Gay-Lussac's gas law is a special case of the ideal gas law where the volume of the gas is held constant. When the volume is held constant, the pressure exerted by a gas is directly proportional to the absolute temperature of the gas. This example problem uses Gay-Lussac's law to find the pressure of a heated container.

### Gay-Lussac's Law Example

A 20 L cylinder containing 6 atm of gas at 27 °C. What would the pressure of the gas be if the gas was heated to 77 °C?

**Solution**

The cylinder's volume remains unchanged while the gas is heated so Gay-Lussac's gas law applies. Gay-Lussac's gas law can be expressed as

P_{i}/T_{i} = P_{f}/T_{f}

where

P_{i} and T_{i} are the initial pressure and absolute temperatures

P_{f} and T_{f} are the final pressure and absolute temperature

First, convert the temperatures to absolute temperatures.

T_{i} = 27 °C = 27 + 273 K = 300 K

T_{f} = 77 °C = 77 + 273 K = 350 K

Use these values in Gay-Lussac's equation and solve for P_{f}.

P_{f} = P_{i}T_{f}/T_{i}

P_{f} = (6 atm)x(350K)/(300 K)

P_{f} = 7 atm**Answer:**

The pressure will increase to 7 atm after heating the gas from 27 °C to 77 °C.

### Another Gay-Lussac's Example

Find the temperature in Celsius needed to change the pressure of 10.0 liters of a gas that has a pressure of 97.0 kPa at 25°C to standard pressure. Standard pressure is 101.325 kPa.

First convert 25°C to Kelvin (298K).

Insert the numbers into the equation to get:

97.0 kPa / 298 K = 101.325 kPa / x

solving for x:

x = (101.325 kPa)(298 K)/(97.0 kPa)

x = 311.3 K

Subtract 273 to get the answer in Celsius.

x = 38.3°C

### Important Points About Gay-Lussac's Law

- Volume and quantity of gas are held constant.
- If temperature of the gas increases, pressure increases.
- If temperature decreases, pressure decreases.

Why does this happen?

Temperature is a measure of the kinetic energy of gas molecules. At a low temperature, the molecules are moving more slowly and will hit the wall of a container less frequently. As temperature increases, so does motion of the molecules. They strike the walls of the container more often, which is seen as an increase in pressure.

The direct relationship only applies if temperature is given in Kelvin. The most common mistakes students make working this type of problem is forgetting to convert to Kelvin or else doing the conversion incorrectly. The other error is neglecting significant figures in the answer. Use the smallest number of significant figures given in the problem.