A sample of octane in equilibrium with its vapor in a closed 1.0 L container has a vapor pressure of 50 torr at 45oC. The container’s volume is increased to 2.0 L at constant temperature and equilibrium is re-established. What is the vapor pressure?
The answer I got was 25 torr, but the correct answer is 50 torr. Why would the pressure not half when the volume is doubled?
vapor pressure is a characteristic of the equilibrium between a liquid and a vapor at a given temperature. It does not depend on volume.
The color of the sky is blue, it does not matter how much of the sky one sees.
The pressure of a gas does not always decrease by half when the volume is doubled, as in the case of the sample of octane in your question. The reason for this lies in Le Chatelier's principle.
Le Chatelier's principle states that when a system is at equilibrium, any changes imposed on the system will cause it to adjust in a way that counteracts the change. In this case, increasing the volume of the container results in a reduction in the concentration of the gas molecules in the system.
When the volume increases from 1.0 L to 2.0 L, the concentration of octane molecules decreases. According to Le Chatelier's principle, the system will attempt to counteract this change by favoring the forward reaction, which in this case is the evaporation of octane to form vapor.
By favoring the forward reaction, more octane molecules will evaporate to maintain equilibrium. Therefore, the number of octane molecules in the gas phase remains relatively constant despite the increase in volume. As a result, the vapor pressure remains at 50 torr, instead of decreasing to 25 torr.
In this scenario, the decrease in concentration caused by doubling the volume is compensated by an increase in the rate of evaporation of octane, so the system can maintain the same equilibrium vapor pressure.