24.2: Sectional versus Continuous
24.2 Sectional versus Continuous
We apply the descriptor “ sectional ” to a binary or ternary form when the first section (the A section) ends on the tonic. (Note: We use lowercase letters to refer to phrases and uppercase letters to refer to sections.)
The term “ continuous ” is used the first section of a binary or ternary form does not end on the tonic chord. While this often means the first section ends in a new key, it can also mean the first section ends on the dominant chord in a half cadence.
In naming any binary or ternary form, use the terms sectional or continuous before binary or ternary, for example “ sectional binary,” “ continuous binary,” “ sectional ternary,” or “ continuous ternary.”
Other descriptors include “ two-reprise ,” which means both the first section (the A section) and second section (the A’ or B section) are repeated, and “rounded,” used in conjunction with binary (“rounded binary”) to specify that the opening material returns after the contrasting section.
In the following sections we will discuss three types of binary forms:
- Balanced Binary
- Rounded Binary
- “Simple” Binary (usually called “binary”)


3.1: Magnetic Fields
If a magnet is suspended in the air, it will always turn and align with Earth's north and south poles. The two ends, called the magnetic poles , are where the force is strongest.
A magnetic field of force is set up between the two poles. You can think of it as invisible lines of force traveling from one pole to the other. The magnetic lines (flux lines) are continuous and always form loops. These invisible lines can be seen if you sprinkle iron filings on a piece of paper placed over a bar magnet (Figure \(\PageIndex{1}\)).
Characteristics of magnetic lines of force
Magnets have some specific rules governing their operation.
Magnetic lines of force possess direction
These lines are continuous and extend from the north pole to the south pole of the magnet (Figure \(\PageIndex{2}\)).
Magnetic lines of force always form complete loops
The lines do not begin and end at the poles but rather pass through the magnet to form complete loops. If you were to cut a magnet in half, you could observe the magnetic field between the two pieces of the magnet (Figure \(\PageIndex{3}\)).
Magnetic lines of force always form tight loops
This rule explains the idea of attraction. The flux lines attempt to pull in as close to the magnet as possible, just like rubber bands. They also try to concentrate at each pole. If you place two unlike poles together, they try to become one big magnet and shorten the lines of force (Figure \(\PageIndex{4}\)).
Magnetic lines of force repel each other
If magnetic lines of force act like rubber bands, why don’t they collapse into the center? The reason is that they repel each other. Look back at Figure 3; notice that the lines tend to diverge as they move away from the poles, rather than converge or even remain parallel. This results from their mutual repulsion.
Magnetic lines of force never cross, but must always form individual loops
The mutual repulsion of each magnetic line accounts for this effect. This explains why like poles repel each other. If the lines cannot cross each other, then they must exert a force against each other. If you could see the lines of force, they would look like the diagram in (Figure \(\PageIndex{5}\)).
Magnetic lines of force can pass more easily through material that can be magnetized
The magnetic lines of force will distort to include a piece of iron in the field. This will have the effect of turning the iron into a temporary magnet. Then the opposite poles of the two magnets will attract each other and try to shorten the flux lines. This accounts for the attraction of unmagnetized ferromagnetic objects (Figure \(\PageIndex{6}\)).
There is no insulation against magnetic lines of force
All magnetic field lines must terminate on the opposite pole, which means there is no way to stop them. Nature must find a way to return the magnetic field lines back to an opposite pole. However, magnetic fields can be rerouted around objects. This is a form of magnetic shielding. By surrounding an object with a material that can “conduct” magnetic flux better than the materials around it, the magnetic field will tend to flow along this material and avoid the objects inside. This allows the field lines to terminate on the opposite poles, but just gives them a different route to follow (Figure \(\PageIndex{7}\)).
Alignment of the atoms
If you took a permanent magnet and cut it in half, you would have two permanent magnets, each with a north and south pole. If you continued cutting each in half, you would have more magnets. This suggests that if you could cut right down to the atom, it would also be a perfect permanent magnet.
This theory can be extended to non-magnetic material as well. Each of the atoms is a magnet, but they are all pointing in different directions. If you can get enough atoms pointing in the same direction, you will have a magnet. All you have to do is expose the piece of metal to flux lines, and the atoms will align.
These atoms tend to form in groups called domains . When the domain becomes large enough, the entire piece of metal becomes the domain and exerts force. When all of the atoms become aligned, the piece has become saturated and cannot get any stronger.


3.4A: Types of Receptors
Receptors, either intracellular or cell-surface, bind to specific ligands, which activate numerous cellular processes.
- Compare internal receptors with cell-surface receptors
Key Points
- Intracellular receptors are located in the cytoplasm of the cell and are activated by hydrophobic ligand molecules that can pass through the plasma membrane.
- Cell-surface receptors bind to an external ligand molecule and convert an extracellular signal into an intracellular signal.
- Three general categories of cell-surface receptors include: ion -channel, G- protein, and enzyme -linked protein receptors.
- Ion channel -linked receptors bind a ligand and open a channel through the membrane that allows specific ions to pass through.
- G-protein-linked receptors bind a ligand and activate a membrane protein called a G-protein, which then interacts with either an ion channel or an enzyme in the membrane.
- Enzyme-linked receptors are cell-surface receptors with intracellular domains that are associated with an enzyme.
Key Terms
- integral protein : a protein molecule (or assembly of proteins) that is permanently attached to the biological membrane
- transcription : the synthesis of RNA under the direction of DNA
EXAMPLES
Bacteria that are pathogenic to humans can release poisons that interrupt specific G-protein-linked receptor function, leading to illness. In cholera, the water-borne bacterium Vibrio cholerae produces a toxin, choleragen, that binds to cells lining the small intestine. The toxin then enters these intestinal cells, where it modifies a G-protein that controls the opening of a chloride channel and causes it to remain continuously active, resulting in large losses of fluids from the body that can lead to potentially fatal dehydration.
Receptors are protein molecules in the target cell or on its surface that bind ligands. There are two types of receptors: internal receptors and cell-surface receptors.
Internal receptors
Internal receptors, also known as intracellular or cytoplasmic receptors, are found in the cytoplasm of the cell and respond to hydrophobic ligand molecules that are able to travel across the plasma membrane. Once inside the cell, many of these molecules bind to proteins that act as regulators of mRNA synthesis to mediate gene expression. Gene expression is the cellular process of transforming the information in a cell’s DNA into a sequence of amino acids that ultimately forms a protein. When the ligand binds to the internal receptor, a conformational change exposes a DNA-binding site on the protein. The ligand-receptor complex moves into the nucleus, binds to specific regulatory regions of the chromosomal DNA, and promotes the initiation of transcription. Internal receptors can directly influence gene expression without having to pass the signal on to other receptors or messengers.
Intracellular Receptors : Hydrophobic signaling molecules typically diffuse across the plasma membrane and interact with intracellular receptors in the cytoplasm. Many intracellular receptors are transcription factors that interact with DNA in the nucleus and regulate gene expression.
Cell-Surface Receptors
Cell-surface receptors, also known as transmembrane receptors, are cell surface, membrane-anchored, or integral proteins that bind to external ligand molecules. This type of receptor spans the plasma membrane and performs signal transduction, converting an extracellular signal into an intracellular signal. Ligands that interact with cell-surface receptors do not have to enter the cell that they affect. Cell-surface receptors are also called cell-specific proteins or markers because they are specific to individual cell types.
Each cell-surface receptor has three main components: an external ligand-binding domain (extracellular domain), a hydrophobic membrane-spanning region, and an intracellular domain inside the cell. The size and extent of each of these domains vary widely, depending on the type of receptor.
Cell-surface receptors are involved in most of the signaling in multicellular organisms. There are three general categories of cell-surface receptors: ion channel-linked receptors, G-protein-linked receptors, and enzyme-linked receptors.
Ion Channel-Linked Receptors
Ion channel-linked receptors bind a ligand and open a channel through the membrane that allows specific ions to pass through. To form a channel, this type of cell-surface receptor has an extensive membrane-spanning region. In order to interact with the phospholipid fatty acid tails that form the center of the plasma membrane, many of the amino acids in the membrane-spanning region are hydrophobic in nature. Conversely, the amino acids that line the inside of the channel are hydrophilic to allow for the passage of water or ions. When a ligand binds to the extracellular region of the channel, there is a conformational change in the protein’s structure that allows ions such as sodium, calcium, magnesium, and hydrogen to pass through.
Gated-Ion Channels : Gated ion channels form a pore through the plasma membrane that opens when the signaling molecule binds. The open pore then allows ions to flow into or out of the cell.
G-Protein Linked Receptors
G-protein-linked receptors bind a ligand and activate a membrane protein called a G-protein. The activated G-protein then interacts with either an ion channel or an enzyme in the membrane. All G-protein-linked receptors have seven transmembrane domains, but each receptor has its own specific extracellular domain and G-protein-binding site.
Cell signaling using G-protein-linked receptors occurs as a cyclic series of events. Before the ligand binds, the inactive G-protein can bind to a newly-revealed site on the receptor specific for its binding. Once the G-protein binds to the receptor, the resultant shape change activates the G-protein, which releases GDP and picks up GTP. The subunits of the G-protein then split into the α subunit and the β subunit. One or both of these G-protein fragments may be able to activate other proteins as a result. Later, the GTP on the active α subunit of the G-protein is hydrolyzed to GDP and the β subunit is deactivated. The subunits reassociate to form the inactive G-protein, and the cycle starts over.
