SCH3U

Gas Laws: Charles Law/Gay Lussacs Law

The Relationship between **Volume and Temperature**: Charles law

Through experiments with hot air balloons, Charles noticed that gases expand when heated. Conversely, when a gas is cooled, it contracts by the same proportion. He noticed that for every rise of 1 °C, the gas expanded 1/273 of its volume at 0 °C. For every decrease of 1 °C, the gas contracted by the same proportion.

Charles’s law states that at **constant external pressure, the volume of a fixed mass of any gas is directly proportional** to its Kelvin Temperature.

This can be expressed mathematically: V1/T1 = V2/T2 (constant pressure and mass)

**Explained by the kinetic molecular theory: **

As temperature of gas increases, the molecules move at higher speeds (have more kinetic energy). As a result, they collide with the walls of the container and with one another more frequently and with greater force. Therefore, they exert a greater pressure on the walls of the container. If the external pressure on the gas stays the same, the gas pressure (on the inside) causes the container to increase in size (volume). *More temperature = more energy = more collisions = expansion*

**Charles Law Sample Problem:**

A balloon is filled with helium gas to a volume of 1.20 L and at a temperature of 15 °C. If the pressure outside remains constant and the temperature rises to 30 °C, what will the new volume of the balloon be?

**Plan your strategy**/

**Act on your strategy**

-Pressure is constant.

-Temperature and volume are changing

-Which law: Charles’ Law / V1/T1 = V2/T2

-Isolate the variable you are looking for (in this case it is V2)

-Remember to convert the temperatures into Kelvin. / V2 = V1T2/T1

Plug the numbers (and units) of the known variables into the equation. / V2 = (1.20 L)(303 K)/(288 K) = 1.26 L

Conclusion: The new volume of the balloon is 1.26 L. This makes sense as the higher temperature causes the gas to expand.

The relationship between Pressure and Temperature: Gay-Lussac’s Law

Gay-Lussac’s law states that at **constant volume, the pressure of a fixed mass of any gas is directly proportional** to its Kelvin temperature.

Mathematically this can be expressed as: P1/T1 = P2/T2 (only use when constant volume and constant mass)

*Explained by the kinetic molecular theory:*

As temperature of a gas increases, the molecules move at higher speeds (have more kinetic energy). As a result, they collide with the walls of the container more frequently and with greater force. As a result, the pressure increases. Higher *temperature = more collisions with walls of container = more pressure*.

**Gay-Lussac’s Law Sample Problem:**

At a temperature of 10 C, a container is filled with gas at a pressure of 225 kPa. What will the pressure be if the container is placed in the hot sun to reach a temperature of 42 C?

**Plan your strategy**/

**Act on your strategy**

-Volume is constant.

-Temperature and pressure are changing

-Which law: Gay-Lussac’s Law / P1/T1 = P2/T2

-Isolate the variable you are looking for (in this case it is P2)

-Remember to convert the temperatures into Kelvin. / P2 = P1T2/T1

Plug the numbers (and units) of the known variables into the equation. / P2 = (225 kPa)(315 K)/(283 K) = 250 kPa

Conclusion: The new pressure of the gas in the container is 250 kPa which makes sense because temperature increase leads to an increase in molecular collisions (pressure).

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