Assume that you have a liquid in a cylinder equipped with a movable piston. There is no air in the cylinder, the volume of space above the liquid is 200 mL, and the equilibrium vapor pressure above the liquid is 28.0 mm Hg. What is the equilibrium pressure above the liquid when the volume of space is decreased from 200 mL to 100 mL at constant temperature?

Verified step by step guidance

1. Identify that the problem involves the concept of gas laws, specifically Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure and volume of the gas are inversely proportional.
2. Write down the initial conditions given: initial volume (V1) = 200 mL, initial pressure (P1) = 28.0 mm Hg.
3. Note the final condition given: final volume (V2) = 100 mL. The temperature remains constant.
4. Apply Boyle's Law, which is expressed as P1 * V1 = P2 * V2, where P2 is the final pressure that needs to be calculated.
5. Rearrange the equation to solve for P2: P2 = (P1 * V1) / V2. Substitute the known values into this equation to find the final pressure.

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. It reflects the tendency of particles to escape from the liquid phase into the vapor phase. In this scenario, the equilibrium vapor pressure of 28.0 mm Hg indicates the pressure exerted by the vapor when the system is at equilibrium, regardless of the volume of the container.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. Although the liquid is not a gas, the behavior of the vapor above the liquid can be approximated using this law, especially when considering changes in volume and pressure. In this case, as the volume decreases, the pressure of the vapor will adjust according to the principles of gas behavior.

Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is subjected to a change in conditions, the system will adjust to counteract that change and restore a new equilibrium. In this question, decreasing the volume above the liquid will increase the pressure of the vapor until a new equilibrium is established, demonstrating how the system responds to the change in volume.