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JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ce165

Take $R = 8.314 J mo l^{- 1} K^{- 1}$ . Which of the following statements about the temperature dependence of equilibrium constants are correct?

AIf $Δ H^{\circ} = 0$ for a reaction, then $K$ is independent of temperature
BThe van't Hoff equation is $\frac{d ln K}{d T} = \frac{Δ H ^{\circ}}{RT}$
CA reaction with $Δ H^{\circ} > 0$ and $Δ S^{\circ} < 0$ attains $K > 1$ at sufficiently high temperature
DFor $Δ H^{\circ} = + 50.0 kJ mo l^{- 1}$ , $K$ increases by a factor of about 1.9 when $T$ is raised from $300 K$ to $310 K$

Answer: A, D

With

Δ H^{\circ} = 0

the slope

- Δ H^{\circ} / R

of

ln K

versus

1/ T

vanishes, so A is true. The correct equation has

R T^{2}

in the denominator, so B is false. For

Δ H^{\circ} > 0

and

Δ S^{\circ} < 0

,

Δ G^{\circ} = Δ H^{\circ} - T Δ S^{\circ}

is positive at every temperature, so

K < 1

always and C is false. For D,

ln (K_{2} / K_{1}) = (50000/8.314) (1/300 - 1/310) = 0.6467

, a factor of 1.91. The same

10 K

rise near

600 K

gives only 1.18.

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