G-proteins : Heterotrimeric G proteins have three subunits: α, β, and γ. When a signaling molecule binds to a G-protein-coupled receptor in the plasma membrane, a GDP molecule associated with the α subunit is exchanged for GTP. The β and γ subunits dissociate from the α subunit, and a cellular response is triggered either by the α subunit or the dissociated β pair. Hydrolysis of GTP to GDP terminates the signal.
Enzyme-Linked Receptors
Enzyme-linked receptors are cell-surface receptors with intracellular domains that are associated with an enzyme. In some cases, the intracellular domain of the receptor itself is an enzyme or the enzyme-linked receptor has an intracellular domain that interacts directly with an enzyme. The enzyme-linked receptors normally have large extracellular and intracellular domains, but the membrane-spanning region consists of a single alpha-helical region of the peptide strand. When a ligand binds to the extracellular domain, a signal is transferred through the membrane and activates the enzyme, which sets off a chain of events within the cell that eventually leads to a response. An example of this type of enzyme-linked receptor is the tyrosine kinase receptor. The tyrosine kinase receptor transfers phosphate groups to tyrosine molecules. Signaling molecules bind to the extracellular domain of two nearby tyrosine kinase receptors, which then dimerize. Phosphates are then added to tyrosine residues on the intracellular domain of the receptors and can then transmit the signal to the next messenger within the cytoplasm.
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1.7: Dalton's Law
Skills to Develop
Make sure you thoroughly understand the following essential ideas which have been presented below.
- One mole of a gas occupies a volume of 22.4 L at STP (standard temperature and pressure, 273K, 1 atm = 103 kPa.)
- The above fact allows us to relate the measurable property of the density of a gas to its molar mass .
- The composition of a mixture of gases is commonly expressed in terms mole fractions ; be sure you know how to calculate them.
- Dalton's Law of partial pressures says that every gas in a mixture acts independently, so the total pressure a gas exerts against the walls of a container is just the sum of the partial pressures of the individual components.
Although all gases closely follow the ideal gas law PV = nRT under appropriate conditions, each gas is also a unique chemical substance consisting of molecular units that have definite masses. In this lesson we will see how these molecular masses affect the properties of gases that conform to the ideal gas law. Following this, we will look at gases that contain more than one kind of molecule— in other words, mixtures of gases. We begin with a review of molar volume and the E.V.E.N. principle, which is central to our understanding of gas mixtures.
The Molar Volume of a Gas
You will recall that the molar mass of a pure substance is the mass of 6.02 x 10 23 ( Avogadro's number ) of particles or molecular units of that substance. Molar masses are commonly expressed in units of grams per mole (g mol –1 ) and are often referred to as molecular weight s. As was explained in the preceding lesson, equal volumes of gases, measured at the same temperature and pressure, contain equal numbers of molecules (this is the "EVEN" principle , more formally known as Avogadro's law . ) Standard temperature and pressure: 273K, 1 atm
The magnitude of this volume will of course depend on the temperature and pressure, so as a means of convenient comparison it is customary to define a set of conditions T = 273 K and P = 1 atm as standard temperature and pressure , usually denoted as STP . Substituting these values into the ideal gas equation of state and solving for V yields a volume of 22.414 liters for 1 mole.
Example \(\PageIndex{1}\)
What would the volume of one mole of air be at 20°C on top of Mauna Kea, Haw'aii (altitude 4.2 km; click on picture for enlarged view ) where the air pressure is approximately 60 kPa?
SOLUTION
Apply Boyle's and Charles' laws as successive correction factors to the standard sea-level pressure of 101.3 kPa:
The standard molar volume 22.4 L mol –1 is a value worth memorizing, but remember that it is valid only at STP. The molar volume at other temperatures and pressures can easily be found by simple proportion. The molar volume of a substance can tell us something about how much space each molecule occupies, as the following example shows.
Example \(\PageIndex{2}\)
Estimate the average distance between the molecules in a gas at 1 atm pressure and 0°C.
SOLUTION
Consider a 1-cm 3 volume of the gas, which will contain
\[\dfrac{6.02 \times 10^{23} \;mol^{–1}}{22,400\; cm^3 \;mol^{–1}} = 2.69 \times 10^{19} cm^{-3}\]
The volume per molecule (not the same as the volume of a molecule, which for an ideal gas is zero!) is just the reciprocal of this, or 3.72E–20 cm 3 . Assume that the molecules are evenly distributed so that each occupies an imaginary box having this volume. The average distance between the centers of the molecules will be defined by the length of this box, which is the cube root of the volume per molecule:
(3.72 × 10 –20 ) 1/3 = 3.38 × 10 –7 cm = 3.4 nm
Under conditions at which the ideal gas model is applicable (that is, almost always unless you are a chemical engineer dealing with high pressures), "a molecule is a molecule", so the volume of Avogadro's number of molecules will be independent of the composition of the gas. The reason, of course, is that the volume of the gas is mostly empty space; the volumes of the molecules themselves are negligible.
Molar Mass and Density of a Gas
The molecular weight (molar mass) of any gas is the mass, expressed in grams, of Avogadro's number of its molecules. This is true regardless of whether the gas is composed of one molecular species or is a mixture. For a mixture of gases, the molar mass will depend on the molar masses of its components, and on the fractional abundance of each kind of molecule in the mixture. The term "average molecular weight" is often used to describe the molar mass of a gas mixture.
The average molar mass (\(\bar{m}\)) of a mixture of gases is just the sum of the mole fractions of each gas, multiplied by the molar mass of that substance:
\[\bar{m}=\sum_i \chi_im_i\]
Example \(\PageIndex{3}\)
Find the average molar mass of dry air whose volume-composition is O 2 (21%), N 2 (78%) and Ar (1%).
SOLUTION
The average molecular weight is the mole-fraction-weighted sum of the molecular weights of its components. The mole fractions, of course, are the same as the volume-fractions (E.V.E.N. principle.)
m = (0.21 x 32) + (0.78 x 28) + (0.01 x 20) = 28
The molar volumes of all gases are the same when measured at the same temperature and pressure. However, the molar masses of different gases will vary. This means that different gases will have different densities (different masses per unit volume). If we know the molecular weight of a gas, we can calculate its density.
Example \(\PageIndex{4}\)
Uranium hexafluoride UF 6 gas is used in the isotopic enrichment of natural uranium. Calculate its density at STP.
SOLUTION
The molecular weight of UF 6 is 352.
\[\dfrac{352\; g \;mol^{–1}}{22.4\, L\, mol^{–1}} = 15.7\; g\; L^{–1}\]
Note: there is no need to look up a "formula" for this calculation; simply combine the molar mass and molar volume in such a way as to make the units come out correctly.
More importantly, if we can measure the density of an unknown gas, we have a convenient means of estimating its molecular weight. This is one of many important examples of how a macroscopic measurement (one made on bulk matter) can yield microscopic information (that is, about molecular-scale objects.)
Gas densities are now measured in industry by electro-mechanical devices such as vibrating reeds which can provide continuous, on-line records at specific locations, as within pipelines. Determination of the molecular weight of a gas from its density is known as the Dumas method , after the French chemist Jean Dumas (1800-1840) who developed it. One simply measures the weight of a known volume of gas and converts this volume to its STP equivalent, using Boyle's and Charles' laws. The weight of the gas divided by its STP volume yields the density of the gas, and the density multiplied by 22.4 mol –1 gives the molecular weight. Pay careful attention to the examples of gas density calculations shown here and in your textbook. You will be expected to carry out calculations of this kind, converting between molecular weight and gas density.
Example \(\PageIndex{5}\)
Calculate the approximate molar mass of a gas whose measured density is 3.33 g/L at 30°C and 780 torr.
SOLUTION
Find the volume that would be occupied by 1 L of the gas at STP; note that correcting to 273 K will reduce the volume, while correcting to 1 atm (760 torr) will increase it:
The number of moles of gas is n = (.924 L) ÷ (22.4 L mol –1 ) = 0.0412 mol
The molecular weight is therefore (33 g L –1 ) ÷ (.0412 mol L –1 ) = 80.7 g mol –1
Density of a Gas Mixture
Gas density measurements can be a useful means of estimating the composition of a mixture of two different gases; this is widely done in industrial chemistry operations in which the compositions of gas streams must be monitored continuously.
Example \(\PageIndex{6}\)
Find the composition of a mixture of CO 2 (44 g/mol) and methane CH 4 (16 g/mol) that has a STP density of 1.214 g/L.
SOLUTION
The density of a mixture of these two gases will be directly proportional to its composition, varying between that of pure methane and pure CO 2 . We begin by finding these two densities:
For CO 2 :
(44 g/mol) ÷ (22.4 L/mol) = 1.964 g/L
For CH 4 :
(16 g/mol) ÷ (22.4 L/mol) = 0.714 g/L
If x is the mole fraction of CO 2 and (1– x ) is the mole fraction of CH 4 , we can write
1.964 x + 0.714 (1–x) = 1.214
(Does this make sense? Notice that if x = 0, the density would be that of pure CH 4 , while if it were 1, it would be that of pure CO 2 .)
Expanding the above equation and solving for x yields the mole fractions of 0.40 for CO 2 and 0.60 for CH 4 .
Expressing the Composition of a Gas Mixture
Because most of the volume occupied by a gas consists of empty space, there is nothing to prevent two or more kinds of gases from occupying the same volume. Homogeneous mixtures of this kind are generally known as solutions , but it is customary to refer to them simply as gaseous mixtures . We can specify the composition of gaseous mixtures in many different ways, but the most common ones are by volumes and by mole fractions .
