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In the following lessons we will examine the properties of gases. Gases have a unique set of properties. Gases will assume the shape and volume of their container (i.e., the volume of a gas equals the volume of its container). Gases also exert a force, called pressure (P), against surfaces they contact. Gases also have low densities and are compressible. By compressible, we mean that we can decrease the volume of a gas by applying a force to it. This is illustrated by the diagram of a piston in Figure 1. When a force is applied to the piston, it will decrease the volume of the gas contained within it.

The three diagrams in Figure 2 illustrate the differences between solids, liquids, and gases at the molecular level. Notice that in liquids and solids the molecules are close to each other; they are held close to one another by intermolecular interactions. A solid is able to hold its own shape and a liquid spreads out on the bottom of the container. In an ideal gas, however, the molecules are spread apart and not interacting with each other (refer back to KMT). Also, notice that the gas fills the volume of the container, whereas the liquid and solid do not.

We can describe the state of a gas in terms of the number of molecules of gas molecules in the sample (n), its pressure (P), its volume (V), and its absolute temperature (T). Absolute temperature is measured in units of Kelvin. The convert from °C to Kelvin you simply add 273.15 to the temperature in Celsius. The coldest temperature possible temperature, which is unachievable, is 0 K, or absolute zero.

These parameters are related to one another by three fundamental relationships, listed below. Boyle’s Law describes the relationship between pressure and volume, Charles’s Law describes the relationship between volume and temperature, and Avogadro’s Law describes the relationship between volume and number of moles in the sample. You don’t need to memorize the name of each relationship.

Boyle's Law: V \propto \frac1P \rightarrow V = \frac kP

Charles' Law: V \propto T \rightarrow V = kT

Avogadro's Law: n \propto V \rightarrow n = kV

Gay-Lussac's Law: P \propto T \rightarrow P = kT

Boyle’s, Charles’, Avogadro’s, and Gay-Lussac's Laws are all proportionalities. Boyle’s law states that V is proportional to 1/P, or we can also say that V is inversely proportional to P. Charles’ Law states that V is proportional to T, Avogadro’s Law states that n is proportional to V, and Gay-Lussac's Law states that P is proportional to T. We can rewrite each proportionality as an equation by adding in a proportionality constant (k), as shown above.

The reason why you don’t need to memorize Boyle’s, Charles', Avogradro’s, and Gay-Lussac's Laws is because all four relationships are reflected in the ideal gas law. The ideal gas law ( PV=nRT ) describes how all four parameters (P, V, n, and T) relate to each other. R is the gas constant, whose value is 0.08206\frac{L·atm}{mol·K} .

Shown below, we see how each of the relationships above relate to the ideal gas law. Starting with Boyle’s law (V=k/P), we can rearrange the ideal gas law to solve it for V (V=nRT/P). This allows us to see that the proportionality constant for Boyle’s Law is nRT (as shown in parentheses on the right side of the table). Thus, Boyle’s Law only holds true when both n and T are constant. We can do the same thing for Charles’s Law, and we see that its proportionality constant equals nR/P (constant n and P),as shown in parentheses on the right side of the table. The same process, applied to Avogadro’s Law, gives us a proportionality constant of P/RT (constant P and T). Finally, we can see that Gay-Lussac's Law gives a proportionality constant of nR/V (constant n and V).