What is the volume of 0.200 mol of an ideal gas at 200. kPa and 400. K? Use the ideal gas law and R = 8.314 L·kPa·mol^{-1}·K^{-1}.

• A. 2.49 L
• B. 0.83 L
• C. 1.66 L
• D. 3.32 L

Answer: (D)

Verified step by step guidance

1. Identify the known variables from the problem: number of moles \(n = 0.200\) mol, pressure \(P = 200.\) kPa, temperature \(T = 400.\) K, and the ideal gas constant \(R = 8.314\) L\cdot kPa \cdot mol^{-1} \cdot K^{-1}$.
2. Recall the ideal gas law formula: \(P \times V = n \times R \times T\), where \(V\) is the volume we need to find.
3. Rearrange the ideal gas law to solve for volume \(V\): \(V = \frac{n \times R \times T}{P}\).
4. Substitute the known values into the equation: \(V = \frac{0.200 \times 8.314 \times 400}{200}\).
5. Perform the arithmetic operations step-by-step to find the volume \(V\) in liters.