boundary that follows a natural feature on the landscape such as a river, mountain range, or lake.
State – a formal region in which the government has sovereignty or control of its own affairs within its territorial boundaries.
Stateless nation – a nation that aspires to become a nation-state but does not yet have their own territory.
Supranational organization – an alliance involving three or more states who have shared objectives that may be economic, political/military, or cultural.
Terrorism – intimidation of a population by violence in order to further political aims.


5.3B: Pyruvic Acid and Metabolism
- Outline the metabolic processes that involve pyruvate
Pyruvic acid (CH 3 COCOOH; is an organic acid, a ketone, and the simplest of the alpha-keto acids. The carboxylate (COO − ) anion of pyruvic acid. The Brønsted–Lowry conjugate base, CH 3 COCOO − , is known as pyruvate, and is a key intersection in several metabolic pathways.
Pyruvic acid can be made from glucose through glycolysis, converted back to carbohydrates (such as glucose) via gluconeogenesis, or to fatty acids through acetyl-CoA. It can also be used to construct the amino acid alanine, and it can be converted into ethanol.
Pyruvic acid supplies energy to living cells through the citric acid cycle (also known as the Krebs cycle) when oxygen is present (aerobic respiration); when oxygen is lacking, it ferments to produce lactic acid. Pyruvate is an important chemical compound in biochemistry. It is the output of the anaerobic metabolism of glucose known as glycolysis. One molecule of glucose breaks down into two molecules of pyruvate, which are then used to provide further energy in one of two ways. Pyruvate is converted into acetyl- coenzyme A, which is the main input for a series of reactions known as the Krebs cycle. Pyruvate is also converted to oxaloacetate by an anaplerotic reaction, which replenishes Krebs cycle intermediates; also, oxaloacetate is used for gluconeogenesis. These reactions are named after Hans Adolf Krebs, the biochemist awarded the 1953 Nobel Prize for physiology, jointly with Fritz Lipmann, for research into metabolic processes. The cycle is also known as the citric acid cycle or tri-carboxylic acid cycle, because citric acid is one of the intermediate compounds formed during the reactions.
If insufficient oxygen is available, the acid is broken down anaerobically, creating lactate in animals and ethanol in plants and microorganisms. Pyruvate from glycolysis is converted by fermentation to lactate using the enzyme lactate dehydrogenase and the coenzyme NADH in lactate fermentation. Alternatively it is converted to acetaldehyde and then to ethanol in alcoholic fermentation.
Pyruvate is a key intersection in the network of metabolic pathways. Pyruvate can be converted into carbohydrates via gluconeogenesis, to fatty acids or energy through acetyl-CoA, to the amino acid alanine, and to ethanol. Therefore, it unites several key metabolic processes.
LICENSES AND ATTRIBUTIONS
CC LICENSED CONTENT, SPECIFIC ATTRIBUTION
- Metabolism. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Metabolism%23Catabolism. License : CC BY-SA: Attribution-ShareAlike
- polymer. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/polymer. License : CC BY-SA: Attribution-ShareAlike
- acetyl CoA. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/acetyl%20CoA. License : CC BY-SA: Attribution-ShareAlike
- catabolism. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/catabolism. License : CC BY-SA: Attribution-ShareAlike
- File:Catabolism schematic.svg - Wikipedia, the free encyclopedia. Provided by : Wikipedia. Located at : en.Wikipedia.org/w/index.php?title=File:Catabolism_schematic.svg&page=1. License : Public Domain: No Known Copyright
- Krebs cycle. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/Krebs_cycle. License : CC BY-SA: Attribution-ShareAlike
- Pyruvic acid. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Pyruvic_acid. License : CC BY-SA: Attribution-ShareAlike
- conjugate base. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/conjugate_base. License : CC BY-SA: Attribution-ShareAlike
- pyruvic acid. Provided by : Wiktionary. Located at : en.wiktionary.org/wiki/pyruvic_acid. License : CC BY-SA: Attribution-ShareAlike
- File:Catabolism schematic.svg - Wikipedia, the free encyclopedia. Provided by : Wikipedia. Located at : en.Wikipedia.org/w/index.php?title=File:Catabolism_schematic.svg&page=1. License : Public Domain: No Known Copyright
- Pyruvic-acid-2D-skeletal. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:Pyruvic-acid-2D-skeletal.png%23filelinks. License : Public Domain: No Known Copyright
Key Points
- Pyruvic acid can be made from glucose through glycolysis, converted back to carbohydrates (such as glucose) via gluconeogenesis, or to fatty acids through acetyl-CoA.
- Pyruvic acid supplies energy to living cells through the citric acid cycle (also known as the Krebs cycle ) when oxygen is present (aerobic respiration); it ferments to produce lactic acid when oxygen is lacking ( fermentation ).
- Pyruvate is the output of the anaerobic metabolism of glucose known as glycolysis.
- Pyruvate can be converted into carbohydrates via gluconeogenesis, to fatty acids or energy through acetyl-CoA, to the amino acid alanine, and to ethanol.
Key Terms
- pyruvic acid : A colourless liquid; an important intermediate in the metabolism of proteins and carbohydrates, and in fermentation.
- conjugate base : Any compound, of general formula Xn+, which can be transformed into a conjugate acid HX(n+1)+ by the gain of a proton.
- Krebs cycle : A series of enzymatic reactions that occurs in all aerobic organisms; it involves the oxidative metabolism of acetyl units and serves as the main source of cellular energy.