A 250 mL container of CO2 exerting a pressure of 1.00 atm is connected through a valve to a 500 mL container of O2 exerting a pressure of 2.00 atm. When the valve is opened, the gases mix, forming a 750 mL mixture of CO2 and O2. What is the total pressure of this mixture? 3.00 atm 1.33 atm 2.50 atm 1.50 atm 1.67 atm

Chemistry
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Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Problem Statement:**

A 250 mL container of CO₂ exerting a pressure of 1.00 atm is connected through a valve to a 500 mL container of O₂ exerting a pressure of 2.00 atm. When the valve is opened, the gases mix, forming a 750 mL mixture of CO₂ and O₂. What is the total pressure of this mixture?

**Options:**
- 3.00 atm
- 1.33 atm
- 2.50 atm
- 1.50 atm
- 1.67 atm

**Explanation:**
To find the total pressure of the gas mixture, we can use the ideal gas law and the concept of partial pressures. Here's a step-by-step breakdown:

1. Calculate the moles of CO₂ using the relation P₁V₁ = nRT:
   - Volume of CO₂ = 250 mL = 0.25 L
   - Pressure of CO₂ = 1.00 atm
   - Since temperature and R (ideal gas constant) are constant, find the initial number of moles.

2. Calculate the moles of O₂:
   - Volume of O₂ = 500 mL = 0.5 L
   - Pressure of O₂ = 2.00 atm
   - Use the ideal gas relation similarly to find the initial number of moles.

3. Calculate the partial pressures in the new volume (750 mL = 0.75 L):
   - Find the partial pressure contributed by CO₂ in 750 mL.
   - Find the partial pressure contributed by O₂ in 750 mL.

4. Add the partial pressures to find the total pressure of the mixture.

This problem is essential for understanding gas laws, particularly Dalton's Law of Partial Pressures, and is crucial for students learning about chemical reactions and gas behavior.

**Answer:**
To solve the problem and select the correct option, apply the described calculations.
Transcribed Image Text:**Problem Statement:** A 250 mL container of CO₂ exerting a pressure of 1.00 atm is connected through a valve to a 500 mL container of O₂ exerting a pressure of 2.00 atm. When the valve is opened, the gases mix, forming a 750 mL mixture of CO₂ and O₂. What is the total pressure of this mixture? **Options:** - 3.00 atm - 1.33 atm - 2.50 atm - 1.50 atm - 1.67 atm **Explanation:** To find the total pressure of the gas mixture, we can use the ideal gas law and the concept of partial pressures. Here's a step-by-step breakdown: 1. Calculate the moles of CO₂ using the relation P₁V₁ = nRT: - Volume of CO₂ = 250 mL = 0.25 L - Pressure of CO₂ = 1.00 atm - Since temperature and R (ideal gas constant) are constant, find the initial number of moles. 2. Calculate the moles of O₂: - Volume of O₂ = 500 mL = 0.5 L - Pressure of O₂ = 2.00 atm - Use the ideal gas relation similarly to find the initial number of moles. 3. Calculate the partial pressures in the new volume (750 mL = 0.75 L): - Find the partial pressure contributed by CO₂ in 750 mL. - Find the partial pressure contributed by O₂ in 750 mL. 4. Add the partial pressures to find the total pressure of the mixture. This problem is essential for understanding gas laws, particularly Dalton's Law of Partial Pressures, and is crucial for students learning about chemical reactions and gas behavior. **Answer:** To solve the problem and select the correct option, apply the described calculations.
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