Gas Laws: Pressure, Volume, and Hot Air

Introduction

This lesson will introduce three ways of predicting the behavior of gases: Boyle’s Law, Charles’ Law, and the Ideal Gas Law.

Objective 1: Basic Terminology

Review terms used to describe the properties and behavior of gases.

Properties of Gases

You can predict the behavior of gases based on the following properties:

Pressure

Volume

Amount (moles)

Temperature

Lets review each of these briefly…

Pressure

Pressure is defined as the force the gas exerts on a given area of the container in which it is contained. The SI unit for pressure is the Pascal, Pa.

• If you’ve ever inflated a tire, you’ve probably made a pressure measurement in pounds (force) per square inch (area).

Volume

Volume is the three-dimensional space inside the container holding the gas. The SI unit for volume is the cubic meter, m3. A more common and convenient unit is the liter, l.

Think of a 2-liter bottle of soda to get an idea of how big a liter is. (OK, how big two of them are…)

Amount (moles)

Amount of substance is tricky. As we’ve already learned, the SI unit for amount of substance is the mole, mol. Since we can’t count molecules, we can convert measured mass (in kg) to the number of moles, n, using the molecular or formula weight of the gas.

By definition, one mole of a substance contains approximately 6.022 x 1023 particles of the substance. You can understand why we use mass and moles!

Temperature

Temperature is the measurement with which you’re probably most familiar (and the most complex to describe completely). For these lessons, we will be using temperature measurements in Kelvin, K.

The Kelvin scale starts at Absolute 0, which is -273.15°C. To convert Celsius to Kelvin, add 273.15.

Objective 2: Boyle’s Law

Boyle’s Law describes the relationship between pressure and volume of gases.

Boyle’s Law

This law is named for Charles Boyle, who studied the relationship between pressure, p, and volume, V, in the mid-1600s.

Boyle determined that for the same amount of a gas at constant temperature,

p * V = constant This defines an inverse relationship:

when one goes up, the other comes down.

pressure

volume

What does Boyle’s Law mean?

p * V = constantSuppose you have a cylinder with a piston in the top so you can change the volume. The cylinder has a gauge to measure pressure, is contained so the amount of gas is constant, and can be maintained at a constant temperature.

A decrease in volume will result in increased pressure.

Application of Boyle’s Law

Boyle’s Law can be used to predict the interaction of pressure and volume.

If you know the initial pressure and volume, and have a target value for one of those variables, you can predict what the other will be for the same amount of gas under constant temperature.

Application of Boyle’s Law

p1 * V1 = p2 * V2

p1 = initial pressure

V1 = initial volume

p2 = final pressure

V2 = final volume

If you know three of the four, you can calculate the fourth.

Application of Boyle’s Law

p1 * V1 = p2 * V2

p1 = 1 KPa

V1 = 4 liters

p2 = 2 KPa

V2 = ?

Solving for V2, the final volume equals 2 liters.

So, to increase the pressure of 4 liters of gas from 1 KPa to 2 KPa, the volume must be reduced to 2 liters.

Objective 3: Charles’ Law

Charles’ Law describes the relationship between volume and temperature of gases.

Charles’ Law

This law is named for Jacques Charles, who studied the relationship volume, V, and temperature, T, around the turn of the 19th century.

He determined that for the same amount of a gas at constant pressure,

V / T = constant This defines a direct relationship:

an increase in one results in an increase in the other.

volume

temperature

What does Charles’ Law mean?

V / T = constantSuppose you have that same cylinder with a piston in the top allowing volume to change, and a heating/cooling element allowing for changing temperature. The force on the piston head is constant to maintain pressure, and the cylinder is contained so the amount of gas is constant.

An increase in temperature results in increased volume.

Application of Charles’ Law

Charles’ Law can be used to predict the interaction of temperature and volume.

If you know the initial temperature and volume, and have a target value for one of those variables, you can predict what the other will be for the same amount of gas under constant pressure.

Application of Charles’ Law

V1 / T1 = V2 / T2

V1 = initial volume

T1 = initial temperature

V2 = final volume

T2 = final temperature

If you know three of the four, you can calculate the fourth.

