Learning Objectives

Gas Laws

Some chemical reactions take place in the gas phase and others produce products that are gases. We need a way to measure the quantity of compounds in a given volume of gas and relate that to moles. We also need to have some familiarity about the way the volume, pressure and temperature of a gas are related. Knowledge of some of the basic behavior of gases is very important in the prevention of some very serious health risks in sports such as scuba diving and white-water rafting.

We previously learned that one mole of a gas occupies 22.4 liters at standard temperature and pressure. Remember that standard temperature is equal to 273 K and standard pressure is equal to 1atmosphere or 760 mm of Hg.

As we learned earlier, atmospheric pressure is caused by the weight of the molecules in the atmosphere. This is equal to 14.7 pounds per square inch at sea level or the pressure needed to support a column of mercury 760 mm high.

It turns out that, for a given quantity of gas, the pressure times the volume divided by the temperature equals a constant. The pressure is given in atmospheres, the volume in liters and the temperature in degrees Kelvin. Remember, when looking at the following illustrations, that room temperature equals about 300 K.

Using the PV/T Relationship

Since PV/T equals a constant, we can understand how any of these variables change with respect to each other.

Pressure and Volume

If the temperature remains constant, then the relationship changes to P x V = constant. If either the pressure or volume is changed, the other must change in the opposite direction.

Therefore, if you increase the pressure, the volume must decrease. This makes sense if you think of a bicycle pump. When you push down on the plunger, the volume inside the pump is decreased and you can feel more pressure the further you push down on the plunger.

How does this relate to the world we live in?

Volume and Temperature

If the pressure remains constant, then the relationship changes to V/T = constant. If either the volume or the temperature is changed, the other must also change exactly the same way.

This also makes sense. If you heat up a gas the volume will increase since the molecules are moving faster.

Try blowing up a balloon on a cold day and carefully measure the circumference with a piece of string. Now bring the balloon indoors and let it warm up to room temperature. If you now measure the circumference, you will see that the balloon has increased in size.

How does this relate to the world we live in?

Pressure and Temperature

If the volume remains constant, then the relationship changes to P/T = constant. If either the pressure or the temperature is changed, the other must also change exactly the same way.

This also makes sense. If you measure the air pressure in the tires of your car and then take a drive on a hot day, you will be amazed at how much the pressure has increased. Tire manufacturers recommend pressures of inflation to account for this increase in pressure.

Solubility of a Gas and Pressure

The relationship of solubility to pressure is given by Henry’s law. Henry’s law states that the amount of gas that will dissolve in a liquid at a given temperature varies directly with the pressure above the liquid.

When you open a can of soda, the dissolved carbon dioxide bubbles out of the solution because the pressure of the container has been lowered.

How does this relate to scuba diving?

Solubility of a Gas and Temperature

Temperature also plays a role in the solubility of a gas in a liquid. As the temperature is increased the solubility of a dissolved gas is actually decreased. You see this every day as bubbles form when a cold glass of water is allowed to warm to room temperature.

Does this relate to scuba diving?

Problems

1. If the pressure of a gas is doubled at constant volume, how will the temperature change?

2. If the temperature of a gas is halved at constant volume, how will the pressure change?

3. If the volume of a gas is doubled at constant pressure, how will the temperature change?

4. If the temperature of a gas is doubled at constant pressure, how will the volume change?

5. If 20 liters of hydrogen at STP react with 10 liters of oxygen at STP, how many grams of water will be formed?

2 H₂ + O₂ ® 2 H₂O

6. If the temperature of a solution of a gas is increased, how will the solubility of the gas change?
7. If the pressure on a solution of a gas is decreased, how will the solubility of the gas change?

Return to the Reviews of Concepts