Unit 33: The Ideal Gas Law

Unit Overview:

In the last unit, you applied the kinetic molecular theory to the behavior of gases, exploring their mathematical descriptions. These mathematical descriptions are known as empirical gas laws.

In this unit, you will synthesize these empirical gas laws into the ideal gas law.

Let’s Review:

What variables are used to explain gases?

Four variables are used to describe gases: amount, volume, temperature, and pressure.

Variable	Symbol	Unit
Amount	n	Mole (mol)
Volume	V	Liters (L)
Temperature	T	Kelvin (K)
Pressure	P	Atmosphere (atm)

What empirical gas laws describe them?

When any two of these variables are held constant, it is possible to determine the relationship between the remaining two variables. These relationships between two variables are referred to as the empirical gas laws:

Empirical Gas Law	Held Constant	Variables	Relationship	Equation
Boyle’s law	Amount of gas Temperature	Pressure Volume	inverse	P ^. V = constant
Charles’ law	Amount of gas Pressure	Temperature Volume	direct	V T	= constant
Gay-Lussac’s law	Amount of gas Volume	Temperature Pressure	direct	P T	= constant
Avogadro’s law	Temperature Pressure	Amount of gas Volume	direct	V n	= constant

What is the Ideal Gas Law?

The ideal gas law mathematically combines the four empirical gas laws together into one equation. This equation relates all four of the variables that describe a gas into one equation. This equation defines the constant and allows us to relate the 4 variables to each other for any sample of gas.

Ideal Gas Law:

PV = nRT

Pressure

Atmosphere (atm)

Volume

Liters (L)

Amount of gas

Mole (mol)

Universal Gas

Constant

0.0821

L ^. atm

K ^. mol

Temperature

Kelvin (K)

Please note: The units for the universal gas law are very specific. So, when using the ideal gas law to solve problems, it is important that the units for all of the variables match.

Let’s look at an example together:

A 50.0 L tank contains hydrogen (H₂) gas at a temperature of 298 K and a pressure of 1.01 atm. How many moles of hydrogen gas is in the tank?

Step 1: Identify all the variables; make sure all the units are as specified in the table above.

P = 1.01 atm

V = 50.0 L

n = ? mol

R = 0.0821 L^.atm/K^.mol

T = 298 K

Step 2: Using the ideal gas law equation, solve for the variable which does not have a value.

PV = nRT

In this case, it is “n.” To solve for “n,” divide both sides of the equation by RT.

nRT

This allows the RT/RT to cancel on the right side, leaving “n” by itself.

Step 3: Plug in your known values and solve for the missing value.

(1.01 atm)(50.0 L)

(0.0821 L^.atm/K^.mol) (298 K)

n = 2.06 mol H₂

Watch the following video to hear a verbal description of how to solve problems using the ideal gas law:

Practice 1: Complete the online problem-solving quiz of the ideal gas law.

What is an ideal gas?

Notice that we refer to this combination of the empirical gas laws as the ideal gas law. Why do we use the word ideal? Recall from Unit 31 that we discussed the kinetic molecular theory. Within that theory, we make assumptions about gas molecules that are not necessarily always valid to make. We call a gas that follows these assumptions an ideal gas; when gas does not, we call it a real gas.

Ideal Gas

Real Gas

1. The molecules have no volume.

2. Collisions between molecules are elastic.

3. There is no attraction between the molecules.

1. Molecules do have volume.

2. Collisions between molecules are not elastic.

3. There is an attraction between molecules.

We use the ideal gas law because it typically works. That is, most gases exhibit ideal behavior under normal conditions.

And now watch this video to watch a demonstration that illustrates the difference between the real and ideal behavior of air in a balloon: Air Balloon

ChemLab: Ideal Gas Behavior

Overview: You will observe the movement of particles of an ideal gas at a variety of temperatures. You will compare graphical representations of different gas samples to consider when gases behave ideal v. real.

Directions:

1. Download the Student Exploration and Vocabulary sheets for the Ideal Gas Behavior.

2. Familiarize yourself with the words on the vocabulary sheet.

3. Log-in to your Explore Learning account.

4. Click on “Temperature and Particle Motion” and launch the gizmo. [PLEASE NOTE: The name of the Gizmo is not the name of your exploration sheet.]

5. Answer the Prior Knowledge Question.

6. Practice using the Gizmo, using the Gizmo warm-up instructions.

7. After you are comfortable using the Gizmo, begin the activity. Use the lab sheet as a guide to complete the 2 activities:

a. Activity A: Molecular Motions

b. Activity B: Average Particle Velocity