Take R = 8.314 J mol^-1 K^-1. A reaction has the following equilibrium constants: K = 1.67 x 10^5 at 300 K, K = 409 at 400 K and K = 11.1 at 500 K. Assume Delta H deg and Delta S deg are constant. Which statements are correct?

Delta H deg lies between -62 and -58 kJ mol^-1

K is between 0.8 and 1.2 at 600 K

K increases when the temperature is raised

Delta H deg lies between -62 and -58 kJ mol^-1

K is between 0.8 and 1.2 at 600 K

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ce162

Take $R = 8.314 J mo l^{- 1} K^{- 1}$ . A reaction has the following equilibrium constants: $K = 1.67 \times 1 0^{5}$ at $300 K$ , $K = 409$ at $400 K$ and $K = 11.1$ at $500 K$ . Assume $Δ H^{\circ}$ and $Δ S^{\circ}$ are constant. Which statements are correct?

K

falls as

T

rises, so the reaction is exothermic and statement A is false. From the first two data points,

Δ H^{\circ} = R ln (K_{400} / K_{300}) / (1/300 - 1/400) = - 60.0 kJ mo l^{- 1}

, and the last two give -60.0, so B is true. Extrapolating from

500 K

with this

Δ H^{\circ}

gives

K_{600} \approx 1.00

, so C is true. Finally

Δ S^{\circ} = (Δ H^{\circ} + RT ln K) / T

400 K

is -100 J/(mol K), negative, so D is false.