Calculate $\Delta$G for the isothermal compression of 1 mol of an ideal monatomic gas from 1.4 atm to 5.6 atm at 24°C.

Question

Quizplus · Accepted Answer

The change in internal energy of an ideal gas undergoing an isothermal process is given by ΔU = 0. Therefore, ΔF = q = -w, where q is the heat added to the system and w is the work done by the system. For an ideal gas, the work done during an isothermal process is given by w = nRT ln(V2/V1), where n is the number of moles of gas, R is the gas constant, T is the temperature in Kelvin, and V2/V1 is the ratio of the final and initial volumes.

In this problem, n = 1 mol, R = 8.31 J/mol*K, T = 24 + 273 = 297 K, and V2/V1 = 1.4/5.6 = 0.25. Therefore, w = -(1 mol)(8.31 J/mol*K)(297 K) ln(0.25) = 3.4 kJ.

Since the process is isothermal, q = w = -3.4 kJ. Therefore, ΔF = q = -3.4 kJ.

Using the equation F = nRT ln(P2/P1) for an ideal gas with constant temperature, we can calculate the change in Helmholtz free energy. Here, n = 1 mol, R = 8.31 J/mol*K, T = 297 K, P1 = 1.4 atm, and P2 = 5.6 atm. Therefore, ΔF = (1 mol)(8.31 J/mol*K)(297 K) ln(5.6/1.4) = 3.4 kJ.

Thus, ΔF = -3.4 kJ, and the answer is B.

Calculate Δ\DeltaΔ G for the Isothermal Compression of 1 Mol of an of an Ideal

Calculate $\Delta$ G for the Isothermal Compression of 1 Mol of an of an Ideal