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 in the air sample is 0.0056 atm, which is calculated using Dalton's Law of partial pressures and the given values for the total pressure and partial pressures of nitrogen, oxygen, and other gases.

Step 1: Write Dalton's Law of partial pressures formula

Dalton's law of partial pressures states that the total pressure in a mixture of gases is equal to the sum of the partial pressures of each individual gas. The formula for Dalton's law is: Total pressure (P_total) = Pressure of nitrogen (P_N2) + Pressure of oxygen (P_O2) + Pressure of other gases (P_other) + Pressure of water vapor (P_H2O)

Step 2: Plug in the given values

We know the total pressure (1.00 atm), partial pressure of nitrogen (0.79 atm), partial pressure of oxygen (0.20 atm), and the partial pressure of all other gases (0.0044 atm). We can plug these values into the formula. 1.00 atm = 0.79 atm + 0.20 atm + 0.0044 atm + P_H2O

Step 3: Solve for the partial pressure of water vapor

Now, we can solve for the partial pressure of water vapor (P_H2O): P_H2O = 1.00 atm - 0.79 atm - 0.20 atm - 0.0044 atm P_H2O = 0.0056 atm

Step 4: State the final answer

The partial pressure of water vapor in the air sample is 0.0056 atm.

Key Concepts

Partial Pressure

Understanding partial pressure is key to grasping how gases behave in a mixture. When we talk about partial pressure, we refer to the pressure that a single type of gas in a mixture would exert if it were the only gas present in the container.
Each gas in a mixture contributes to the overall pressure based on its concentration and temperature.
Dalton's Law provides insight into this concept by stating:

• The total pressure is the sum of the partial pressures of all gases present.
• Each component gas contributes to total pressure proportional to its quantity, assuming ideal gas behavior.

This is crucial because it allows us to measure gases individually, even when they are part of a mixture.

Mixture of Gases

A mixture of gases is not uncommon in various scenarios, from Earth's atmosphere to lab environments. This mixture consists of different gases that are mingling together without reacting chemically.
For example, the air we breathe is a mixture of gases like nitrogen, oxygen, water vapor, carbon dioxide, and other trace gases.
In such a mixture:

• Each gas behaves independently but is subject to the same conditions of volume, temperature, and pressure as part of the mixture.
• The behavior of each gas affects the overall properties of the mixture, such as total pressure and temperature.

This independent behavior allows us to apply Dalton's Law to determine individual pressures within the mixture.

Pressure Calculation

Calculating pressure in a mixture of gases involves using tools like Dalton’s Law. This process is simpler than it sounds. We start by recognizing that:

• Total pressure in the container is the sum of the partial pressures of all individual gases.
• To find a specific gas's pressure, we rearrange the formula to solve for the unknown.

Let's break it down with an example:
Suppose the total pressure is 1.00 atm, with given partial pressures for nitrogen, oxygen, and other gases.
Introduce the equation from Dalton's Law: \[ P_{\text{total}} = P_{\text{N}_2} + P_{\text{O}_2} + P_{\text{other}} + P_{\text{H}_2\text{O}} \] Plugging in known values helps us isolate and calculate unknown partial pressures easily.

Gas Pressure in Atmospheres

In scientific studies, the pressure of gases is commonly measured in atmospheres (atm). This unit is convenient because it represents a standard atmospheric pressure at sea level on Earth.
Understanding this measurement scale is vital for interpreting gas laws and atmospheric phenomena.
When working with gases:

• 1 atm is equivalent to the Earth's atmospheric pressure, making it a familiar baseline.
• Partial pressures often are given in atm, allowing easy calculations using Dalton’s Law.

By using atmospheres, scientists can communicate findings effectively and maintain accuracy when comparing gas behaviors under different conditions.