Question

A beaker of water is placed in a closed container. Predict the effect on the vapor pressure of the water when (a) its temperature is lowered, (b) the volume of the container is doubled, (c) more water is added to the beaker.

Short answer

The vapor pressure of the water will (a) decrease when its temperature is lowered, (b) remain the same when the volume of the container is doubled, and (c) remain the same when more water is added to the beaker.

Step-by-step solution

Analyze the effect of temperature on vapor pressure

Vapor pressure of a liquid is the pressure exerted by its vapor when the liquid and vapor are in equilibrium. It's affected by the temperature of the liquid, due to the fact that increasing temperature increases the kinetic energy of the molecules, this will make more molecules escape from the liquid phase to the gas phase thus increasing the vapor pressure. Therefore, when the temperature is lowered, the vapor pressure of the water will decrease.

Analyze the effect of container volume on vapor pressure

When the volume of the closed container is doubled, the overall pressure will decrease since pressure is inversely proportional to volume \(P = \frac{nRT}{V}\) (according to the ideal gas law), where P is the pressure, n is number of moles, R is the gas constant, T is temperature and V is volume. However, the vapor pressure is a property of the liquid itself and is not affected by the total volume of the container as it only depends on the temperature and the nature of the liquid.

Analyze the effect of additional water on vapor pressure

Adding more water to the beaker doesn't affect the vapor pressure. Vapor pressure is a surface phenomena, so only the temperature and the nature of the liquid can change it. Increasing the amount of water will just increase the time it takes to reach equilibrium.