Problem 12 - Chemistry Matter and Change

Question

Calculate Suppose two gases in a container have a total pressure of 1.20 atm. What is the pressure of Gas \(B\) if the partial pressure of Gas A is 0.75 atm?

Step-by-Step Solution

Answer

The pressure of Gas B is 0.45 atm.

Step 1: Understanding Total Pressure

Total pressure in a container is the sum of the partial pressures of all the gases present in it. Given that the total pressure is 1.20 atm.

Step 2: Identifying Partial Pressure of Gas A

From the problem, we know that Gas A has a partial pressure of 0.75 atm.

Step 3: Using Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure is the sum of the partial pressures of individual gases. Therefore, we can write: \[ P_\text{Total} = P_\text{A} + P_\text{B} \]where \( P_\text{Total} = 1.20 \) atm and \( P_\text{A} = 0.75 \) atm.

Step 4: Calculating the Pressure of Gas B

Rearrange the equation to solve for \( P_\text{B} \):\[ P_\text{B} = P_\text{Total} - P_\text{A} \]Substitute the known values into the equation:\[ P_\text{B} = 1.20 - 0.75 = 0.45 \] atm.

Key Concepts

Partial Pressure

Partial pressure is the pressure that a single gas in a mixture exerts if it occupied the whole volume by itself. Imagine it like this: if you let loose a gas in a room, the force it exerts against the walls of that room is its partial pressure. Each gas in a mixture contributes its part to the total pressure. This can be particularly useful when calculating the unknown quantity of one gas in a mixture if the others are known. In the context of the given problem, Gas A exerts a partial pressure of 0.75 atm. This is important for applying Dalton's Law. You know the partial pressure of one gas, and you can use this to find out the partial pressure of Gas B if the total pressure is given. Remember, partial pressures are always additive, so they help us break down a complex system into simpler parts.

Total Pressure

The total pressure is the sum of all the partial pressures in a gas mixture. Think of it as the overall force exerted by all gases combined against the walls of their container. Whether you're dealing with a mixture of two gases or even more, the total pressure is essentially their collective contribution. In our exercise, the total pressure provided is 1.20 atm. This is the cumulative pressure from all gases in the container. It's essential to know the total pressure when you want to use it to find unknown partial pressures. Dalton’s Law comes in handy here, as it links the known total pressure with the partial pressures of individual gases, allowing us to find unknown quantities, like the pressure of Gas B.

Gas Laws

Gas laws are the principles that describe the behavior of gases. They are crucial for understanding how gases interact with each other and their environments. Dalton's Law of Partial Pressures is one of these important principles. It states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each gas.When you're working through gas problems, you'll frequently encounter equations involving words like 'pressure,' 'volume,' and 'temperature.' These are vital concepts that help us predict and explain how gases will behave under different conditions. In our problem, Dalton's Law specifically is applied which means the equation looks like this:\[ P_\text{Total} = P_\text{A} + P_\text{B} \]Through this formula, you calculate pressures missing from the total, which is incredibly useful when dealing with mixtures of gases. This allows for a deeper understanding of both simple and complex systems involving gases.