Final answer:
The entropy change per mole of an ideal gas compressed isothermally to one-fifth its original volume is –Rln(5).
Step-by-step explanation:
The question asks about the entropy change per mole for an ideal gas that is compressed isothermally to one-fifth of its original volume at a constant temperature of 300 K. The entropy change, ΔS, for an isothermal process can be calculated using the formula ΔS = nRln(V2/V1) where n is the number of moles, R is the ideal gas constant, V1 is the initial volume and V2 is the final volume.
Because the volume is compressed to one-fifth of its original volume, V2/V1 = 1/5 and thus ΔS = nRln(1/5). This simplifies to ΔS = -nRln(5), per mole n=1, hence the entropy change per mole is -Rln(5).
The entropy change per mole of an ideal gas during an isothermal compression is given by the formula: ΔS = -Rln(Vf/Vi), where R is the gas constant, Vf is the final volume, and Vi is the initial volume.
In this case, the gas is compressed to one-fifth its original volume. So, Vf/Vi = 1/5. Substituting this into the formula, the entropy change per mole of the gas is given by: ΔS = -Rln(1/5) = Rln5 = b) Rln5