Charles' Law (Grade 11 NSC Matric Physical Sciences): Revision Notes

Demonstration: Charles' Law in Action

Aim: To demonstrate Charles' Law

Equipment needed:

• Empty glass bottle
• Balloon
• Water bath or beaker
• Hot plate
• Water

Method:

1. Place the balloon over the opening of the empty bottle
2. Fill the beaker with water and place it on the hot plate
3. Stand the bottle in the water bath and turn on the hot plate
4. Observe what happens to the balloon as the water heats up

Results: The balloon expands as the air inside the bottle is heated. The pressure inside cannot change much, so the increased temperature causes the air to expand into the balloon.

Alternative observation: Place the bottle and balloon in a freezer. The balloon will shrink as the temperature decreases.

Conclusion: Temperature and volume are directly related. As temperature increases, volume increases. As temperature decreases, volume decreases.

Worked Example: Volume Change with Temperature Decrease

Question: A sample of CO₂ gas occupies 6 L at 298 K. What temperature will the gas be at if its volume is reduced to 5.5 L? The pressure remains constant.

Solution:

Step 1: Write down known information

• $V_1 = 6$ L
• $V_2 = 5.5$ L
• $T_1 = 298$ K
• $T_2 = ?$

Step 2: Check units

Temperature is already in Kelvin, so no conversion needed.

Step 3: Choose appropriate equation

Since pressure and amount of gas are constant, use Charles' Law:

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Step 4: Substitute and calculate

$\frac{6}{298} = \frac{5.5}{T_2}$

Cross multiply:

$6 \times T_2 = 5.5 \times 298$

$T_2 = \frac{5.5 \times 298}{6} = 273.2 \text{ K}$

Step 5: Check the answer

Volume decreased, so temperature should decrease. Our answer shows temperature dropping from 298 K to 273.2 K, which is correct.

Worked Example: Volume Change with Temperature Increase

Question: A gas syringe contains ammonia at 20°C with a volume of 122 mL. The syringe is placed in a water bath at 32°C. What will the volume reading be after one hour?

Solution:

Step 1: Write down known information

• $V_1 = 122$ mL
• $V_2 = ?$
• $T_1 = 20°C$
• $T_2 = 32°C$

Step 2: Convert temperatures to Kelvin

$T_1 = 20 + 273 = 293 \text{ K}$

$T_2 = 32 + 273 = 305 \text{ K}$

Step 3: Use Charles' Law equation

$\frac{V_1}{T_1} = \frac{V_2}{T_2}$

Rearranging: $V_2 = \frac{V_1 \times T_2}{T_1}$

Step 4: Substitute and calculate

$V_2 = \frac{122 \times 305}{293} = 127 \text{ mL}$

Step 5: Check the answer

Temperature increased, so volume should increase. Our answer shows volume increasing from 122 mL to 127 mL, which is correct.