Question

We often collect small samples of gases in the laboratory by bubbling the gas into a bottle or flask containing water. Explain why the gas becomes saturated with water vapor and how we must take the presence of water vapor into account when calculating the properties of the gas sample.

Short answer

A gas bubbled through water becomes saturated with water vapor as it comes into contact with water molecules and equilibrium is reached between the evaporation and condensation of water molecules. When calculating the properties of the gas sample, we must consider the partial pressure of the water vapor. The total pressure of the gas sample is the sum of the partial pressures of the original gas and the water vapor. To account for the presence of water vapor, subtract the vapor pressure of water from the total pressure to find the partial pressure of the original gas. Use this partial pressure value when calculating the properties of the gas sample using the Ideal Gas Law or other relevant gas laws.

Step-by-step solution

Understanding gas saturation

When a gas is bubbled through water, the gas molecules come into contact with water molecules. As the gas and water interact, some of the water molecules evaporate and become part of the gas, creating a mixture of the original gas and water vapor. The process continues until equilibrium is reached, which means that the rate of water molecules evaporating is equal to the rate of water molecules condensing back into the water. At this point, the gas is said to be saturated with water vapor.

The partial pressure concept

In a mixture of gases, each gas component contributes to the total pressure exerted by the mixture. This contribution is known as the partial pressure of that specific gas and is directly proportional to its mole fraction in the mixture. Dalton's law of partial pressures states that the total pressure exerted by the mixture is equal to the sum of the partial pressures of each gas component. Consequently, we must consider the partial pressure of the water vapor present when analyzing the gas sample's properties.

Collecting the necessary data

To calculate the properties of the gas sample, we need to know the temperature and pressure of the system. We also need the vapor pressure of water at that particular temperature. The vapor pressure is the pressure exerted by the water vapor at equilibrium and can be found in steam tables or determined experimentally.

Accounting for water vapor presence

Since the gas is saturated with water vapor, the total pressure (P_total) of the gas sample is the sum of the partial pressures of the original gas (P_gas) and the water vapor (P_water_vapor). Using the formula: \[P_\text{total} = P_\text{gas} + P_\text{water vapor}\] We can find the partial pressure of the original gas by subtracting the vapor pressure of water from the total pressure: \[P_\text{gas} = P_\text{total} - P_\text{water vapor}\]

Calculating the properties of the gas sample

With the partial pressure of the original gas known, we can calculate its properties using the Ideal Gas Law or other relevant gas laws, but always using \(P_\text{gas}\) instead of \(P_\text{total}\). By doing this, we accurately account for the presence of water vapor and obtain a more precise understanding of the gas sample's properties.