Problem 46 - Chemistry Matter and Change

Question

What is the total gas pressure in a sealed flask that contains oxygen at a partial pressure of 0.41 atm and water vapor at a partial pressure of 0.58 atm?

Step-by-Step Solution

Answer

The total gas pressure in the sealed flask containing oxygen and water vapor is \(0.99 \: atm\).

Step 1: Identify the given information and relevant equation

We are given the partial pressures of oxygen (0.41 atm) and water vapor (0.58 atm), and we need to find the total pressure in the flask. To do this, we will use Dalton's Law of partial pressures: Total Pressure = Partial Pressure of Oxygen + Partial Pressure of Water Vapor

Step 2: Add the partial pressures together

Now, we will add the two partial pressures to find the total pressure in the flask: Total Pressure = 0.41 atm (Oxygen) + 0.58 atm (Water Vapor) Calculate the sum: Total Pressure = 0.99 atm (rounded to two decimal places)

Step 3: Write the final answer

The total gas pressure in the sealed flask containing oxygen and water vapor is 0.99 atm.

Key Concepts

Understanding Partial Pressure

Partial pressure is a concept used in the field of gas laws to describe the pressure exerted by a single type of gas within a mixture of gases. Imagine a balloon filled with a mix of oxygen and carbon dioxide. Each gas in the balloon exerts its own pressure, known as its partial pressure.

Let's break it down further:

• If a single gas alone occupied the entire volume of the container, the pressure it would exert is called its partial pressure.
• Partial pressure helps in understanding how gases behave in a mixture, which is crucial in fields like chemistry and biology.

For example, in our original exercise, the oxygen in the sealed flask has a partial pressure of 0.41 atm. This means that if there were only oxygen in the flask, it would exert 0.41 atm of pressure.

Total Pressure and Its Calculation

Total pressure is another important concept in the study of gases. It refers to the sum of the partial pressures of all gases present in a mixture.

Understanding total pressure is key for calculations involving gases in a container:

• According to Dalton's Law of Partial Pressures, the total pressure is equal to the sum of individual partial pressures.
• This law is helpful when you want to know how much total pressure your gas mixture is exerting.

In our example with the sealed flask, the partial pressures of oxygen and water vapor are added: \[ \text{Total Pressure} = 0.41 \text{ atm (Oxygen)} + 0.58 \text{ atm (Water Vapor)} = 0.99 \text{ atm} \]. This gives us the total pressure within the flask.

Introduction to Gas Laws

Gas laws are fundamental rules in chemistry that explain how gases behave under different conditions of pressure, volume, and temperature.

Some key aspects of gas laws include:

• Boyle's Law: This relates the pressure and volume of a gas at constant temperature, showing that they are inversely proportional.
• Charles's Law: This connects volume and temperature at constant pressure, indicating that they are directly proportional.
• Dalton's Law: As used in the exercise, it explains how partial pressures contribute to the total pressure.

These laws help scientists and engineers to predict how gases will react to changes in their environment. It's important to note that gas laws assume the gases behave ideally, which means they follow these laws perfectly under all conditions. However, real gases approximate these ideal behaviors, which is good enough for most applications.