Volume Fractions
From Avogadro's Law we know that "equal volumes contains equal numbers of molecules". This means that the volumes of gases, unlike those of solids and liquids, are additive. So if a partitioned container has two volumes of gas A in one section and one mole of gas B in the other (both at the same temperature and pressure), and we remove the partition, the volume remains unchanged.
We can specify the composition of this mixture by saying that the volume fraction of A is 1/3 and that of B is 2/3.
Volume fractions are often called partial volumes:
\[V_i = \dfrac{v_i}{\sum_v_i}\]
Don't let this type of notation put you off! The summation sign Σ (Greek Sigma) simply means to add up the v 's (volumes) of every gas. Thus if Gas A is the " i -th" substance as in the expression immediately above, the summation runs from i =1 through i =2. Note that we can employ partial volumes to specify the composition of a mixture even if it had never actually been made by combining the pure gases.
When we say that air, for example, is 21 percent oxygen and 78 percent nitrogen by volume, this is the same as saying that these same percentages of the molecules in air consist of O 2 and N 2 . Similarly, in 1.0 mole of air, there is 0.21 mol of O 2 and 0.78 mol of N 2 (the other 0.1 mole consists of various trace gases, but is mostly neon.) Note that you could never assume a similar equivalence with mixtures of liquids or solids, to which the E.V.E.N. principle does not apply.
Mole Fractions
These last two numbers (0.21 and 0.78) also express the mole fractions of oxygen and nitrogen in air. Mole fraction means exactly what it says: the fraction of the molecules that consist of a specific substance. This is expressed algebraically by
\[X_i = \dfrac{n_i}{\sum_i n_i}\]
so in the case of oxygen in the air, its mole fraction is
\[ X_{O_2} = \dfrac{n_{O_2}}{n_{O_2}+n_{N_2}+n_{Ar}}= \dfrac{0.21}{1}=0.21\]
Example \(\PageIndex{7}\)
A mixture of \(O_2\) and nitrous oxide, \(N_2O\), is sometimes used as a mild anesthetic in dental surgery. A certain mixture of these gases has a density of 1.482 g L –1 at 25 and 0.980 atm. What was the mole-percent of \(N_2O\) in this mixture?
SOLUTION
First, find the density the gas would have at STP:
The molar mass of the mixture is (1.65 g L –1 )(22.4 L mol –1 ) = 37.0 g mol –1 . The molecular weights of \(O_2\) and \(N_2\) are 32 and 44, respectively. 37.0 is 5/12 of the difference between the molar masses of the two pure gases. Since the density of a gas mixture is directly proportional to its average molar mass, the mole fraction of the heavier gas in the mixture is also 5/12:
\[\dfrac{37-32}{44-32}=\dfrac{5}{12}=0.42\]
Example \(\PageIndex{8}\)
What is the mole fraction of carbon dioxide in a mixture consisting of equal masses of CO 2 (MW=44) and neon (MW=20.2)?
SOLUTION
Assume any arbitrary mass, such as 100 g, find the equivalent numbers of moles of each gas, and then substitute into the definition of mole fraction:
n CO2 = (100 g) ÷ (44 g mol –1 ) = 2.3 mol
n Ne = (100 g) ÷ (20.2 g mol –1 ) = 4.9 mol
X Ne = (2.3 mol) ÷ (2.3 mol + 4.9 mol) = 0.32
Dalton's Law of Partial Pressures
The ideal gas equation of state applies to mixtures just as to pure gases. It was in fact with a gas mixture, ordinary air, that Boyle, Gay-Lussac and Charles did their early experiments. The only new concept we need in order to deal with gas mixtures is the partial pressure , a concept invented by the famous English chemist John Dalton (1766-1844). Dalton reasoned that the low density and high compressibility of gases indicates that they consist mostly of empty space; from this it follows that when two or more different gases occupy the same volume, they behave entirely independently.
The contribution that each component of a gaseous mixture makes to the total pressure of the gas is known as the partial pressure of that gas. Dalton himself stated this law in the simple and vivid way shown at the left.
The usual way of stating Dalton's Law of Partial Pressures is
The total pressure of a gas is the sum of the partial pressures of its components
which is expressed algebraically as
\[P_{total}=P_1+P_2+P_3 ... = \sum_i P_i\]
or, equivalently
\[ P_{total} = \dfrac{RT}{V} \sum_i n_i\]
There is also a similar relationship based on volume fractions , known as Amagat's law of partial volumes . It is exactly analogous to Dalton's law, in that it states that the total volume of a mixture is just the sum of the partial volumes of its components. But there are two important differences: Amagat's law holds only for ideal gases which must all be at the same temperature and pressure. Dalton's law has neither of these restrictions. Although Amagat's law seems intuitively obvious, it sometimes proves useful in chemical engineering applications. We will make no use of it in this course.
Example \(\PageIndex{9}\)
Calculate the mass of each component present in a mixture of fluorine (MW and xenon (MW 131.3) contained in a 2.0-L flask. The partial pressure of Xe is 350 torr and the total pressure is 724 torr at 25°C.
SOLUTION
From Dalton's law, the partial pressure of F 2 is (724 – 350) = 374 torr:
The mole fractions are X Xe = 350/724 = .48 and X F2 = 374/724 = 0.52 . The total number of moles of gas is
The mass of \(Xe\) is (131.3 g mol –1 ) × (0.48 × 0.078 mol) = 4.9 g
Example \(\PageIndex{10}\)
Three flasks having different volumes and containing different gases at various pressures are connected by stopcocks as shown. When the stopcocks are opened,
- What will be the pressure in the system?
- Which gas will be most abundant in the mixture?
Assume that the temperature is uniform and that the volume of the connecting tubes is negligible.
SOLUTION
The trick here is to note that the total number of moles n T and the temperature remain unchanged, so we can make use of Boyle's law PV = constant. We will work out the details for CO 2 only, denoted by subscripts a.
For CO 2 ,
P a V a = (2.13 atm)(1.50 L) = 3.19 L-atm.
Adding the PV products for each separate container, we obtain
Σ P i V i = 6.36 L-atm = n T RT .
We will call this sum P 1 V 1 . After the stopcocks have been opened and the gases mix, the new conditions are denoted by P 2 V 2 .
From Boyle's law,
P 1 V 1 = P 2 V 2 = 6.36 L-atm . V 2 = Σ V i = 4.50 L.
Solving for the final pressure P 2 we obtain (6.36 L-atm)/(4.50 L) = 1.41 atm .
For part (b) , note that the number of moles of each gas is n = PV/RT . The mole fraction if any one gas is X i = n i / n T . For CO 2 , this works out to (3.19/ RT ) / (6.36/ RT ) = 0.501. Because this exceeds 0.5, we know that this is the most abundant gas in the final mixture.
Application of Dalton's Law: Collecting Gases over Water
A common laboratory method of collecting the gaseous product of a chemical reaction is to conduct it into an inverted tube or bottle filled with water, the opening of which is immersed in a larger container of water. This arrangement is called a pneumatic trough , and was widely used in the early days of chemistry. As the gas enters the bottle it displaces the water and becomes trapped in the upper part.
The volume of the gas can be observed by means of a calibrated scale on the bottle, but what about its pressure? The total pressure confining the gas is just that of the atmosphere transmitting its force through the water. (An exact calculation would also have to take into account the height of the water column in the inverted tube.) But liquid water itself is always in equilibrium with its vapor, so the space in the top of the tube is a mixture of two gases: the gas being collected, and gaseous H 2 O. The partial pressure of H 2 O is known as the vapor pressure of water and it depends on the temperature. In order to determine the quantity of gas we have collected, we must use Dalton's Law to find the partial pressure of that gas.
Example \(\PageIndex{11}\)
Oxygen gas was collected over water as shown above. The atmospheric pressure was 754 torr, the temperature was 22°C, and the volume of the gas was 155 mL. The vapor pressure of water at 22°C is 19.8 torr. Use this information to estimate the number of moles of \(O_2\) produced.
SOLUTION
From Dalton's law, \(P_{O_2} = P_{total} – P_{H_2O} = 754 – 19.8 = 734 \; torr = 0.966\; atm\).
Application of Dalton's Law: Scuba diving
Our respiratory systems are designed to maintain the proper oxygen concentration in the blood when the partial pressure of O 2 is 0.21 atm, its normal sea-level value. Below the water surface, the pressure increases by 1 atm for each 10.3 m increase in depth; thus a scuba diver at 10.3 m experiences a total of 2 atm pressure pressing on the body. In order to prevent the lungs from collapsing, the air the diver breathes should also be at about the same pressure.
Figure
But at a total pressure of 2 atm, the partial pressure of \(O_2\) in ordinary air would be 0.42 atm; at a depth of 100 ft (about 30 m), the \(O_2\) pressure of .8 atm would be far too high for health. For this reason, the air mixture in the pressurized tanks that scuba divers wear must contain a smaller fraction of \(O_2\). This can be achieved most simply by raising the nitrogen content, but high partial pressures of N 2 can also be dangerous, resulting in a condition known as nitrogen narcosis. The preferred diluting agent for sustained deep diving is helium, which has very little tendency to dissolve in the blood even at high pressures.


4.8: Establishing Trademark Protection
After completing this section, you will be able to
- Identify the reasons for establishing trademark registration.
- Understand the process of trademark protection.
Establishing Your Trademark Protection
Before reading this section, please watch the overview video below covering the “spectrum of distinctiveness” and other fancy-sounding legal terms and what they really mean in the real world of commerce and consumerism.
