Question

a student measures the ratio (\frac{p}{t}) for a sample of gaseous (c_{2}h_{4}) at three different volumes in a sealed syringe of variable - volume. at all times the syringe is held at a temperature of 300 k. the data are shown in the table.

volume	ratio (\frac{p}{t})
10.0 ml	0.0790
5.00 ml	0.0718

10 which of the following best explains the trend in the data as the volume decreases? a the (c_{2}h_{4}) molecules decompose as the volume decreases, creating more moles of gas. b the volume of the (c_{2}h_{4}) molecules becomes more significant as the volume decreases. c the intermolecular forces between (c_{2}h_{4}) molecules become more significant. d the average kinetic energy of the (c_{2}h_{4}) molecules decreases as the volume decreases.

Explanation:

Step1: Analyze option A

There is no indication that $C_{4}H_{8}$ molecules decompose under these conditions. No chemical reaction evidence is given in the problem - context, so this option is incorrect.

Step2: Analyze option B

The volume of the molecules themselves is not the main factor here. The focus is on the behavior of the gas as a whole with volume - change, and the volume of individual molecules doesn't explain the trend in the $\frac{P}{T}$ ratio, so this option is incorrect.

Step3: Analyze option C

As the volume decreases, the intermolecular forces between $C_{4}H_{8}$ molecules become more significant. Real - gas behavior starts to deviate from ideal - gas behavior. Ideal gas law assumes negligible intermolecular forces. When volume is reduced, the molecules are closer together and intermolecular forces play a larger role, which can explain the change in the $\frac{P}{T}$ ratio. This option is correct.

Step4: Analyze option D

The temperature is held constant at 300 K. Average kinetic energy is directly proportional to temperature ($KE=\frac{3}{2}kT$). Since $T$ is constant, the average kinetic energy of the $C_{4}H_{8}$ molecules does not change, so this option is incorrect.

Answer:

C. The intermolecular forces between $C_{4}H_{8}$ molecules become more significant as the volume decreases.