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?

Short answer

(a) The temperature of the water in both pans is the same, probably around 100°C. The difference between boiling vigorously and gently is the rate at which the water is turning into vapor, which does not affect the temperature. (b) Since the large container and the small one are at the same temperature, their vapor pressures will also be the same. The size of the container does not affect the vapor pressure of the substance when both are at the same temperature.

Step-by-step solution

a) Compare the temperature of water in two pans

To determine the temperature of water in the two pans, we need to understand the concept of boiling point. Water boils at a specific temperature, which is 100°C (212°F) at sea level. At this temperature, the water molecules have enough energy to turn into vapor. Once water reaches its boiling point and starts boiling, it remains at the same temperature, no matter how vigorous the boiling looks. The amount of heat determines the vigor of boiling, which indicates how quickly the water molecules are turning into vapor. The temperature of the water in two pans can be said to be the same because they are both boiling, probably around 100°C. The difference between boiling vigorously and gently is the rate at which the water is turning into vapor, which does not affect the actual temperature of the water.

b) Compare the vapor pressures of water in two containers

To compare the vapor pressures of water in a large container and a small one, we need to understand the concept of vapor pressure. Vapor pressure is the pressure exerted by the vapor present above a liquid held in equilibrium with the vapor. It depends only on the temperature and the properties of the substance, not on the amount of liquid or the size of the container. Since the large container and the small one are at the same temperature, their vapor pressures will also be the same. The size of the container does not affect the vapor pressure of the substance when both are at the same temperature.

Key concepts

Vapor Pressure

Vapor pressure is a fascinating concept in chemistry that describes the pressure exerted by the vapor present above a liquid when the liquid and vapor are in equilibrium. This means that the rate at which molecules are escaping from the liquid to the vapor phase is equal to the rate at which vapor molecules are returning to the liquid. Importantly, vapor pressure is determined solely by the temperature and the nature of the liquid, rather than the volume of the liquid or the size of the container holding the liquid.

In practical terms, if two containers of water are at the same temperature, their vapor pressures will also be equal. This is because the energy provided to the molecules is the same in both cases, leading to equivalently energetic escape and return rates between the liquid and vapor phases, irrespective of the container size.

This property is crucial in understanding how liquids evaporate or boil under different conditions, and it also explains why the vapor pressure of pure substances can be found in standard tables for different temperatures.

Equilibrium

Equilibrium occurs when a system is in a state of balance with no net change over time. In the context of vapor pressure, equilibrium refers to the condition where the rate of evaporation of a liquid matches the rate of condensation of its vapor. At this point, the pressure exerted by the vapor remains constant, and this is known as vapor pressure.

This concept of equilibrium is central to understanding the behavior of boiling water. When water in a pan reaches its boiling point, it achieves a dynamic equilibrium: the number of water molecules escaping from the liquid to form steam equals the number coming back as water. This is why boiling water maintains a constant temperature even though it appears different in vigor. Vigorous boiling simply means more molecules are transitioning per unit time, but the temperature is unchanged.

The significance of equilibrium extends to many areas in chemistry, helping predict how reactions progress and how substances behave under different conditions.

Temperature

Temperature is a fundamental concept that measures the average kinetic energy of molecules in a substance. It plays a critical role in determining the physical state of substances and their phase changes, like boiling and condensing.

At a specified atmospheric pressure, like at sea level, water boils at 100°C (212°F). This boiling point is fixed; thus, when heating multiple pans of water on a stove, both will eventually reach and maintain this temperature as they boil. The excitement in the boiling behavior — whether gentle or vigorous — does not alter the temperature; rather, it indicates how rapidly molecules are leaving the liquid phase to become vapor.

Understanding temperature helps in predicting how substances interact, how fast chemical and physical processes happen, and it is key in explaining why different substances have different responses to heat.

Phase Changes

Phase changes describe the transformations between different states of matter: solid, liquid, and gas. Water exhibits these transformations in various forms, such as melting, freezing, condensation, and boiling. These processes are highly influenced by changes in temperature and pressure.

During boiling, for instance, water transitions from liquid to gas. This change occurs when the temperature reaches the boiling point, where the vapor pressure of the water equals the external atmospheric pressure. At this juncture, energy input converts liquid water into vapor without increasing temperature.

Conversely, condensation is the transformation from vapor back to liquid, usually caused by cooling, which lowers vapor pressure below the atmospheric pressure. These phase changes are vital in numerous natural phenomena and industrial processes, such as weather systems and the distillation of liquids, owing to their predictable behavior based on temperature and pressure manipulation.