Question

(a) Two pans of water are on different burners of a stove. One pan of water is boiling vigorously, while the other is boiling gently. What can be said about the temperature of the water in the two pans? (b) A large container of water and a small one are at the same temperature. What can be said about the relative vapor pressures of the water in the containers?

Short answer

(a) The temperature of the water in both pans is equal to the boiling point of water, which is 100°C (212°F) at standard atmospheric pressure. The boiling intensity does not affect the temperature as long as the atmospheric pressure is constant. (b) The vapor pressures of the water in both the large and small containers are the same since vapor pressure depends on the temperature and the nature of the substance, not the size of the container.

Step-by-step solution

Understanding the boiling point and vapor pressure

Boiling point is the temperature at which the vapor pressure of a liquid equals the external pressure. Vapor pressure is the pressure exerted by the vapor in equilibrium with its liquid at a given temperature. It depends on the temperature and the nature of the substance.

Analyzing the temperature of water in two pans

(a) In this case, we have two pans of water on different burners of a stove. One pan is boiling vigorously, while the other is boiling gently. Since both pans are boiling, the temperature of the water in both pans is equal to the boiling point of water, which is 100°C (212°F) at standard atmospheric pressure. Regardless of how vigorously or gently the water is boiling, the temperature remains constant at the boiling point as long as the atmospheric pressure is constant.

Analyzing the vapor pressure in a large and small container

(b) When we have a large container of water and a small one at the same temperature, the vapor pressures of the water in both containers are also the same. This is because vapor pressure is dependent on the temperature and the nature of the substance, not the size of the container. So, when both containers are at the same temperature, their vapor pressures are the same, regardless of the container's size.

Key concepts

Vapor Pressure

Vapor pressure is a fascinating topic that explains a lot about how substances change from liquid to vapor. It's the pressure exerted by the vapor that forms above a liquid in a closed container, and it reaches an equilibrium with the liquid below. At a given temperature, this pressure remains constant for a specific substance. This is because, at equilibrium, the rate at which molecules evaporate from the liquid to become vapor is equal to the rate at which they condense back into the liquid.

• Vapor pressure depends on temperature: As temperature increases, the kinetic energy of the particles also rises, leading to more particles entering the vapor phase and increasing the vapor pressure.
• The nature of the substance also affects vapor pressure: Different liquids have different tendencies to evaporate due to the nature of their intermolecular forces.

Thus, even if you have two containers, one large and one small, as long as they hold the same liquid at the same temperature, the vapor pressure will be the same.

Temperature

Temperature plays a crucial role in determining when boiling occurs in a liquid. It's a measure of the average kinetic energy of the particles in a substance. In the context of boiling, it sets the stage for understanding when a liquid transforms into a gas.

• Boiling occurs at a specific temperature called the boiling point, where the vapor pressure of the liquid equals the external atmospheric pressure.
• Even if two pots of water are boiling differently—one vigorously and one gently—the temperature of the water in both is the same if the atmospheric pressure remains constant.

This means that for water, as long as you're at sea level (standard atmospheric pressure), the temperature remains fixed at 100°C whether the boil is gentle or vigorous. The energy added by turning up the heat is used to convert more liquid into vapor, not to increase the temperature.

Phase Equilibrium

Phase equilibrium is a state where different phases of a substance coexist without net change. At phase equilibrium, the conditions allow a balanced transformation between phases such as solid, liquid, and gas. This is prominently observed during boiling.

• During boiling, liquid water and its vapor phase are in equilibrium.
• The temperature of the water remains constant at the boiling point as long as equilibrium is maintained.
• At this point, any added energy does not increase the temperature but provides the energy needed for the phase transition from liquid to gas.

Thus, in phase equilibrium, the system stabilizes, showing both vapor and liquid phases in balance. This understanding helps us see why, despite varying degrees of boil, the temperature and vapor pressures behave consistently.