A gas is confined in a graduated cylinder enclosed by a movable piston. When the temperature of the room is 24.4 °C , the volume of the gas at atmospheric pressure is found to be 39.4 mL. The cylinder is them immersed in a bath containing a liquid and solid benzene. The piston moves to maintain constant atmospheric pressure. The volume of the gas at the freezing point is 39.6 mL. Calculate the freezing point of benzene.

To determine the freezing point of benzene based on the changes in gas volume, we can apply Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This relationship can be expressed mathematically as:

Charles's Law Formula

The formula is given by:

V1/T1 = V2/T2

Where:

• V1 = initial volume of the gas
• T1 = initial temperature of the gas (in Kelvin)
• V2 = final volume of the gas
• T2 = final temperature of the gas (in Kelvin)

Step-by-Step Calculation

Let’s break down the problem using the information provided:

• The initial volume (V1) is 39.4 mL.
• The initial temperature (T1) is 24.4 °C, which we need to convert to Kelvin:

T1 = 24.4 + 273.15 = 297.55 K

• The final volume (V2) is 39.6 mL.
• We need to find the final temperature (T2), which corresponds to the freezing point of benzene.

Applying Charles's Law

Now we can plug the values into the Charles's Law equation:

V1/T1 = V2/T2

Substituting the known values:

39.4 mL / 297.55 K = 39.6 mL / T2

Solving for T2

To find T2, we can rearrange the equation:

T2 = (39.6 mL * 297.55 K) / 39.4 mL

Now, calculating T2:

T2 = (39.6 * 297.55) / 39.4

T2 ≈ 297.96 K

Converting Back to Celsius

Finally, we convert T2 back to Celsius to find the freezing point of benzene:

Freezing Point = T2 - 273.15

Freezing Point ≈ 297.96 - 273.15 ≈ 24.81 °C

Final Result

The freezing point of benzene, based on the gas volume changes, is approximately 24.81 °C. This calculation illustrates how gas behavior can be used to infer temperature changes in a controlled environment.