Using the ideal gas law, how many moles of an ideal gas are present in a 1.00 L cylinder at a temperature of 600. K and a pressure of 1.00 atm?

• A. 0.0408 mol
• B. 0.020 mol
• C. 0.0204 mol
• D. 0.041 mol

Answer: (C)

Verified step by step guidance

1. Identify the known variables from the problem: volume \(V = 1.00\) L, temperature \(T = 600.\) K, and pressure \(P = 1.00\) atm.
2. Recall the ideal gas law equation: \(P \times V = n \times R \times T\), where \(n\) is the number of moles and \(R\) is the ideal gas constant.
3. Choose the appropriate value for the ideal gas constant \(R\) that matches the units of pressure in atm, volume in liters, and temperature in Kelvin. The common value is \(R = 0.0821 \frac{L \cdot atm}{mol \cdot K}\).
4. Rearrange the ideal gas law to solve for the number of moles \(n\): \(n = \frac{P \times V}{R \times T}\).
5. Substitute the known values into the rearranged formula: \(n = \frac{1.00 \times 1.00}{0.0821 \times 600.}\) and simplify to find the number of moles.