Question

A sample of gas occupies 10 L at 300 K and 2 atm. What will be its volume at 400 K and 1 atm?

• A. 15 L
• B. 26.6 L
• C. 25 L
• D. 30 L

Hint:

Always use the combined gas law for calculations involving changes in pressure, volume, and temperature.

Answer 1

The Correct Option is B

Gas Volume Calculation via Combined Gas Law

Input Data:

• Initial Volume (\( V_1 \)): \( 10\ \text{L} \)
• Initial Temperature (\( T_1 \)): \( 300\ \text{K} \)
• Initial Pressure (\( P_1 \)): \( 2\ \text{atm} \)
• Final Temperature (\( T_2 \)): \( 400\ \text{K} \)
• Final Pressure (\( P_2 \)): \( 1\ \text{atm} \)

Governing Equation:

Combined Gas Law: \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \)

Rearranged for \( V_2 \): \( V_2 = \frac{P_1 V_1 T_2}{P_2 T_1} \)

Calculation:

Substituting the given values: \( V_2 = \frac{2\ \text{atm} \times 10\ \text{L} \times 400\ \text{K}}{1\ \text{atm} \times 300\ \text{K}} = \frac{8000}{300}\ \text{L} \approx 26.67\ \text{L} \)

✅ Result:

The final volume (\( V_2 \)) is approximately \( \boxed{26.67\ \text{L}} \).