Using the ideal gas law, how many moles of gas are present in a 20 L container at a pressure of 2 atm and a temperature of 400 K? (Use R = 0.0821 L·atm·mol^{-1}·K^{-1})

• A. 1.22 mol
• B. 2.44 mol
• C. 0.41 mol
• D. 0.98 mol

Answer: (A)

Verified step by step guidance

1. Identify the known variables from the problem: volume \(V = 20\) L, pressure \(P = 2\) atm, temperature \(T = 400\) K, and the ideal gas constant \(R = 0.0821\) L\cdot atm\cdot mol^{-1}\cdot K^{-1}$.
2. Recall the ideal gas law equation: \(P \times V = n \times R \times T\), where \(n\) is the number of moles of gas.
3. Rearrange the ideal gas law to solve for \(n\): \(n = \frac{P \times V}{R \times T}\).
4. Substitute the known values into the rearranged equation: \(n = \frac{2 \times 20}{0.0821 \times 400}\).
5. Perform the arithmetic to find the value of \(n\), which represents the number of moles of gas in the container.