Four containers each hold 1.0 mol of an ideal gas at different conditions. Which container has the gas stored at the highest temperature?A) 2.0 L at 1.0 atmB) 4.0 L at 1.0 atmC) 2.0 L at 2.0 atmD) 1.0 L at 1.0 atm

• A. A) 2.0 L at 1.0 atm
• B. C) 2.0 L at 2.0 atm
• C. D) 1.0 L at 1.0 atm
• D. B) 4.0 L at 1.0 atm

Answer: (D)

Verified step by step guidance

1. Recall the Ideal Gas Law: \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles of gas, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.
2. Since each container has the same amount of gas (\(n = 1.0\) mol) and \(R\) is a constant, rearrange the equation to solve for temperature: \(T = \frac{P \times V}{n \times R}\).
3. For each container, calculate the product \(P \times V\) because \(n\) and \(R\) are the same for all, so the container with the highest \(P \times V\) will have the highest temperature.
4. Compare the values of \(P \times V\) for each container: - Container A: \$1.0\, \text{atm} \times 2.0\, \text{L}$ - Container B: \$1.0\, \text{atm} \times 4.0\, \text{L}$ - Container C: \$2.0\, \text{atm} \times 2.0\, \text{L}$ - Container D: \$1.0\, \text{atm} \times 1.0\, \text{L}$
5. Identify which container has the largest \(P \times V\) value; that container corresponds to the highest temperature according to the ideal gas law.