One mole of an ideal gas is expanded from a volume of 1.00 L to a volume of 10.18 L against a constant external pressure of 1.07 atm. Calculate the work. (1 L•atm = 101.3 J)

Question

Quizplus · Accepted Answer

The work done by the gas during expansion against a constant external pressure can be calculated using the formula $W = -P_{\text{ext}} \Delta V$, where $W$ is the work done, $P_{\text{ext}}$ is the external pressure, and $\Delta V$ is the change in volume. Given $P_{\text{ext}} = 1.07 \, \text{atm}$ and $\Delta V = 10.18 \, \text{L} - 1.00 \, \text{L} = 9.18 \, \text{L}$, the work done in L•atm is $W = -1.07 \, \text{atm} \times 9.18 \, \text{L} = -9.82 \, \text{L•atm}$. Converting L•atm to Joules using $1 \, \text{L•atm} = 101.3 \, \text{J}$, we get $W = -9.82 \, \text{L•atm} \times 101.3 \, \text{J/L•atm} = -994.746 \, \text{J}$, which rounds to $-9.95 \times 10^2 \, \text{J}$, matching choice E.

One Mole of an Ideal Gas Is Expanded from a Volume