A 40.0-L container is divided into two equal parts by a rubber membrane. One half of the container has 1.80 moles of an ideal monatomic gas at 270 K, and the other half is a vacuum. The container does not allow any gas to escape but is free to exchange heat with the surroundings. The membrane breaks, the gas expands isothermally and eventually the gas reaches a new equilibrium condition occupying the entire volume. What is the change in entropy of the gas?
A) 10.4 J/K
B) 9.16 J/K
C) 12.5 J/K
D) 14.3 J/K
E) 16.4 J/K

Question

Quizplus · Accepted Answer

The change in entropy is given by:$$\Delta S = nR\ln(\frac{V_f}{V_i})$$where:* n is the number of moles of gas* R is the ideal gas constant* V_f is the final volume* V_i is the initial volumeIn this case, n = 1.80 moles, R = 8.31 J/mol*K, V_f = 40.0 L, and V_i = 20.0 L. Substituting these values into the equation, we get:$$\Delta S = 1.80 mol * 8.31 J/mol*K * \ln(\frac{40.0 L}{20.0 L}) = 10.4 J/K$$

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