A balloon contains 2.0 mol of an ideal gas at a pressure of 1.0 atm and a temperature of 273 K. What volume will the balloon occupy?

• A. 2.0 L
• B. 44.8 L
• C. 11.2 L
• D. 22.4 L

Answer: (B)

Verified step by step guidance

1. Identify the known variables from the problem: number of moles \(n = 2.0\) mol, pressure \(P = 1.0\) atm, and temperature \(T = 273\) K.
2. Recall the Ideal Gas Law equation: \(P \times V = n \times R \times T\), where \(V\) is the volume, 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 and volume in liters, which is \(R = 0.0821 \ \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}\).
4. Rearrange the Ideal Gas Law to solve for volume \(V\): \(V = \frac{n \times R \times T}{P}\)
5. Substitute the known values into the equation: \(V = \frac{2.0 \ \text{mol} \times 0.0821 \ \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \times 273 \ \text{K}}{1.0 \ \text{atm}}\) This will give the volume the balloon occupies.