To calculate the entropy change S of an ideal monatomic gas during an isothermal expansion, we can use the formula:S = n * R * ln Vf / Vi where n is the number of moles of the gas, R is the ideal gas constant 8.314 J/molK , Vf is the final volume, and Vi is the initial volume.First, we need to find the number of moles n of the gas. We can use the ideal gas law:PV = nRTwhere P is the pressure 1 atm , V is the volume, T is the temperature 300 K , and R is the ideal gas constant 0.0821 Latm/molK when using atm for pressure .Rearranging the equation to solve for n:n = PV / RTWe don't have the initial volume Vi given, but we can still calculate the entropy change in terms of Vi. The final volume Vf is 5 times the initial volume:Vf = 5 * ViNow, we can plug in the values into the entropy change formula:S = PV / RT * R * ln Vf / Vi Notice that R cancels out:S = PV / T * ln Vf / Vi Now, plug in the values for P, T, Vf, and Vi:S = 1 atm * 5 * Vi / 300 K * ln 5 * Vi / Vi Simplify the equation:S = 5 * Vi / 300 K * ln 5 S = Vi / 60 K * ln 5 Since we don't have the initial volume Vi , we cannot calculate the exact numerical value for the entropy change. However, we have the expression for S in terms of Vi:S = Vi / 60 K * ln 5 This expression shows that the entropy change depends on the initial volume of the gas and is directly proportional to it.