Using the ideal gas law, what is the volume (in liters) occupied by 2.0 moles of an ideal gas at 25°C and 380 mmHg?

• A. 49 L
• B. 11.2 L
• C. 22.4 L
• D. 97 L

Answer: (D)

Verified step by step guidance

1. Identify the known variables from the problem: number of moles \(n = 2.0\) mol, temperature \(T = 25^\circ C\), and pressure \(P = 380\) mmHg.
2. Convert the temperature from Celsius to Kelvin using the formula \(T(K) = T(^\circ C) + 273.15\) to get the absolute temperature required for the ideal gas law.
3. Convert the pressure from mmHg to atmospheres (atm) because the ideal gas constant \(R\) is commonly given in units involving atm. Use the conversion \$1 \text{ atm} = 760 \text{ mmHg}\(, so \)P(\text{atm}) = \frac{380}{760}$ atm.
4. Recall the ideal gas law equation: \(P \times V = n \times R \times T\), where \(R\) is the ideal gas constant. Use \(R = 0.0821 \frac{L \cdot atm}{mol \cdot K}\) for consistency with the units of pressure and volume.
5. Rearrange the ideal gas law to solve for volume \(V\): \(V = \frac{n \times R \times T}{P}\). Substitute the values of \(n\), \(R\), \(T\), and \(P\) (in atm and K) into this equation to find the volume in liters.