As in the case with copyrights, trademarks do not necessarily have to be registered with the federal government, but doing so has benefits. The owners of unregistered trademarks have the exclusive right to use the mark concerning similar goods and services in the geographic area of actual use of the mark, the right to bring civil action against infringers, and protection against false advertising. Unregistered trademarks are usually identified by the “TM” symbol displayed on the product, package, or advertising used to promote them. Trademarks formally registered with the USPTO, however, receive additional benefits:
- A legal presumption of ownership of the mark and exclusive right to use the mark nationwide on or in connection with the goods/services listed in the registration.
- Public notice of claim of ownership of the mark.
- The ability to bring an action concerning the mark in federal court.
- The use of the U.S. registration as a basis to obtain registration in foreign countries.
- The ability to record the U.S. registration with the U.S. Customs and Border Protection (CBP) Service to prevent importation of infringing foreign goods.
- The right to use the federal registration symbol ®
- Listing in the United States Patent and Trademark Office’s online databases. xxxv
Because registration costs money, many small businesses choose to rely upon the common law protections afforded trademarks, especially when just starting up. A case in point was Google, which used an unregistered trademark for its first six years in operation. Only in 2006 did the company formally apply for a registered trademark for “Google.” It was registered in 2012.
But trademark protection can be vital to a small business, as one recent case amply demonstrates. Payam “Peter” Tabibian first registered the 1950s-style red, white, and yellow logo for his start-up Z-Burger chain in 2007, a few months before he opened his first restaurant the next year in a hip Washington neighborhood. As the New York Times reported, “his first restaurant was an immediate hit, attracting students from nearby American University. The place [later] drew public praise when it gave free food to federal workers who were furloughed from their jobs during government budget cutbacks.”
But Mr. Tabibian eventually fell out with his partners, who then tried to stop him from continuing to use his Z-Burger brand with his expanding chain of restaurants; they also demanded he transfer the trademarks to them.
But because Mr. Tabibian had done his homework and taken the time to properly register his trademarks, a federal judge ruled in August of 2015 that he was the legitimate owner of the trademarks and could continue to use them.
As James Gibson, law professor at the University of Richmond School of Law, told the New York Times , the Z-Burger case shows why “it is very important early on to pick a trademark that’s going to work, and make sure ownership is sewn on. That’s particularly true if nobody knows who you are and you’re operating in a limited area. The federal trademark gives you a lot of nationwide rights.”
In order for your trademark to be eligible for registration with the USPTO, however, you must actually use it in conjunction with commercial activity—i.e., with the marketing and sale of products and services—or be about to use it within six months. Absent the selling of athletic shoes and other sports attire, Nike’s $20 billion “Swoosh” logo would be nothing more than a worthless doodle.
When applying for trademark registration, the applicant must file an affidavit attesting to the date the mark was first used in commerce as well as a specimen showing how the mark was first used, whether in advertising or on the product in a store setting. It is imperative that the applicant identify the earliest provable date of first use in commerce, to lessen the likelihood that another party can claim prior use of that mark and invalidate the trademark.
The USPTO also offers an “intent-to-use” application, which allows an entity to apply for a trademark that is not yet used in commerce.
“If you have not yet used the mark but plan to do so in the future, you may file based on a good faith or bona fide intent to use the mark in commerce,” notes a USPTO publication. “A bona fide intent to use the mark is more than an idea, [but] less than market ready. For example, having a business plan, creating sample products, or performing other initial business activities may reflect a bona fide intent to use the mark.” xxxvi
The mark must then be put into use within six months of receiving a “notice of allowance” from the USPTO or the applicant risks having to pay extension fees or losing the mark entirely.
If the trademark is still in commercial use five years after registration, the owner is eligible to receive an additional protection known as “incontestability,” which immunizes the mark from many challenges, including challenges to validity, ownership, registration, and descriptiveness. (Incontestable marks can still be challenged on some grounds, such as genericism, functionality, and abandonment.) To receive incontestability status, a § 15 Declaration must be submitted to the USPTO.
Once incontestability is achieved, no one can contest the validity, ownership, or registration of the mark, nor can anyone contest the owner’s exclusive right to use the mark. An individual or a corporate entity can register a mark.
A trademark can be assigned to others in the event of purchase or acquisition by another entity.
The §15 Declaration must include:
- The registration number and the date of registration.
- The fee for each class of goods/services in the registration to which the Declaration pertains.
- A statement that declares: -The mark has been in continuous use in commerce for a period of five years and is still in use in commerce -No final decision exists adverse to the owner’s claim of ownership of the mark for the goods/services, or to the owner’s right to register the mark or to keep the same on the register -No pending proceeding exists involving the claimed rights in the USPTO or in the courts
- A signed and dated affidavit or declaration under 37 C.F.R. §2.20 xxxvii
There are other reasons why an owner might assign trademarks to another party, including a business name change, a security agreement, a license, a lien, as collateral for a loan, or as a result of a bankruptcy procedure. Ford used its trademarks as collateral for a $23.5 billion loan. Ford was still able to use its trademarks, but if the company had defaulted on the loan, the trademarks would have been assigned to the lender. xxxviii
Just like tangible assets, trademarks and other intellectual property such as patents and copyrights often have enormous value. In fact, some sources estimate that in contrast to 40 years ago, when plant, equipment, and other tangible assets comprised 80 percent of the market value of most public companies, today it is intangible assets like intellectual property, business methods, and know-how that make up roughly 80 percent of the value of public companies. xxxix
Trademarks can also be licensed to others. In 2012, licensed trademarks generated $5.45 billion for North American owners, reported the Licensing Industry Merchandisers’ Association. That same year, the top 150 global brand licensors earned $230 billion in sales of trademarked products, with the Walt Disney Company alone accounting for nearly $40 billion in sales.
Abandonment of a mark results in loss of ownership and the associated rights of the mark. For a mark to be considered abandoned, it must be discontinued from active use in commerce with no intent to resume the commercial use of the mark. Evidence of nonuse for three consecutive years is usually considered to be sufficient proof of abandonment. Upon abandonment, the trademark owner loses the right to prevent others from infringing the mark.
Footnotes
- xxxv Derived from: http://www.uspto.gov/faq/trademarks.jsp#_Toc275426681
- xxxvi Protecting Your Trademark: Basic Facts About Trademarks , U.S. Patent and Trademark Office, derived from: http://www.uspto.gov/trademarks/basics/BasicFacts.pdf
- xxxvii United States Patent and Trademark Office. (21 August, 2012). Maintain/Renew a Registration: How to Keep a Registration Alive . Retrieved from http://www.uspto.gov/trademarks/proc...tain/prfaq.jsp
- xxxviii CBS News. (23 May, 2012). Ford Regains Assets, Including Blue Logo, After Credit Upgrade . Retrieved from http://www.cbsnews.com/8301-505164_1...redit-upgrade/
- xxxix “Intangible Asset Market Value,” Ocean Tomo, Retrieved from: http://bit.ly/1gldnWL


6.3: §47. The Latin suffix -ITUDO (> E -itude)
Although -itudo is a less productive Latin noun-forming suffix than -itas , it has exactly the same function and meaning. There appears to be no logical reason why the Latin language attached -itas to some adjectives and -itudo to others. You will easily recognize -itudo as the source of English nouns that end in -itude . Many of these have come directly from Latin, and others through French; a few are modern coinages on the analogy of those older forms. Again, the examples speak for themselves:
| L | gratus (“thankful”) | > | gratitudo (“thankfulness”) | > | E | gratitude |
| latus (“wide”) | > | latitudo (“width”) | > | latitude | ||
| longus (“long”) | > | longitudo (“length”) | > | longitude | ||
| altus (“high”) | > | altitudo (“height”) | > | altitude | ||
| magnus (“great”) | > | magnitudo (“greatness”) | > | magnitude | ||
| solus (“alone”) | > | solitudo (“loneliness”) | > | solitude | ||
| fortis (“strong”) | > | fortitudo (“strength”) | > | fortitude | ||
| similis (“like”) | > | similitudo (“likeness”) | > | similitude |
Sometimes this suffix could be attached to a part of speech other than an adjective. The noun servus (“slave”) gave rise to the abstract noun servitudo (“slavery”) > E servitude . There is an odd-looking Latin adverb vicissim , that means “in turn”; this produced the Latin noun vicissitudo and the wonderful English word vicissitude , which is applied to the alternating turns of human fortune. Plenitude is a learned synonym for “fullness,” and is derived regularly from Latin plenitudo < plenus (“full”). It is also the trademark for a facial cream (to get that full-fed appearance?). In later antiquity, there was a variant noun form plenitas , which is the origin of E plenty (as modified by French). A declining awareness of Latin in our own day is perhaps rendering obsolete such English words as rectitude (“uprightness”), pulchritude (“beauty”), and lassitude (“weariness”)—though teachers can still be dismissed for moral turpitude (“foulness of character”). One polysyllabic Latin derivative is still widely used and understood, however; that is the compound noun verisimilitude , from ver-i-simil-itudo (“likeness to the truth”).


3.7.11: Medicare
Medicare specifically covers healthcare for people over the age of 65. Originally it provided only hospital insurance (part A) and medical insurance (part B). Medicare Advantage plans now allow private insurance to supplement coverage (called Part C), and since 2003, drug costs are now covered (with Part D). To fund this program, workers pay medicare taxes, and those who may not have paid enough medicare taxes over their working years will pay premiums while using Medicare insurance once they retire. Additionally, Medicare only assists with paying for healthcare costs, they are not covered entirely. There are still deductibles, co-insurance and copayments for many healthcare services. However, some expenses like drug costs can be kept significantly lower (for both Medicare and Medicaid), due to government mandated negotiations with pharmaceutical companies.


3.3: The Italian Renaissance
- Understand how the Italian Rennaisance affected the progression of management theory.