Application of Charles’ Law

V1 / T1 = V2 / T2 V1 = 2.5 litersT1 = 250 KV2 = 4.5 litersT2 = ?Solving for T2, the final temperature equals 450 K.So, increasing the volume of a gas at constant pressure from 2.5 to 4.5 liters results in a temperature increase of 200 K.

Objective 4: Ideal Gas Law

Ideal Gas Law combines all the properties of gases into a single equation.

Ideal Gas Law

Combining Boyle’s and Charles’ laws allows for developing a single equation:

P*V = n*R*TP = pressure

V = volume

n = number of moles

R = universal gas constant (we’ll get to that in a minute…)

T = temperature

Ideal Gas Law

P*V = n*R*TThis is one of the few equations in chemistry that you should commit to memory!

By remembering this single equation, you can predict how any two variables will behave when the others are held constant.

Gas Constant

The Ideal Gas Law as presented includes use of the Universal Gas Constant.

The value of the constant depends on the units used to define the other variables.

For the purposes of this lesson, we will use the equation only to predict gas behavior qualitatively. Specific calculations and units will be part of our classroom work.

Putting p*V=n*R*T to Work

After using Boyle’s and Charles’ law for predicting gas behavior, use of the Ideal Gas Law should be relatively straightforward.

Use NASA’s Animated Gas Lab to explore the interaction of these variables on gas behavior.

Follow the directions on the page for changing values for the variables.

When you’re finished, click the Back button on your browser to return to this lesson.

Link to site: Animated Gas Lab

Ideal Gas Law: Summary

P*V = n*R*T Learn it! Use it!

This single equation can be used to predict how any two variables will behave when the others are held constant.

Lesson 4 Complete!

This concludes Lesson 4 on the Ideal Gas Law!

Click the Main Menu button below, then select Review to try some questions based on these lessons.

Review

This review contains multiple choice questions on the material covered by Lessons 1 – 4. Select an answer by clicking the corresponding letter.

If you choose an incorrect answer, you will be given feedback and a chance to try again. If you want to return to a lesson to review the material, click on the Main Menu button, then select the lesson. When you’re ready to complete the review again, go back to the Main Menu and click the Review button.

Question 1

Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are:

a. Inversely proportional: if one goes up, the other comes down.

b. Directly proportional: if one goes up, the other goes up.c. Not related

Question 1 is Correct!

Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are:

a. Inversely proportional: if one goes up, the other comes down.

Decreasing volume increases pressure. Increasing volume decreases pressure.

pressure

volume

Try Question 1 again…

Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are:

a. Inversely proportional: if one goes up, the other comes down.

b. Directly proportional: if one goes up, the other goes up.c. Not related

You selected b. While pressure and volume are related, it is not a direct proportion. Try again!

Try Question 1 again…

Based on Boyle’s Law (p * V = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and temperature (T) are held constant, pressure and volume are:

a. Inversely proportional: if one goes up, the other comes down.

b. Directly proportional: if one goes up, the other goes up.c. Not related

You selected c. Pressure and volume are related. Is the relationship inverse or direct?

Question 2

Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are:

a. Inversely proportional: if one goes up, the other comes down.

b. Directly proportional: if one goes up, the other goes up.c. Not related

Question 2 is Correct!

Based on Charles’ Law (V / T = constant) or the Ideal Gas Law (p*V=n*R*T), when the number of moles (n) and pressure (p) are held constant, volume and temperature are:

b. Directly proportional: if one goes up, the other goes up.

Increasing temperature increases volume. Decreasing temperature decreases volume.

volume

temperature

Question 3

Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire?

a. Increase the force pressing on the outside of the tire.b. Increase the temperature of the gas (air) in the tire.c. Increase the amount (number of moles) of gas in the tire.

Question 3 is Correct!

Lets put the Ideal Gas Law (p*V=n*R*T) to some practical use. To inflate a tire of fixed volume, what is the most effective way to increase the pressure in the tire?

a. Increase the force pressing on the outside of the tire.b. Increase the temperature of the gas (air) in the tire.c. Increase the amount (number of moles) of gas in the tire.

When you inflate a tire with a pump, you are adding air, or increasing the amount of air in the tire. This will often result in a slight increase in temperature because a tire is not a controlled environment. Such deviations and quirks will be discussed in class!