The equilibrium constant of a reaction is 4.0 x 10^2 at 300 K and 15 at 350 K. Assuming Delta H deg and Delta S deg are constant and R = 8.314 J mol^-1K^-1, find Delta S deg in J mol^-1K^-1 (nearest integer).

JEE Advanced levelNumerical answerDifficulty 3 of 3td214

The equilibrium constant of a reaction is $4.0 \times 1 0^{2}$ at $300 K$ and $15$ at $350 K$ . Assuming $Δ H^{\circ}$ and $Δ S^{\circ}$ are constant and $R = 8.314 J mo l^{- 1} K^{- 1}$ , find $Δ S^{\circ}$ in $J mo l^{- 1} K^{- 1}$ (nearest integer).

Numerical answer type, answer in J mol^-1 K^-1, tolerance 1.

Van't Hoff:

ln (K_{2} / K_{1}) = - (Δ H^{\circ} / R) (1/ T_{2} - 1/ T_{1})

gives

Δ H^{\circ} = - 57.33 kJ mo l^{- 1}

. At

300 K

Δ G^{\circ} = - RT ln K_{1} = - 14.94 kJ mo l^{- 1}

. Then

Δ S^{\circ} = (Δ H^{\circ} - Δ G^{\circ}) / T = (- 57326 - (- 14944)) /300 = - 141.3 J mo l^{- 1} K^{- 1}

, about -141.