To calculate the change in entropy for an irreversible process, we can first calculate the entropy change for a reversible process and then apply it to the irreversible process since entropy is a state function and depends only on the initial and final states.For an ideal gas undergoing isothermal compression, we can use the formula for entropy change:S = n * R * ln V2/V1 where S is the change in entropy, n is the number of moles, R is the gas constant 8.314 J/molK , V1 is the initial volume, and V2 is the final volume.Given:n = 1 moleR = 8.314 J/molKT = 298 KV1 = 4 L = 0.004 m 1 L = 0.001 m V2 = 1 L = 0.001 mNow, we can plug these values into the formula:S = 1 mol * 8.314 J/molK * ln 0.001 m / 0.004 m S = 8.314 J/K * ln 1/4 S = 8.314 J/K * -1.386 since ln 1/4 = -1.386 S = -11.52 J/KThe change in entropy when 1 mole of an ideal gas is compressed from 4 L to 1 L irreversibly at a temperature of 298 K is -11.52 J/K.