Final answer:
The change of entropy per mole for three moles of an ideal gas undergoing a reversible isothermal compression at 25°C with 1950 J of work done on the gas is -2.18 J/(K·mol).
Step-by-step explanation:
The question asks about the change of entropy per mole of an ideal gas during a reversible isothermal compression at 25°C where 1950 J of work is done on the gas. In thermodynamics, especially when dealing with ideal gases, the entropy change (ΔS) can be determined using the formula ΔS = Q/T where Q is the heat exchanged and T is the temperature in Kelvin. For an isothermal process, the heat exchanged is equal but opposite in sign to the work done on the system.
First, we convert the given temperature to Kelvin: T = 25°C + 273.15 = 298.15 K. Next, since the work is done on the gas, Q = -1950 J (the negative sign indicates that the energy is entering the system). Therefore, the total entropy change for the gas is ΔS = -1950 J / 298.15 K.
To find the entropy change per mole, we simply divide the total entropy change by the number of moles. For three moles of gas: ΔS (per mole) = (-1950 J) / (298.15 K * 3 moles) = -2.18 J/(K·mol).