Calculate ΔG for the isothermal compression of 1 mol of an ideal monatomic gas from 1.4 atm to 5.0 atm at 25°C.

Question

Quizplus · Accepted Answer

The change in Gibbs free energy (ΔG) for an isothermal process can be calculated using the equation ΔG = -nRT ln(P2/P1), where n is the number of moles, R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and P1 and P2 are the initial and final pressures, respectively. Converting 25°C to Kelvin gives 298.15 K. Substituting the given values (n = 1 mol, R = 8.314 J/(mol·K), T = 298.15 K, P1 = 1.4 atm, P2 = 5.0 atm) and converting atm to Pa for consistency with R's units (1 atm = 101325 Pa), we get ΔG = -1(8.314)(298.15) ln(5.0/1.4). This calculation results in a positive value, indicating work is done on the system, which corresponds to choice B, 3.2 × 10^3 J.

Calculate ΔG for the Isothermal Compression of 1 Mol of an Ideal