What volume is occupied by 1.00 mole of an ideal gas at a pressure of 2.00 atm and a temperature of 20.0 °C?

• A. 24.4 L
• B. 22.4 L
• C. 12.2 L
• D. 44.8 L

Answer: (C)

Verified step by step guidance

1. Identify the known variables from the problem: number of moles \(n = 1.00\) mole, pressure \(P = 2.00\) atm, and temperature \(T = 20.0\ ^\circ\mathrm{C}\).
2. Convert the temperature from Celsius to Kelvin using the formula \(T(K) = T(^\circ\mathrm{C}) + 273.15\), so \(T = 20.0 + 273.15\) K.
3. Recall the ideal gas law equation: \(P \times V = n \times R \times T\), where \(V\) is the volume, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin.
4. Use the value of the ideal gas constant \(R = 0.0821\ \mathrm{L \cdot atm / mol \cdot K}\), which is appropriate for the units given (atm, L, mol, K).
5. Rearrange the ideal gas law to solve for volume \(V\): \(V = \frac{n \times R \times T}{P}\). Substitute the known values of \(n\), \(R\), \(T\), and \(P\) into this equation to find the volume.