Final answer:
To calculate dS(mix) for the mixing of ideal gases, use the formula dS(mix) = nR ln(V_f/V_i) which corresponds to answer choice a). This formula is applied when considering the expansion of gas volume and the increase in entropy due to that expansion.
Step-by-step explanation:
To calculate the entropy change upon mixing ideal gases, denoted as dS(mix), we use the formula dS(mix) = nR ln(V_f/V_i), where 'n' is the number of moles of gas, 'R' is the universal gas constant, and V_f/V_i is the ratio of the final volume to the initial volume of the gas. This corresponds to answer choice a) dS(mix) = nR ln(V_f/V_i). The equation represents the increase in entropy when a gas expands from an initial volume V_i to a final volume V_f due to an increase in the number of accessible microstates.
Additionally, when dealing with changes in pressure, the entropy of an ideal gas can also be related to the pressures through the formula dS(mix) = -nR ln(P_f/P_i) under isothermal conditions, where P_f and P_i are the final and initial pressures, respectively. They show how entropy changes when the gas goes from one pressure to another keeping the temperature constant. However, this formula is not the one asked in the question regarding the mixing of gases.
Note that the entropy change due to temperature change at constant pressure can be expressed using the heat capacity at constant pressure (Cp) as dS = nCp ln(T_f/T_i), but this is not directly related to the entropy of mixing.