Question

A flask of hydrogen gas is collected at 1.023 atm and \(35^{\circ} \mathrm{C}\) by displacement of water from the flask. The vapor pressure of water at \(35^{\circ} \mathrm{C}\) is \(42.2 \mathrm{mm} \mathrm{Hg}\). What is the partial pressure of hydrogen gas in the flask?

Short answer

The partial pressure of hydrogen gas in the flask is \(0.9675 \mathrm{atm}\).

Step-by-step solution

Convert given units to atm

The vapor pressure of water is given in mm Hg. Convert this value to atm. Use the conversion factor 1 atm = 760 mm Hg. Vapor pressure of water (in atm) = \(\frac{42.2 \mathrm{mm} \mathrm{Hg}}{760 \mathrm{mm} \mathrm{Hg} \cdot \mathrm{1} \mathrm{atm}} = 0.0555 \mathrm{atm}\).

Use Dalton's Law of Partial Pressures

According to Dalton's Law of Partial Pressures, the total pressure in the flask (1.023 atm) is the sum of the partial pressures of hydrogen gas and water vapor. In other words, \(P_{total} = P_{H_2} + P_{H_2O}\). We have the total pressure and the vapor pressure of water. Plug in the values and solve for the partial pressure of hydrogen gas. \(P_{H_2} = P_{total} - P_{H_2O} = 1.023 \mathrm{atm} - 0.0555 \mathrm{atm}\).

Calculate the partial pressure of hydrogen gas

Subtract the vapor pressure of water from the total pressure to find the partial pressure of hydrogen gas. \(P_{H_2} = 1.023 \mathrm{atm} - 0.0555 \mathrm{atm} = 0.9675 \mathrm{atm}\). The partial pressure of hydrogen gas in the flask is 0.9675 atm.

Key concepts

Partial Pressure

In the realm of gases, partial pressure is an essential concept that indicates the pressure exerted by a single type of gas within a mixture. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the individual partial pressures of each gas present. If you have a mixture of gases like hydrogen and water vapor, each one contributes to the total pressure.

For example, if the total pressure inside a flask is 1.023 atm and it contains both hydrogen gas and water vapor, the partial pressure of each gas can be determined by subtracting the pressures of the other constituents from the total pressure. Using Dalton’s Law, you can find the partial pressure of hydrogen gas in the flask by calculating the difference between the total pressure and the vapor pressure of water.

Vapor Pressure

Vapor pressure is the pressure exerted by the vapor of a liquid in equilibrium with its liquid phase. This concept is crucial, particularly when gases are collected by water displacement. When you collect a gas like hydrogen over water, the space above the water contains both the gas and water vapor.

At a given temperature, water exerts a known vapor pressure, which can be found in charts or tables. In the problem, the vapor pressure of water at 35°C is given as 42.2 mm Hg. If you want to find the pressure due to the gas alone, you need to account for this vapor pressure and use it to adjust the measured total pressure.

Hydrogen Gas

Hydrogen gas is the simplest and most abundant element in the universe. It is composed of diatomic molecules, each containing two hydrogen atoms. When studying gases, hydrogen serves as a common subject because of its simple properties and ubiquitous nature.

In experiments, hydrogen is often collected over water, where it displaces water and produces a mixture of hydrogen and water vapor. To find the actual pressure due to hydrogen within the flask, it’s essential to consider how much pressure is from the water vapor and then apply Dalton's Law to determine the hydrogen's partial pressure.

Unit Conversion

Unit conversion plays a significant role when dealing with different measures of pressure. Pressures can be measured in several units, such as millimeters of mercury (mm Hg) and atmospheres (atm). Ensuring uniformity in units is vital for accurate calculations.

For instance, in the exercise, the vapor pressure of water is initially provided in mm Hg. To use Dalton's Law effectively, you need to convert this pressure to atmospheres using the conversion factor, where 1 atm equals 760 mm Hg. Performing this conversion ensures that all pressures are in the same units, simplifying the process and avoiding errors in calculations.