Problem 53 - Chemistry The Central Science In Si Units

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 two containers?

Step-by-Step Solution

Answer

(a) Both pans have water at 100°C. (b) Both containers have the same vapor pressure.

Step 1: Analyze Boiling Water Temperatures

When water is boiling, it means it has reached its boiling point. The boiling point for water at standard atmospheric pressure is 100°C (212°F). Regardless of how vigorously or gently the water is boiling, the temperature of the water remains at its boiling point, 100°C. Thus, although one pan is boiling more vigorously, both pans have water at the same temperature.

Step 2: Understand Boiling Intensity Effects

The intensity of boiling, such as vigorous or gentle boiling, reflects the rate of heat input and steam production, but it does not change the boiling temperature under constant atmospheric conditions.

Step 3: Consider Vapor Pressure Dependencies

Vapor pressure depends on the temperature of the liquid, not the size or volume of the container. If both the large and small containers are at the same temperature, their vapor pressures are also the same. This is because vapor pressure is a function of the surface liquid temperature alone.

Step 4: Relate Vapor Pressure to Container Size

Since vapor pressure is determined solely by temperature, the size of the container does not affect it. Therefore, both containers will have the same vapor pressure if they are at the same temperature.

Key Concepts

Vapor Pressure

Vapor pressure is a key concept when examining boiling and other phase transitions. It refers to the pressure exerted by the vapor in equilibrium with its liquid. When a liquid is in a closed container, molecules of the liquid evaporate and exert pressure over the liquid surface. This pressure is the vapor pressure, which mainly depends on the liquid's temperature.

As temperature increases, more molecules have enough kinetic energy to escape the liquid's surface, increasing the vapor pressure. It's important to note that vapor pressure is not influenced by the amount of liquid or the size of the container. Essentially, as long as temperature remains constant, so does the vapor pressure. This is why both a large and small container of water at the same temperature will exhibit the same vapor pressure.

• Vapor pressure increases with temperature.
• Not dependent on liquid volume or container size.
• Important in determining when a liquid will start boiling.

Heat Input

The concept of heat input is crucial in understanding how boiling occurs. Heat input refers to the amount of thermal energy added to a substance. In our context, when water is heated, energy is being added, and this energy is required to bring water to its boiling point.

Once water reaches its boiling point, any additional heat input does not increase the temperature but rather increases the rate of vaporization. This is why water can boil vigorously without a change in temperature. The amount of heat supplied influences how aggressively the water vaporizes, but it doesn’t alter the boiling temperature.

• Heat raises the temperature to the boiling point.
• Additional heat increases the rate of evaporation, not temperature.
• Quantity of heat input affects boiling intensity.

Boiling Intensity

Boiling intensity, often thought of as either vigorous or gentle, is a measure of how energetically boiling occurs. While it might seem like boiling intensity might be related to temperature, it is actually determined by the amount of heat supplied.

At the boiling point, water bubbles form rapidly and rise to the surface, and the intensity simply indicates how rapid this process is occurring. A more vigorous boil means a higher rate of bubble formation and steam production due to greater heat input.

Despite the differing intensities, the water boils at a steady temperature, demonstrating that boiling intensity and temperature are not directly linked. Instead, the intensity is directly influenced by the thermal energy being applied.

• Boiling can be vigorous or gentle.
• Determined by the heat input rate.
• Does not affect the boiling temperature.