Question

Cyclopropane and oxygen at partial pressures 170 torr and 570 torr are mixed in a gas cylinder. What is the ratio of the number of moles of cyclopropane to the number of moles of oxygen?

• A. $\frac{170\times42}{570\times32}=0.39$
• B. $\frac{170}{42}\Bigg/\Bigg(\frac{170}{42}+\frac{570}{32}\Bigg)\approx0.19$
• C. $\frac{170}{740}=0.23$
• D. $\frac{170}{570}=0.30$

Answer 1

The Correct Option is D

To determine the ratio of the number of moles of cyclopropane to the number of moles of oxygen, we need to use the relationship between the partial pressure of a gas and the number of moles, which can be derived from Dalton's law of partial pressures and the ideal gas law.

The ideal gas law is given by:

PV = nRT

where:

• P is the pressure,
• V is the volume,
• n is the number of moles,
• R is the universal gas constant,
• T is the temperature in Kelvin.

For a mixture of gases in a container, Dalton's law states that the total pressure is the sum of the partial pressures of the individual gases. Thus, the partial pressure of a gas is directly proportional to the number of moles of that gas if the volume and temperature are constant. Hence, the ratio of the moles of two gases can be determined directly by the ratio of their partial pressures.

Given:

• Partial pressure of cyclopropane, P_{\text{cyclopropane}} = 170 \, \text{torr}
• Partial pressure of oxygen, P_{\text{oxygen}} = 570 \, \text{torr}

The ratio of the number of moles of cyclopropane to the number of moles of oxygen is:

\text{Ratio} = \frac{n_{\text{cyclopropane}}}{n_{\text{oxygen}}} = \frac{P_{\text{cyclopropane}}}{P_{\text{oxygen}}} = \frac{170}{570}

Calculating this gives:

\frac{170}{570} = 0.298245614 \approx 0.30

Therefore, the correct answer is:

\frac{170}{570}=0.30

This aligns with the given correct option.