Using the ideal gas law, what is the volume (in liters) occupied by 2.5 moles of nitrogen gas at a pressure of 1.75 atm and a temperature of 475 K? (Use R = 0.0821 L·atm·mol^{-1}·K^{-1})

• A. 22.3 L
• B. 55.6 L
• C. 11.1 L
• D. 35.0 L

Answer: (B)

Verified step by step guidance

1. Identify the known variables from the problem: number of moles \(n = 2.5\) mol, pressure \(P = 1.75\) atm, temperature \(T = 475\) K, and the ideal gas constant \(R = 0.0821\) L\cdot atm\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: \(V = \frac{2.5 \times 0.0821 \times 475}{1.75}\).
5. Perform the arithmetic operations step-by-step: multiply \(n\), \(R\), and \(T\) first, then divide the result by \(P\) to find the volume \(V\) in liters.