Question

The vapour pressure of water at \(0^{\circ} \mathrm{C}\) is (1) \(76 \mathrm{~cm}\) (2) \(760 \mathrm{~cm}\) (3) \(0.1\) atm (4) \(0 \mathrm{~atm}\)

Short answer

The vapour pressure of water at 0°C is approximately 0.1 atm, matching option (3).

Step-by-step solution

Understand the Vapour Pressure

Vapour pressure is the pressure exerted by a vapour in equilibrium with its liquid at a given temperature. For water at different temperatures, it has been experimentally determined and tabulated.

Recall Standard Vapour Pressure of Water

At standard temperature and pressure, the vapour pressure of water is commonly known. Specifically, at 0°C, water has a typical vapour pressure.

Compare Given Options

Now, analyze the four options provided: (1) 76 cm, (2) 760 cm, (3) 0.1 atm, and (4) 0 atm. Convert any non-standard units if necessary.

Identify the Correct Option

Given the standard information, the vapour pressure of water at 0°C is well-documented to be approximately 0.1 atm. This matches the third option provided.

Key concepts

Vapour Pressure

Vapour pressure is a key concept in understanding how liquids and gases interact. When you have a liquid in a closed container, some of the liquid molecules escape into the air and become vapor. This vapor exerts a pressure on the surface of the liquid.
The vapour pressure is the pressure exerted by this vapor when the liquid and vapor are in equilibrium.
This means that the rate at which liquid molecules turn into vapor equals the rate at which vapor molecules condense back into liquid.
Vapour pressure depends on temperature. As temperature increases, more molecules have enough energy to escape into the vapor phase, leading to higher vapour pressure.
For example:

• At higher temperatures, the vapour pressure increases.
• At lower temperatures, the vapour pressure decreases.

In the problem, you are looking at the vapour pressure of water specifically at 0°C.

Equilibrium

Equilibrium in the context of vapour pressure refers to a state where the rate of evaporation of a liquid equals the rate of condensation of the vapor. In simpler terms, it’s when the number of molecules leaving the liquid equals the number of molecules returning.
This balance is crucial because it means that the vapour pressure is stable at a given temperature.
To understand it deeply:

• Imagine a closed container filled partly with liquid water. Initially, only evaporation happens, increasing the vapor in the container.
• As more molecules evaporate, they start to condense back into the liquid state once the space above the liquid becomes saturated with vapor.
• This point, where the rates of evaporation and condensation balance out, is the equilibrium point.

When temperatures stay constant, this equilibrium helps in defining the vapour pressure of that liquid at that temperature. In the exercise, we are considering the equilibrium state at 0°C.

Standard Temperature and Pressure

Standard temperature and pressure (STP) are conditions often used as reference points in measurements and experiments. At STP, the temperatures and pressures are set to define standard conditions for reactions and calculations.
Specifically, STP is defined as:

• A temperature of 0°C (273.15 K)
• A pressure of 1 atm

Knowing this allows chemists and physicists to compare different sets of data under consistent conditions. In the context of your exercise, STP helps in understanding and comparing the vapour pressure of water. At 0°C (one of the conditions of STP), the vapour pressure of water is approximately 0.1 atm.
This means at 0°C, the water has a very low tendency to convert to vapor due to low thermal energy available to its molecules, which results in a lower vapour pressure.