Physical Properties of Gases

As mentioned in the previous section, there are four key properties that can describe the behavior of an ideal gas: pressure (P), temperature (T), volume (V), and the number of moles of gas substance (n). In the next two sections we will discuss the mathematical relationships between these variables. For now, let's go into some detail about what they mean, the units we use to measure them, and other useful information.

Amount (n)

In the past, we have measured amounts of materials using mass. Many of the properties of an ideal gas, however, are determined by the number of gas particles present, not their mass; it makes more sense to use the number of moles to measure the amount of gas present since the number of moles measures the number of particles directly.

The units of amount (n) are moles (mol).

Recall that one more of a chemical substance contains 6.02 x 10²³ atoms (or molecules) and its mass is just its atomic (or molecular) weight in grams.

If you know the number of moles of something you have, you know how many of them there are, even if you don’t know WHAT they are. For this reason, we can use moles of gas particles instead of the actual number of gas particles when we are dealing with the properties of gases. We will mostly not use Avogadro's number in this setting, but we will frequently need to convert from grams to moles or vice versa. This should be a well-developed skill, which you should practice here to make sure it is still sharp.

Practice:

a. Convert 87.7 g of nitrogen monoxide (NO) to moles.

b. Convert 0.560 mol of hydrogen chloride (HCl) to grams

Answers:

a. 2.92 mol

b. 20.4 g

Volume (V)

Because the particles travel independently of one another, they will occupy the entire volume of whatever container they are in. Therefore, the volume of a gas is actually nothing more than the volume of its container. This volume, of course, is mostly empty space.

The units of volume (V) are liters (L) or milliliters (mL).

Other units of volume you might encounter are cm³/cc’s (cubic centimeters), which are the same as mL. These are the most common units used in chemistry. It is a simple matter to convert between these and English units such as ounces, quarts, gallons, and so on, using conversion factors found in standard tables. If you need to, you can review the relevant lessons from Chemistry 104.

Practice:

a. Convert 1.425 L to mL

b. Convert 754 cc to L

Answers:

a. 1425 mL

b. 0.754 L

Temperature (T)

Temperature is a measure of the average energy of motion – the kinetic energy – of atoms and molecules. Since this energy determines the force with which they strike the walls of their container, the properties of gases depend on their temperature. Temperature must be measured in Kelvin rather than the usual degrees Celsius. We’ll discuss why this is in the next section on “Gas Laws.”

The units of temperature (T) are Kelvin (K).

To convert between °C and K, you simply add or subtract 273. So a temperature of 58.8 °C would be 58.8 + 273 = 331.8 K. This conversion is quite simple, but you must not forget to perform it. Using Celsius temperatures is one of the most common places for students to go wrong in gas law calculations.

*Technically the value is 273.15, but for most temperatures we will work with the extra 0.15 K will be negligible.

Temperature is a measure of the “concentration” of the heat (energy) in a substance and it is related to the average kinetic energy of the molecules. Heat would be the total amount of kinetic energy rather than the average. Kinetic energy is determined by both the speed of motion of a particle and its mass. If two particles have the same kinetic energy but different masses, the lighter particle must be traveling more rapidly than the heavier particle in order to have the same energy.

Practice:

a. Convert 15.2 °C to K

b. Convert 557 K to °C

Answers:

a. 288.2 K

b. 284 °C

Pressure (P)

The pressure exerted by a gas is the force per unit area it exerts on the walls of its container. For example, we measure the pressure of the air in a tire in units that reflect this: psi, or pounds per square inch.

On the scale of ordinary objects, gravity has no effect on the particles of a gas, so that they tend to strike the top, sides, and bottom of their container all with the same average force. Therefore the pressure inside an ordinary size container is the same everywhere. If you had a container that was a container that was a thousand feet high, however, the effect of gravity would be noticeable and the pressure would be slightly higher at the bottom of the container. To make a really significant difference, the container would have to be about a mile or more high (this is why Denver, a mile above sea level, has noticeably lower air pressure than at lower elevations).

The units of pressure (P) are atmospheres (atm).

Practice:

a. Convert 36.2 psi to torr

b. Convert 975 mbar to atm (note the prefix!)

Answers:

a. 18780 torr

b. 0.962 atm