Take R = 8.314 J mol^-1 K^-1. The equilibrium constant of a reaction is 0.25 at 350 K and 1.8 at 400 K. Assuming Delta H deg and Delta S deg are constant, calculate Delta S deg in J mol^-1 K^-1 (nearest integer).

JEE Advanced levelNumerical answerDifficulty 3 of 3ce159

Take $R = 8.314 J mo l^{- 1} K^{- 1}$ . The equilibrium constant of a reaction is $0.25$ at $350 K$ and $1.8$ at $400 K$ . Assuming $Δ H^{\circ}$ and $Δ S^{\circ}$ are constant, calculate $Δ S^{\circ}$ in $J mo l^{- 1} K^{- 1}$ (nearest integer).

Numerical answer type, answer in J/(mol K), tolerance 1.

Δ H^{\circ} = R ln (K_{2} / K_{1}) / (1/ T_{1} - 1/ T_{2}) = 8.314 \times 1.9741/3.5714 \times 1 0^{- 4} = 45955 J mo l^{- 1}

. At

350 K

Δ G^{\circ} = - RT ln K_{1} = 4034 J mo l^{- 1}

. Then

Δ S^{\circ} = (Δ H^{\circ} - Δ G^{\circ}) / T = (45955 - 4034) /350 = 119.77

, i.e. 120 J/(mol K).