Final answer:
To calculate the entropy change during an isothermal reversible expansion of argon gas, the formula ΔS = Q_{ rev}/T is used, where heat transfer is equated to work done. The work done is obtained using W = nRT ln(V_2/V_1), and the total entropy change is zero in a reversible process.
Step-by-step explanation:
To calculate the change in the entropies of the system and the surroundings for an isothermal reversible expansion of argon gas, we use the formula for entropy change ΔS = Q_{ rev}/T, where Q_{ rev} is the reversible heat transfer and T is the absolute temperature. Since the expansion is isothermal and reversible, the heat transferred to the gas is equal to the work done by the gas during the expansion, and we can use the ideal gas law PV = nRT to find this. In this case, we can calculate the work done using the equation W = nRT ln(V_2/V_1), where V_1 and V_2 are the initial and final volumes, n is the number of moles of argon, and R is the gas constant. The change in entropy for the surroundings is equal in magnitude and opposite in sign to the change in entropy for the system, as in a reversible process the total entropy change is zero.