In the 11th, 12th, and 13th centuries, Europeans went on a series of military expeditions to recover the Holy Land from the Muslims. These expeditions, called the Crusades, brought wealth and technological advances into Europe from the Muslim world. 8
In the 14th century, a movement of cultural change and astounding achievements in all spheres of life began in northern Italy. The Italian Renaissance saw the reintroduction of classical knowledge and the emergence of new knowledge and learning, much of which had economic and business implications. The emergence of the basic printing press allowed for these ideas and knowledge to spread throughout Europe. The combination of these factors led to the creation of new wealth as a new emphasis on trade and wealth creation developed. In Italy, we see the emergence of modern enterprise and the emergence of the need for people to run these new enterprises. As Muldoon and Marin 9 write:
Their industrious countrymen were improving mining operations and developing the shipping and banking industries, which created the underlying conditions for the migration of the Italian Renaissance’s commercial and intellectual culture from its native Italian soil (Haynes, 1991). The increasing scope and complexity of these commercial activities may well have prompted such inventions as double-entry bookkeeping and motivated companies to hire business managers to coordinate and direct their operations (Witzel, 2002).
Organizations called corporations developed to carry out these commercial activities, not only within a country, but among many countries. The first multinational corporations were located in Italy but had branches across Europe. The Florence Company of Bardi was a multinational bank that provided loans to various kings, including Edward III of England. 10 As their commercial enterprises flourished, the Italians provided manuals for merchants, which spread the ideas of commerce throughout Europe.
- What was the Italian Renaissance?
- What managerial legacy did it leave?
References
8. Ruggiero, Guido. The Renaissance in Italy: A Social and Cultural History of the Rinascimento (Cambridge University Press, 2015).
9. Muldoon, J., & Marin, D. B. (2012). John Florio and the introduction of management into the English vocabulary. Journal of Management History, 18(2), 129-136.
10. Haynes, M.S. (1991), The Italian Renaissance and Its Influence on Western Civilization, University Press of America, New York, NY.


7.2: What Is a Fluid?
Learning Objectives
- State the common phases of matter.
- Explain the physical characteristics of solids, liquids, and gases.
- Describe the arrangement of atoms in solids, liquids, and gases.
Matter most commonly exists as a solid, liquid, or gas; these states are known as the three common phases of matter . Solids have a definite shape and a specific volume, liquids have a definite volume but their shape changes depending on the container in which they are held, and gases have neither a definite shape nor a specific volume as their molecules move to fill the container in which they are held. (See Figure \(\PageIndex{1}\).) Liquids and gases are considered to be fluids because they yield to shearing forces, whereas solids resist them. Note that the extent to which fluids yield to shearing forces (and hence flow easily and quickly) depends on a quantity called the viscosity. We can understand the phases of matter and what constitutes a fluid by considering the forces between atoms that make up matter in the three phases.
Atoms in solids are in close contact, with forces between them that allow the atoms to vibrate but not to change positions with neighboring atoms. (These forces can be thought of as springs that can be stretched or compressed, but not easily broken.) Thus a solid resists all types of stress. A solid cannot be easily deformed because the atoms that make up the solid are not able to move about freely. Solids also resist compression, because their atoms form part of a lattice structure in which the atoms are a relatively fixed distance apart. Under compression, the atoms would be forced into one another. Most of the examples we have studied so far have involved solid objects which deform very little when stressed.
CONNECTIONS: SUBMICROSCOPIC EXPLANATION OF SOLIDS AND LIQUIDS
Atomic and molecular characteristics explain and underlie the macroscopic characteristics of solids and fluids. This present section is devoted entirely to the submicroscopic explanation of solids and liquids.
In contrast, liquids deform easily when stressed and do not spring back to their original shape once the force is removed because the atoms are free to slide about and change neighbors—that is, they flow (so they are a type of fluid), with the molecules held together by their mutual attraction. When a liquid is placed in a container with no lid on, it remains in the container (providing the container has no holes below the surface of the liquid!). Because the atoms are closely packed, liquids, like solids, resist compression.
Atoms in gases are separated by distances that are large compared with the size of the atoms. The forces between gas atoms are therefore very weak, except when the atoms collide with one another. Gases thus not only flow (and are therefore considered to be fluids) but they are relatively easy to compress because there is much space and little force between atoms. When placed in an open container gases, unlike liquids, will escape. The major distinction is that gases are easily compressed, whereas liquids are not. We shall generally refer to both gases and liquids simply as fluids , and make a distinction between them only when they behave differently.
Section Summary
- A fluid is a state of matter that yields to sideways or shearing forces. Liquids and gases are both fluids. Fluid statics is the physics of stationary fluids.
Glossary
- fluids
- liquids and gases; a fluid is a state of matter that yields to shearing forces


11.6: Monopoly in Public Policy
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Social Impacts of Monopoly
A monopoly can diminish consumer choice, reduce incentives to innovate, and control supply to enforce inequitable prices in a society.
learning objectives
- Outline the effect of a monopoly on producer, consumer, and total surplus
The Value of Competition
To understand why trends towards consolidation are so dangerous it is useful to frame why competition is of such critical value to equitable markets, particular from a consumer perspective. In a perfectly competitive market, the antithesis of a monopoly, demand is completely elastic and the production quantity and price point align perfectly with marginal costs and actual costs. This allows for revenues, costs, price, and quantity to achieve a balance where the consumer is provided with the optimal amount of a good at the most equitable price.
Perfect Competition Economics : This is a graphical illustration of economics within the context of a perfectly competitive market (theoretically). Note that the overall returns derived, costs incurred, quantity produced, and price point all align perfectly to generate an equitable market position. While this is an idealistic representation of markets, it is useful as a frame of reference to identify departures from ideal competitive circumstances.
However, perfect competition is more of a theoretical competitive framework because markets will naturally deviate to varying degrees (in order to capture profitable returns). As such, the perfect competition model is most useful in identifying and measuring deviations or departures from the competitive ideal. The farther an industry or market moves from a perfectly competitive model the more value is potentially migrating from the consumers to the suppliers. In order to ensure that suppliers do not take on too much power (such as the case of monopolies and oligopolies), government regulations and antitrust laws are a necessary component of the economic perspective.
Societal Risks of Monopolies
The accumulation of power and leverage on behalf of the suppliers largely revolves around the fact that monopolies can ultimately control supply in its entirety for a specified product or service. Through utilizing this control strategically, a profit-maximizing monopoly could create the following societal risks:
- Price Discrimination: This concept is often strongly emphasized as a potential economic risk of monopolies and the economic justification is easily illustrated. Picture a supply and demand chart, where supply and demand intersect to generate a fair price point and overall quantity provided. Now assume one company has the entire supply under it’s control, and can discriminate prices along the demand curve to capture higher prices than the available supply should allow. This allows monopolies to charge customers with a higher willingness to pay a higher price, while still charging consumers with a lower willingness to pay the standard prices. This is unfair to consumers, who will be forced to pay whatever is asked as a result of no alternative options.
- Reduced Efficiency: A less direct societal risk of monopolies is the fact that competition is closely linked to incentives. As a result, no competition will provide the monopoly very little reason to improve internal inefficiencies or cut costs. A competitive market will see constant strives to reduce costs in order to capture higher market share and provide goods at lower prices, while monopolies do not have this incentive.
- Reduced Innovation: A monopoly will also have limited motivation to innovate, as there is little value in differentiation in a thoroughly controlled market (for the only incumbent). As a result there is reduced improvements that could substantially improve the ability of the firm to fulfill the needs of the consumer.
- Deadweight Loss: A monopoly will choose to produce less and charge more than would occur in a perfectly competitive market. As a result, a monopoly causes deadweight loss, an inefficient economic outcome.
In summarizing these various societal drawbacks, monopolies pose the risk of reducing consumer choice and consumer power to incentivize companies to innovate and reduce costs, as there is limited prospective returns on investment. A monopoly with total control over the supply can charge any price that the consumer is willing to pay, and therefore can generate excessive margins while doing very little to improve their product/service or relevant processes.
Antitrust Laws
Antitrust laws ensure that competitive environments are preserved in order to maintain an efficient and equitable capitalistic system.
learning objectives
- Discuss antitrust laws aimed to improve competition and prevent monopolies from becoming more powerful
Antitrust laws perform the critical task of ensuring that competitive environments are preserved in order to maintain an efficient and equitable capitalistic system for firms to operate in. The concept of antitrust largely revolves around governmental restrictions that limit incumbents in any given industry from consolidating too much power.
The worst case scenario of consolidation results in a monopoly, which is when one company or organization becomes the sole supplier of a given product or service. In such a situation it is relatively easy for that provider to erect barriers to entry for new entrants and dictate price points through manipulating the supply. The adverse effects of these manipulations can be seen in, which underlines the economic threat monopolies pose the end consumer. Antitrust law is in place to ensure such circumstances do not arise, or when they do that they are regulated appropriate to minimize adverse societal effects.
Regulating Competition
The regulation of competitive markets has roots as far back as the Roman Empire, resulting in increasingly complex models as capitalism has evolved over time. Indeed, due to the increasingly international focus for many large corporations, antitrust laws and other competitive regulations must function not only at the country level but on a global level. Organizations such as the World Trade Organization (WTO) attempt to garner international support for the establishment of global standards in competitive markets in conjunction with the internal competitive laws which govern each nation individually. While these antitrust laws differ from nation to nation, they can loosely be summarized in three components:
- Actively ensuring that no agreements in place are counter to a competitive market. This revolves largely around avoiding cartels, or collaboration between the big players which would allow for market manipulation.
