Problem 4 - Chemistry Matter and Change

Question

What is the partial pressure of hydrogen gas in a mixture of hydrogen and helium if the total pressure is 600 mm Hg and the partial pressure of helium is 439 mm Hg?

Step-by-Step Solution

Answer

The partial pressure of hydrogen gas (P_H2) in the mixture can be found using Dalton's Law of Partial Pressures. Given the total pressure (P_total) of 600 mm Hg and the partial pressure of helium (P_He) as 439 mm Hg, we can calculate P_H2 as: \[P_{H2} = P_{total} - P_{He} = 600 \,\textrm{mm Hg} - 439 \,\textrm{mm Hg} = 161 \,\textrm{mm Hg}\] Thus, the partial pressure of hydrogen gas in the mixture is \(161 \,\textrm{mm Hg}\).

Step 1: Write down the given information

We are given the following information: - The total pressure of the gas mixture (P_total) is 600 mm Hg. - The partial pressure of helium (P_He) is 439 mm Hg. We need to find the partial pressure of hydrogen gas (P_H2).

Step 2: Use the formula for total pressure to find the partial pressure of H2

According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of its components. Mathematically, it can be written as: \[P_{total} = P_{H2} + P_{He}\] We need to find \(P_{H2}\), so we can rearrange the formula to: \[P_{H2} = P_{total} - P_{He}\]

Step 3: Substitute the given values and solve for P_H2

Substitute the given values for \(P_{total}\) and \(P_{He}\) into the equation and find the partial pressure of hydrogen gas. \(P_{H2} = 600 \,\textrm{mm Hg} - 439 \,\textrm{mm Hg}\)

Step 4: Calculate P_H2

Perform the subtraction to find the partial pressure of hydrogen gas: \(P_{H2} = 161 \,\textrm{mm Hg}\) So, the partial pressure of hydrogen gas in the mixture is 161 mm Hg.

Key Concepts

Partial Pressure

In a gas mixture, each gas component exerts its own pressure independently of the others. This is known as "partial pressure." Think of it as the pressure contribution of an individual gas in a mixture. Even though gases are mixed, each one behaves as if it were alone in the container. This concept helps us understand how gases behave when combined.

The partial pressure of a gas can be expressed in units such as mm Hg, atmospheres (atm), or Pascals (Pa). The important thing to remember is that the partial pressure of a gas is related to the amount of that gas present and the temperature of the mixture. According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of all gases present.

• Each gas in a mixture has its own partial pressure.
• Partial pressures add up to the total pressure.
• Partial pressure is proportional to the number of moles of the gas, assuming constant temperature.

Total Pressure

The total pressure of a gas mixture is the combined pressure exerted by all the gases in the mixture. It is a fundamental concept in understanding gas behavior. In our example with hydrogen and helium, the total pressure of 600 mm Hg is the sum of the pressures from both gases.

According to Dalton's Law of Partial Pressures, total pressure can be calculated by adding up the partial pressures of each gas component. If you have the partial pressures of the gases, finding the total pressure is straightforward.

• The formula is: \( P_{total} = P_1 + P_2 + \ldots + P_n \)
• The total pressure gives a comprehensive picture of the gas mixture's behavior.
• Knowing either the total pressure or partial pressures allows you to compute the missing value using Dalton's Law.

Understanding total pressure is crucial for applications in real-world scenarios like breathing air composition, industrial processes, and more.

Gas Mixtures

A gas mixture is a combination of two or more gases that are present together in a container. These gases occupy the same volume but still exert their own individual pressures. Our exercise involving hydrogen and helium is a perfect example of a gas mixture.

In a gas mixture, each gas behaves according to its characteristics, which brings us to the concept of partial pressures—where each gas contributes its own part to the total pressure. Despite being mixed, each gas is "invisible" to the others, maintaining its own set of properties.

• Gas mixtures may include gases like oxygen, nitrogen, carbon dioxide, and more common in air.
• The components of a gas mixture do not chemically combine; they coexist separately.
• This property allows us to use Dalton's Law to calculate pressures effectively.

Gas mixtures are widespread in environmental science, medical applications, and chemical studies. Understanding the behavior of gas mixtures helps in figuring out concentrations and interactions within a mixture.