Question

Certain mass of a gas occupy 500 ml at 2 atm and 27°C. Calculate the volume (in L) occupied by same mass of the gas at 0.3 atm and 227°C. The compressibility factors of gas at the given condition are 0.8 and 0.9, respectively.

• A. 6.25 L
• B. 5.25 L
• C. 7.25 L
• D. 8.25 L

Answer 1

Answer: (A)

6.25 L

Answer 2

For a fixed mass of gas, the relationship derived from the compressibility factor ($Z = \frac{PV}{nRT}$) is $\frac{P_1V_1}{Z_1T_1} = \frac{P_2V_2}{Z_2T_2}$. $T_1 = 27^\circ\text{C} = 300$ K, $T_2 = 227^\circ\text{C} = 500$ K. $V_1 = 500$ ml $= 0.5$ L. $V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{Z_2}{Z_1} \times \frac{T_2}{T_1} = 0.5 \text{ L} \times \frac{2 \text{ atm}}{0.3 \text{ atm}} \times \frac{0.9}{0.8} \times \frac{500 \text{ K}}{300 \text{ K}} = 6.25 \text{ L}$.