- Regulating against strategic actions that may result in diminishing the competitive elements of a market. This is usually targeted at dominate players in an industry, who may have a tendency to price gauge or other manipulations.
- Overseeing mergers, acquisitions, joint ventures and other strategic alliances to avoid consolidation that may be damaging to free markets.
Relevant Statutes
European Union (EU) – In the EU, competition law began in 1951 with the European Coal and Steel Community (ECSC), which included France, Italy, Belgium and the Netherlands. The purpose of this was to reduce the ability for one country/region to gain a monopoly on critical natural resources. Shortly after, in 1957, the European Economic Community (ECC) was established as a part of the Treaty of Rome. This document enacted provisions to eliminate anti-competitive agreements. This was more recently updated via the Treaty of Lisbon, which further addresses mergers and acquisitions and bans price fixing and collusion.
United States (U.S.) – In the U.S., antitrust policy finds its roots in 1890 with the Sherman Antitrust Act. While the basic premise was the same as modern day competitive law, it was fairly rudimentary in scale and scope. The Sherman Act dealt with avoiding or limiting the power of trusts, or essentially the creation of price-controlling cartels. This act was expanded upon in 1914, with two more competitive laws: The Clayton Antitrust Act and the Federal Trade Commission Act. Both of these acts sought to organize a governmental body equipped to protect consumers from unfair competitive practices.
Regulation of Natural Monopoly
Natural monopolies are conducive to industries where the largest supplier derives cost advantages and must be regulated to minimize risks.
learning objectives
- Discuss the reasons for government regulation of monopolies
A monopoly is a business or organization that maintains exclusivity of the supply of a particular product or service, and can evolve naturally or be designed specifically based on the nature of a particular market or industry. Monopolies on the whole are governed under antitrust laws, both on a national level in most countries and on an international level via institutions such as the World Trade Organization (WTO).
The evolution of a monopoly is a critical component in recognizing which industries are at high risk of monopolization, and how these risks may be realized operationally. A natural monopoly is defined by an incumbent in an industry where the largest supplier can theoretically create the lowest production prices, generally through economies of scale or economies of scope. In this type of circumstance, the industry naturally lends itself to providing advantages for the single largest provider at the cost of allowing for competitive forces. Natural monopolistic conditions are therefore at high risk of creating actual monopolies, and society benefits from regulating these situations to even the playing field.
Price Advantage for Natural Monopolies : While monopolies are generally poor economic constructs for creating value, natural monopolies are predicated on the fact that a single supplier can achieve the greatest economies of scale (cost advantages). This graph demonstrates this concept.
Regulating Natural Monopolies
The consolidation of an industry into one sole supplier can represent a substantial threat to free markets and their consumers, as price can be easily manipulated through a thorough control of the supply. As a result, monopolies are generally viewed as illegal entities. Regulating industries to minimize monopolization and maintain competitive equality can be pursued in a number of ways:
- Average cost pricing: As the name implies, this regulatory approach is defined as enforcing a price point for a given product or service that matches the overall costs incurred by the company producing or providing. This reduces the pricing flexibility of a company and ensures that the monopoly cannot capture margins above and beyond what is reasonable.
- Price ceiling: Another way a natural monopoly may be regulated is through the enforcement of a maximum potential price being charged. A price ceiling is a regulatory strategy of stating a specific product or service cannot be sold for above a certain price.
- Rate of return regulations: This is quite similar to average cost pricing, but deviates via allowing a model that can create consistent returns for the company involved. The percentage net profit brought in a by company must be below a government specified percentage to insure compliance with this regulatory approach (i.e. 5%).
- Tax or subsidy: The last way a governmental body can alleviate a natural monopoly is through higher taxes on larger players or subsidies for smaller players. In short, the government can provide financial support via subsidies to new entrants to ensure the competitive environment is more equitable.
As with most regulatory approaches, none of these are perfect solutions and consolidation within industries conducive to a natural monopoly will continue to arise. Antitrust laws and the careful control of mergers, acquisitions, joint ventures, and other strategic alliances are critical in the regulation of natural monopolies. In extreme circumstances it is also a viable option for governments to break up monopolies through the legal processes.
When A Monopoly Works
While the concept of a monopoly is generally perceived as a threat to free markets, there are specific circumstances where natural monopolies are either pragmatically useful (cost effective) or virtually unavoidable. In these circumstances the regulatory approaches above (price ceilings, average cost pricing, etc.) are even more critical to ensuring consumers are protected. AT&T is a classic example of a government-backed monopoly in the middle of the 20th century, as the fixed investment of land lines for phones at that time was substantial. It was not practical to foster competition as a result, and the government recognized the necessity for a monopoly (until 1984, when AT&T was divested).
Key Points
- In a perfectly competitive market, the antithesis of a monopoly, demand is completely elastic and the production quantity and price point align perfectly with marginal costs and actual costs.
- Perfect competition is a theoretical competitive framework. However, markets will naturally deviate to varying degrees (in order to capture profitable returns). As such, the perfect competition model is most useful in identifying and measuring deviations or departures from the competitive ideal.
- The accumulation of power and leverage on behalf of the suppliers largely revolves around the fact that monopolies can ultimately control supply in its entirety for a specified product or service.
- A monopoly with total control over the supply can charge any price that the consumer is willing to pay, and therefore can generate excessive margins while doing very little to improve their product/service or relevant processes.
- The concept of antitrust largely revolves around governmental restrictions that limit incumbents in any given industry from consolidating too much power.
- Organizations such as the World Trade Organization (WTO) attempt to garner international support for the establishment of global standards in competitive markets in conjunction with the internal competitive laws which govern each nation individually.
- In the U.S., antitrust policy finds its roots in 1890 with the Sherman Antitrust Act, and saw substantial expansion in 1914 via the Clayton Antitrust Act and the Federal Trade Commission Act.
- As capitalistic markets evolve they show some tendency towards consolidation, and this consolidation puts consumers at risk of hugely powerful corporate suppliers. Antitrust policy is designed to intervene on behalf of the consumer.
- As capitalistic markets evolve they show some tendency towards consolidation, and this consolidation puts consumers at risk of hugely powerful corporate suppliers. Antitrust policy is designed to intervene on behalf of the consumer.
- A natural monopoly is defined by an incumbent in an industry where the largest supplier can theoretically create the lowest production prices, generally through economies of scale or economies of scope.
- Natural monopolistic conditions are therefore at high risk of creating actual monopolies, and society benefits from regulating these situations to even the playing field.
- Regulating industries to minimize monopolization and maintain competitive equality can be pursued through average cost pricing, price ceilings, rate of return regulations, taxes and subsidies.
- While the concept of a monopoly is generally perceived as a threat to free markets, there are specific circumstances where natural monopolies are either pragmatically useful (cost effective) or virtually unavoidable.
Key Terms
- price discrimination : The practice of selling identical goods or services at different prices from the same provider.
- Antitrust : A law opposed to or against the establishment or existence of trusts (monopolies), usually referring to legislation.
- monopoly : A situation, by legal privilege or other agreement, in which solely one party (company, cartel etc. ) exclusively provides a particular product or service, dominating that market and generally exerting powerful control over it.
- consolidation : The combination of multiple businesses.
- economies of scale : The characteristics of a production process in which an increase in the scale of the firm causes a decrease in the long run average cost of each unit.
- subsidy : Government assistance to a business or economic sector.
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2.3: Group Activity
Read the following passage from Hesiod’s Works and Days , then, within your group, consider which two or three literary theories serve best to analyze the passage. Be prepared to explain your decision by connecting points of insight to examples from the text. If time allows, consider which literary theory doesn’t work well for analyzing the text, and explain why.
From Hesiod’s Works and Days
(ll. 109-120) First of all the deathless gods who dwell on Olympus made a golden race of mortal men who lived in the time of Kronos when he was reigning in heaven. And they lived like gods without sorrow of heart, remote and free from toil and grief: miserable age rested not on them; but with legs and arms never failing they made merry with feasting beyond the reach of all evils. When they died, it was as though they were overcome with sleep, and they had all good things; for the fruitful earth unforced bare them fruit abundantly and without stint. They dwelt in ease and peace upon their lands with many good things, rich in flocks and loved by the blessed gods.
(ll. 121-139) But after earth had covered this generation—they are called pure spirits dwelling on the earth, and are kindly, delivering from harm, and guardians of mortal men; for they roam everywhere over the earth, clothed in mist and keep watch on judgements and cruel deeds, givers of wealth; for this royal right also they received;—then they who dwell on Olympus made a second generation which was of silver and less noble by far. It was like the golden race neither in body nor in spirit.  But when they were full grown and were come to the full measure of their prime, they lived only a little time in sorrow because of their foolishness, for they could not keep from sinning and from wronging one another, nor would they serve the immortals, nor sacrifice on the holy altars of the blessed ones as it is right for men to do wherever they dwell. Then Zeus the son of Kronos was angry and put them away, because they would not give honor to the blessed gods who live on Olympus.
(ll. 140-155) But when earth had covered this generation also—they are called blessed spirits of the underworld by men, and, though they are of second order, yet honor attends them also—Zeus the Father made a third generation of mortal men, a brazen race, sprung from ash-trees; and it was in no way equal to the silver age, but was terrible and strong. They loved the lamentable works of Ares and deeds of violence; they ate no bread, but were hard of heart like adamant, fearful men. Great was their strength and unconquerable the arms which grew from their shoulders on their strong limbs. Their armor was of bronze, and their houses of bronze, and of bronze were their implements: there was no black iron. These were destroyed by their own hands and passed to the dank house of chill Hades, and left no name: terrible though they were, black Death seized them, and they left the bright light of the sun.
