Question

Describe how you would measure, by either chemical or physical means, the partial pressures of a mixture of gases of the following composition: (a) \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\), (b) \(\mathrm{He}\) and \(\mathrm{N}_{2}\).

Short answer

Use chemical absorption for CO2 and H2, and cooling for He and N2.

Step-by-step solution

Understand the Context of Partial Pressure

Partial pressure is the pressure that each gas in a mixture would exert if it occupied the entire volume by itself at the same temperature. In a mixture of gases, the total pressure is the sum of the partial pressures of all the individual gases present.

Choose the Appropriate Method for CO2 and H2 Mixture

For a mixture of CO2 and H2, use the chemical absorption method to selectively remove CO2. Pass the gas mixture through a solution of a base, such as potassium hydroxide (KOH), to absorb CO2. Measure the pressure before and after this process. The decrease in pressure represents the partial pressure of CO2. The remaining pressure is the partial pressure of H2.

Measure Initial Total Pressure for He and N2

For the mixture of He and N2, begin by measuring the total pressure of the gas mixture using a manometer or pressure sensor to obtain the combined pressure exerted by both gases.

Use Physical Separation to Determine Individual Pressure of He

Cool the gas mixture to a very low temperature, near the liquefaction temperature of N2 but above that of He. N2 will condense into a liquid while He remains in gaseous form. Measure the pressure of the remaining gas to determine the partial pressure of He. The difference between the total pressure and the pressure of He will give the partial pressure of N2.

Key concepts

Understanding Gas Mixtures

When we talk about gas mixtures, we are referring to a combination of different gases, which occupy the same space. Imagine a container filled with various gases; each gas exerts its own pressure within that container. The behavior of gases in a mixture is guided by Dalton’s Law of Partial Pressures. This law states that the total pressure exerted by a gas mixture is the sum of the partial pressures of all individual gases present. Each gas in the mixture acts independently, as though it alone occupies the whole volume of the mixture. Hence, understanding this concept is crucial to measuring partial pressures in gas mixtures. Measuring these partial pressures accurately is essential for various applications including scientific experiments and industrial processes. It is the baseline for more specific methods used in practical situations.

Understanding the Chemical Absorption Method

The chemical absorption method is a clever way to separate specific gases from a mixture, such as CO2 from a mixture of CO2 and H2. This method involves using a chemical solution that selectively reacts with one of the gases. In this process, the gas mixture is passed through a solution that absorbs one of the components—often using substances like potassium hydroxide (KOH). When CO2 interacts with a KOH solution, it forms potassium carbonate, thus removing CO2 from the mixture. This absorption causes a decrease in the pressure, which precisely indicates the partial pressure of the absorbed gas. Once the CO2 is removed, the remaining pressure in the container directly correlates to the partial pressure of H2. By comparing pressures before and after the chemical process, you can determine the individual partial pressures in the gas mixture.

How a Manometer Works

A manometer is a device used to measure pressure, which operates based on the balance of liquid columns. It's an essential tool when working with gas mixtures, like He and N2. A simple manometer consists of a U-shaped tube filled with a liquid, typically mercury or water. When a gas is introduced, the pressure it exerts causes the liquid in the tube to move, allowing you to measure the pressure exerted by the gas. In practice, the difference between the liquid levels on each side of the U-tube corresponds to the pressure of the gas. This reading is directly translated into the total pressure of the gas mixture. Initial measurements obtained from a manometer help in understanding how to separate gases later, as this sets the baseline for any further physical separation techniques, like cooling the gas mixture.

Principles of Liquefaction for Gas Separation

Liquefaction involves cooling a gas until it becomes a liquid, a principle that is used to separate gases, especially when dealing with mixtures like He and N2. Each gas has a unique temperature at which it changes from a vapor to a liquid, called the liquefaction temperature. By lowering the temperature of a gas mixture, gases with higher liquefaction temperatures can be liquefied and separated from those with lower ones. For instance, cooling a mixture of He and N2 close to the liquefaction point of N2 results in N2 turning into liquid. Helium, having a much lower liquefaction point, remains gaseous. After liquefying N2, the remaining pressure measured is from helium, indicating its partial pressure. This process provides a clear method for determining the partial pressures of gases in a mixture by physically separating them based on their liquefaction temperatures.