Problem 45 - Chemistry Matter and Change

Question

What is the partial pressure of water vapor in an air sample when the total pressure is 1.00 atm, the partial pressure of nitrogen is 0.79 atm, the partial pressure of oxygen is 0.20 atm, and the partial pressure of all other gases in air is 0.0044 atm?

Step-by-Step Solution

Answer

The partial pressure of water vapor is 0.0056 atm.

Step 1: Understand Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture. The relationship is given by the formula: \[ P_{total} = P_{N_2} + P_{O_2} + P_{other} + P_{H_2O} \] where \(P_{total}\) is the total pressure, and \(P_{N_2}, P_{O_2}, P_{other}, P_{H_2O}\) are the partial pressures of nitrogen, oxygen, other gases, and water vapor, respectively.

Step 2: Set Up the Equation

Given the problem, we identify the known variables: \(P_{total} = 1.00\) atm, \(P_{N_2} = 0.79\) atm, \(P_{O_2} = 0.20\) atm, and \(P_{other} = 0.0044\) atm. We need to solve for \(P_{H_2O}\), the partial pressure of water vapor. Substitute the known values into the formula from Step 1:\[ 1.00 = 0.79 + 0.20 + 0.0044 + P_{H_2O} \]

Step 3: Solve for Partial Pressure of Water Vapor

Rearrange the equation to isolate \(P_{H_2O}\): \[ P_{H_2O} = 1.00 - (0.79 + 0.20 + 0.0044) \]Calculate the sum of the known partial pressures: \[ P_{H_2O} = 1.00 - 0.9944 = 0.0056\] atm.

Key Concepts

Partial Pressure

Partial pressure is an essential concept when studying gases, especially when dealing with gas mixtures. It refers to the pressure that a single gas component in a mixture would exert if it occupied the entire volume by itself. It helps us understand how much a particular gas contributes to the overall pressure of the mixture.

This concept is critical in fields such as chemistry and physics, where mixtures of gases are common.

• The partial pressure is denoted by the symbol \( P \) with a subscript denoting the specific gas (e.g., \( P_{N_2} \) for nitrogen).
• Partial pressures allow us to predict how gases will behave, react, or dissolve in different situations.

Understanding partial pressure also aids in calculating other properties of the gas, such as its concentration or role in chemical reactions.

Gas Mixture

A gas mixture involves combining two or more gases, each contributing to the total pressure. In many everyday contexts, air is the gas mixture most encountered. Air itself is mainly composed of oxygen, nitrogen, water vapor, and trace gases.

When examining a gas mixture, it's crucial to understand how each gas component contributes to the overall properties of the mixture. Each gas in the mixture retains its own chemical properties and exerts its own partial pressure.

• The behavior of each gas component is described by its partial pressure.
• In a mixture, gases interact and influence factors such as diffusion, reaction rates, and thermal conductivity.

Knowing the composition and individual contributions of a gas mixture is vital for predicting and manipulating its behavior in different contexts, such as biological systems, industrial processes, and environmental monitoring.

Total Pressure

Total pressure is the cumulative pressure exerted by all the gas components in a gas mixture. According to Dalton's Law of Partial Pressures, the total pressure is the sum of the partial pressures of each individual gas in the mixture.

Dalton's Law is mathematically expressed as:\[ P_{total} = P_{N_2} + P_{O_2} + P_{other} + P_{H_2O} \]where \( P_{total} \) represents the total pressure and the terms on the right side represent the partial pressures of nitrogen, oxygen, other gases, and water vapor, respectively.

• Total pressure is helpful in determining the concentration of gases in a mixture.
• Understanding total pressure is pivotal when dealing with systems under pressure, like scuba diving, aviation, and chemical industries.

By knowing the total pressure, we can determine how different gases contribute to the system and predict how they will behave under different conditions.

Water Vapor Pressure

Water vapor pressure refers to the partial pressure of water vapor present in a gas mixture. It indicates the contribution of water vapor to the total pressure. Understanding this concept is crucial as it influences various natural and industrial processes, including weather patterns and physical changes in materials.

In our context, we seek to determine how much water vapor contributes to the air sample's total pressure. Water vapor pressure plays a key role in

• Regulating humidity levels in the atmosphere.
• Affecting thermal comfort and meteorological phenomena.

To find the water vapor pressure in a mixture, one can rearrange Dalton's Equation to isolate the water vapor component and solve for its partial pressure. This can reveal insights into evaporation, condensation, and gas solubility events.