(ll. 156-169b) But when earth had covered this generation also, Zeus the son of Kronos made yet another, the fourth, upon the fruitful earth, which was nobler and more righteous, a god-like race of hero-men who are called demi-gods, the race before our own, throughout the boundless earth. Grim war and dread battle destroyed a part of them, some in the land of Cadmus at seven-gated Thebe when they fought for the flocks of Oedipus, and some, when it had brought them in ships over the great sea gulf to Troy for rich-haired Helen’s sake: there death’s end enshrouded a part of them. But to the others father Zeus the son of Kronos gave a living and an abode apart from men, and made them dwell at the ends of earth. And they live untouched by sorrow in the islands of the blessed along the shore of deep swirling Ocean, happy heroes for whom the grain-giving earth bears honey-sweet fruit flourishing thrice a year, far from the deathless gods, and Kronos rules over them; for the father of men and gods released him from his bonds. And these last equally have honor and glory.
(ll. 169c-169d) And again far-seeing Zeus made yet another generation, the fifth, of men who are upon the bounteous earth.
(ll. 170-201) Thereafter, would that I were not among the men of the fifth generation, but either had died before or been born afterwards. For now truly is a race of iron, and men never rest from labor and sorrow by day, and from perishing by night; and the gods shall lay sore trouble upon them. But, notwithstanding, even these shall have some good mingled with their evils. And Zeus will destroy this race of mortal men also when they come to have gray hair on the temples at their birth. The father will not agree with his children, nor the children with their father, nor guest with his host, nor comrade with comrade; nor will brother be dear to brother as aforetime. Men will dishonor their parents as they grow quickly old, and will carp at them, chiding them with bitter words, hard-hearted they, not knowing the fear of the gods. They will not repay their aged parents the cost their nurture, for might shall be their right: and one man will sack another’s city. There will be no favor for the man who keeps his oath or for the just or for the good; but rather men will praise the evil-doer and his violent dealing. Strength will be right and reverence will cease to be; and the wicked will hurt the worthy man, speaking false words against him, and will swear an oath upon them. Envy, foul-mouthed, delighting in evil, with scowling face, will go along with wretched men one and all. And then Aidos and Nemesis, with their sweet forms wrapped in white robes, will go from the wide-pathed earth and forsake mankind to join the company of the deathless gods: and bitter sorrows will be left for mortal men, and there will be no help against evil.


2.13: The Five-Step Procedure for Establishing Pricing Policy
By the end of this section, you will be able to
- List the five-step procedure for establishing pricing policy.
- Describe ways to determine the pricing objective.
- Identify ways to estimate demand.
- List ways to estimate costs.
- Explain how to analyze the external environment.
- Discuss selecting pricing strategies or tactics.
Determine Pricing Objectives
Whether a product is new to the market or established, marketers face the challenge of setting prices. Recall that the main objective for pricing is for the buyer to perceive value in the product while the company maximizes profits. Marketers often use a five-step approach for establishing pricing policies (see Figure \(\PageIndex{1}\)).
During the first step in establishing pricing policies, the marketing team will set the pricing objectives (see Table \(\PageIndex{1}\)). The most common pricing objectives are based on customer value, cost, sales orientation, market share, target return, competition, and being customer-driven. It is not uncommon for more than one objective to be set within the company. Let’s take a look at each of the pricing objectives in more detail.
| Objective | Description |
|---|---|
| Customer value | Based on a product’s added value |
| Cost | Based on the cost to produce a product |
| Sales orientation | Developed to boost sales volume(s) of a product |
| Market share | Focused on increasing market share |
| Target return | Focused on a specific profit at a specific time |
| Competition | Developed based on competitors’ prices |
| Customer-driven | Focus on what the customer is willing to pay |
Customer Value-Based Objective
As you’ve already learned, it’s essential to have a deep understanding of the value a product will provide for customers. Before Jim Semick and his team launched GoToMeeting , a conferencing app, they developed the pricing of $49 “all you can meet flat-rate pricing.” This pricing was unique to the industry, and Semick stated that they determined this pricing structure based on dozens of interviews with potential customers. From these interviews, the GoToMeeting team discovered key areas that would provide value to customers not only through the product itself but also through the flat-rate price structure that was easy to understand (Semick, 2015). Semick utilized the customer value–based objective , one in which the company understands the value-added benefits of a product and sets its price accordingly.
Cost-Based Objective
A fairly simple way to price products and services is to use the cost-based objective . This pricing objective sets prices based on the costs of doing business, which were explained earlier in the chapter. The biggest pitfall of utilizing this pricing objective is that it might not align well with the customer’s value perception. Remember, customers don’t know (or care) what the cost of doing business is, so long as they receive value in their purchase. Therefore, marketers run the risk of overpricing the product. Marketers using this objective also risk pricing their products too low and failing to maximize profits.
Consider the manufacturing of a smartphone. Assume the total cost to the manufacturer to produce one smartphone is $3,000. This cost includes all expenses to the company for producing this one smartphone (product costs, variable and fixed expenses). According to Bhasin (2021), the company chooses to set the selling price of this smartphone to include these costs plus a profit of 10 percent, which sets the final price at
Sales-Oriented Objective
A company may wish to seek a boost in the sales volume of a product. In this case, marketers would choose the sales-oriented objective . The goal of a sales-oriented objective is to increase the volume, or units sold, of a product against the company’s sales over a period of time. This objective is achieved by raising or lowering prices to increase sales. An increase in sales assumes a direct impact on profits, thus maximizing profits. Consider the smartphone manufacturer again. Executives have set a sales goal of 1,000 units within the first quarter. Marketers may choose to lower the price of the smartphone to meet the goal. So perhaps the company changes the price from $3,300 to $3,100 for a short period until the sales goal is reached. Note that the company is still covering the cost of manufacturing the product and still making some profit.
Market Share–Oriented Objective
A market share–oriented objective is one in which the company’s pricing objective is to set prices based on those of the competition. This strategy involves comparing similar products offered in the market and pricing at, below, or above those prices depending on the products offered. The cell phone market is one example of an industry that leans on market share orientation. The biggest suppliers of cell phones— Apple , Google , and Samsung —take their pricing cues from one another and are priced very similarly (Campbell, 2020).
Target Return Objective
A target return objective is one in which marketers calculate the price so that it returns a specific profit in a given period. Suppose a company has invested $1 million into a new product. Company executives wish to recuperate 10% of those costs in year one of sales. If it costs the company $2 to manufacture one unit of product and marketers estimate that it will sell 50,000 products in the first year, marketers know they will need to price the product high enough to yield the desired results. The obvious drawback to this objective is that much of the decision is based on estimations of units sold in a given time frame.
Competition Objective
A competition-based objective , as its name suggests, is when a company sets its prices according to the prices of its competitors. Amazon often uses this pricing objective for some of its most popular products. Using data intelligence, the company gathers the prices of its competitors' products and sets its prices just below the price set by competitors (Prisync, 2018).
Customer-Driven Objective
Some companies choose to set prices based on customer-driven objectives —what the customer is willing to pay for a product or service. Auctions, e-trades, and bids are common examples of customer-driven objectives. eBay , for example, allows a company (or individual) to place an item for sale on its website. The interested buyer will often bid on the item, thus stating what they are willing to pay. The highest bidder is then able to buy the product.
Estimate Demand
After setting the pricing objectives, marketers will estimate the product or service demand. Demand is an economic term that refers to the buyer’s desire and willingness to purchase a product or service at various prices. All other factors being consistent, a price increase will result in a decrease in demand. The demand curve is a visual representation to understand demand.
Understanding the Demand Curve
The demand curve is a graph that shows how the demand for a product or service varies with the change in price. As you can see from Figure \(\PageIndex{2}\), the price (p) is located on the vertical axis, and the quantity (q) demanded is located on the horizontal axis. As the price of a product increases, demand for the product decreases.
The relationship between price and demand shown in the figure above is contingent on certain conditions remaining constant. Such conditions include substitute goods, personal income, and consumer tastes, which are further discussed below. Changes in these conditions can cause a change in demand that might not follow this basic concept of the demand curve.
The Demand Curve for Prestige Products
One pricing strategy that negates the demand curve is prestige pricing. Prestige pricing is a strategy that marketers use to set high prices, knowing that demand will increase with higher prices because the higher price increases the perceived value of the product. Prestige pricing is closely tied to brand image and appeals to buyers who see value in elevated status. Consider these brands of shoes. The Adidas Yeezy Boost 750 costs around $76 to produce but sometimes sells for over $1,000, while the D Rose 5 Boost costs around $43 and sells for around $100. So why the large price difference? The Yeezy Boost 750 pricing strategy is that of prestige pricing. The allure and exclusivity of the Yeezy Boost 750 allowed the company to price the shoes much higher (Fuchs, 2021).
In this article, HubSpot explores the pros and cons of prestige pricing and things to consider when implementing this strategy. Included are several prestige pricing examples such as the Adidas Yeezy Boost and the D Rose 5 Boost, as well as diamonds, cars, AirPods, and T-shirts.
Demand Elasticity
What will the impact of demand for a product be if the price is changed? If the product is discounted, will demand increase? If the price goes up, will demand decrease? The concept of demand elasticity helps marketers answer these questions. In short, demand elasticity is a measure of the change in the quantity demanded in relation to the change in its price. Mathematically, it is derived from the percentage change in quantity demanded divided by the percentage change in price. If you have been considering buying a new home, would the prices of homes sway your decision? Perhaps so. Home prices are considered elastic because the price greatly impacts the demand for new homes. Additionally, there are many options for housing, including apartments, roommates, living with relatives, condos, etc. (Hall, 2022).
As a second example, consider gasoline. Because we need gasoline to get to work, school, the grocery store, and meetups with friends, it is considered relatively inelastic. There are very few substitutes for gasoline. Because gasoline has inelastic demand, the price may fluctuate considerably, but the demand for gasoline remains relatively the same. Consider the higher gas prices of 2022, averaging over $5.00/gallon across the United States and even higher globally. Even though the prices have risen, the demand for gasoline has not changed because people still must travel to work and other essential places (Eitches & Crain, 2016).
In summary, if a product is determined to be inelastic, the demanded quantity does not change with a change in price. Conversely, if the product is elastic, the demanded quantity will change with a change in price. You might be asking: What makes a product elastic or inelastic? Several factors help determine how elastic a product or service will be.
Factors in Demand Elasticity
When determining the demand elasticity of products and services, there are several factors to keep in mind. These include substitutes, the effect of income, time, and cross-elasticity of demand (see Figure \(\PageIndex{3}\)). Let’s explore each of these in depth.
Availability of Substitutes
Substitutes are products and services that are similar to the one being offered. If a buyer can easily choose a different product when the prices change, the demand will be more elastic. For example, if you normally buy English muffins at the grocery store but the store is out, you can easily purchase bagels instead. Conversely, if there are relatively few alternatives, demand will be more inelastic. Consider the generic need for gasoline. It is fairly inelastic. The availability of substitutes for car travel is inconvenient. However, the demand for gasoline at specific gas stations is considered elastic because buyers can choose the gas station they prefer based on price. If two gas stations are located within a convenient geographic region for the buyer, they will choose the station with lower prices.
 The income effect is how buyers see the change in price affecting their real income. Generally, a price increase indicates that the buyer will have less money left over to spend; therefore, they will choose to buy less of a product, decreasing demand. The opposite is also true: the lower the price, the more money buyers have to buy more of the product, thus increasing demand. Consider the 8.6% inflation the United States saw between May 2021 and May 2022. Because inflation is a general rise in prices, consumers noticed that their purchases of goods and services caused their real income to decline. In other words, consumers had less money to spend on products and ultimately chose to purchase less.
Time
When the price of a good or service is changed, it takes time for buyers to adjust to the change in price. The time factor of price elasticity indicates that the product’s elasticity of demand is dependent upon the time it takes buyers to adjust to the new prices. For example, if there is a sharp decrease in the price of automobiles, buyers would not immediately go out and buy a new vehicle. Rather, it would take some time to save money for a down payment, secure a loan, and generally go through the buying process. Therefore, the demand for automobiles would increase, but over time rather than immediately.
Cross-Elasticity of Demand
What happens when one of two similar products has a price increase or decrease? If the price of coffee increases, it would be expected that the demand for tea (a substitute product) would also increase. Buyers see the price increase and look for lower-priced substitutes to replace the higher-priced item. The cross-elasticity of demand measures the amount demanded for one good when the price for a similar good or service changes (Hayes, 2022).
Estimate Costs
The next step in determining a pricing policy is to estimate the total cost of producing a product or service. Recall that maximizing profits is the goal of a pricing strategy and marketers must factor the cost of doing business into pricing considerations. When estimating total costs, it is important to divide costs into fixed and variable costs.
Fixed and Variable Costs
As mentioned earlier in this chapter, costs are categorized as either fixed or variable. Fixed costs are those expenses that do not change regardless of the number of units sold. Consider the example used earlier in the chapter of manufacturing a smartphone. If the company manufactures 1,000 or 100,000 smartphones, it must pay the same amount for its lease on the property on which the plant is located. The lease payment does not change based on the number of units produced. Alternatively, variable costs do change based on the number of units produced. In this example, the amount manufacturing spends depends on the number of smartphones produced.
Analyze the External Environment
The fourth step in determining prices is to analyze the external environment. The external environment comprises factors outside of the organization that impact marketing decisions. While marketers cannot directly change these factors, they should know how they might impact pricing decisions.
One way to remember the external environment factors is through the acronym PESTLE : political, economic, social, technological, legal, and environmental (Aguilar, 1967). Questions to consider in a PESTLE analysis when analyzing the external environment as it relates to pricing are included in Table 10.2.
| Factors | Question | Example |
|---|---|---|
| Political | What is the current political situation as it relates to the market? | A price cap on certain pharmaceuticals would limit the price a company could charge. |
| Economic | What is the current economic climate? | During inflation or deflation, prices may need to increase or decrease. |
| Social | How is culture changing or shaping the industry? | During the latter months of the year, the Indian market purchases more vehicles than at other times of the year. |
| Technological | What technologies are trending? | If a product's technology is becoming obsolete, a price decrease may be necessary. |
| Legal | What current legislation is impacting the industry? | A new vehicle emission law may require new technology, thus increasing the price of vehicles. |
| Environmental | What are the environmental concerns of the product? | A highly toxic product or process may need a higher price to properly and safely dispose of byproducts. |
Hundreds of online resources discuss PESTLE. Here are a few to start with:
- The Corporate Finance Institute provides a PESTLE walk-through .
- The Oxford College of Marketing outlines the advantages and disadvantages of a PESTLE analysis .
- Business-to-you provides a video, sample analysis, and a full list of PESTLE factors .
Competitors’ Costs, Prices, and Products
It probably seems obvious by now that analyzing the competition is key in setting prices. Marketers must constantly analyze current and potential market competition to understand how their products will measure up to that of the competition. If a competitor is planning to introduce a nearly identical product to one that your organization already has on the market—but at a much lower price—you will need to consider how that will affect your sales and analyze how it is offering such a lower price. Should you lower your price? Consider changing suppliers for lowered costs? Take a cut in profits to stay competitive? All of these questions, and more, will help you as a marketer determine what pricing strategy should be used.
Stage in the Product Life Cycle
How long a product—and its substitutes—have been in the market will impact the marketer’s choice of pricing strategies. Recall that the product life cycle consists of four stages: introduction, growth, maturity, and decline. During the introduction stage, marketers must choose pricing strategies wisely to capture the intended market and begin recuperating research and development costs. As a product moves through the other stages of the life cycle, prices may need to be changed to stay relevant to consumers.
Status of the Economy
As you can imagine, the state of the economy at any given time will impact the buyer’s ability to purchase products and their willingness to spend. Marketers should be aware of economic factors when considering demand for products, including employment, inflation, interest rates, and consumer confidence (Maverick, 2022).
One of the main factors that influences consumer demand is the employment rate. The unemployment rate is a measure of the number of people who are not employed but are actively seeking work in a given period—usually one month. When employed and receiving steady income, buyers are more likely to use discretionary income. Discretionary income is the money left over after all taxes and necessities—such as food and housing—are paid. When discretionary income decreases, demand for nonessential items also decreases.
Inflation is an economic measure of the rate of rising prices of goods and services in an economy. When inflation occurs, prices for most goods and services rise. Therefore, a buyer's discretionary income decreases, and demand for nonessential goods and services also decreases. Consider the high inflation in the United States economy from 2021 to 2022, which was 8.6% as of May 2022 (U.S. Inflation Calculator, 2022). The inflation rate is currently the highest that it has been since 1981. Because of the higher price of goods and services within the economy, consumers spend more of their earned income on necessities such as food and shelter. This, in turn, causes them to purchase fewer nonessential items such as vacations, toys, and the like. Inflation also impacts pensions and other retirement accounts. Hence, as inflation rises considerably, people are even less likely to spend their discretionary income and more likely to save anything left over after essentials for future use (Amadeo, 2021).
Even consumers who do not have a deep understanding of the economy have some degree of optimism regarding the overall state of the economy. This is known as consumer confidence —it measures how optimistic consumers are about the economy and their own finances (The Conference Board, 2022). When consumers have little optimism in the economy, they are more likely to save their discretionary income than spend it.
The overall status of the economy—current and future—is important for marketers to be aware of as it directly impacts buyers' ability and willingness to spend money. Choosing pricing strategies that are aligned with the health of the economy will have a greater chance of success.
Select Pricing Strategies or Tactics
After gathering all the data explained in the previous steps, marketers are ready to set specific pricing strategies or tactics. The strategies and tactics chosen for a product or service should align with the other marketing mix elements, create customer value, and maximize company profits. In the next section, we will discuss specific strategies and tactics and how to optimize each.


12.14: References
American Dental Society. (2012). How to floss. Retrieved from http :// www . mouthhealthy . org /~/ media / MouthHealthy / Files / Kids _ Section / ADAHowToFloss _ Eng . ashx
Center for Disease Control (2014). When and how to wash your hands. Retrieved from www . cdc . gov / handwashing / when – how – handwashing . html
Centers for Disease Control and Prevention. (2012, May 18). Lesson 1: Introduction to epidemiology. In Principles of epidemiology in public health practice . An introduction to applied epidemiology and biostatistics (3rd ed.). Retrieved from http :// www . cdc . gov / ophss / csels / dsepd / ss 1978 / lesson 1 / section 10. html
Craven, R. F., & Hirnle, C. J. (2009). Fundamentals of nursing : Human health and function (6th ed.). Philadelphia, PA: Wolters Kluwer.
Leahy, W., Fuzy, J., & Grafe, J. (2013). Providing home care : A textbook for home health aides (4th ed.). Albuquerque, NM: Hartman.
Sorrentino, S. A. & Remmert, L. N. (2012). Mosby ’ s textbook for nursing assistants (8th ed.). Saint Louis, MO: Mosby.