Take R = 8.314 J mol^-1 K^-1. For a decomposition reaction Delta H deg = +178 kJ mol^-1 and Delta S deg = +161 J mol^-1 K^-1, both constant. Which statements are correct?

K > 1 for temperatures above about 1106 K

The intercept of the plot of ln K against 1/T is about +19.4

K > 1 for temperatures above about 1106 K

The slope of a plot of ln K against 1/T is positive, about +2.14 x 10^4 K

The intercept of the plot of ln K against 1/T is about +19.4

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ce161

Take $R = 8.314 J mo l^{- 1} K^{- 1}$ . For a decomposition reaction $Δ H^{\circ} = + 178 kJ mo l^{- 1}$ and $Δ S^{\circ} = + 161 J mo l^{- 1} K^{- 1}$ , both constant. Which statements are correct?

A $K > 1$ for temperatures above about $1106 K$
B $K < 1$ at $800 K$
CThe slope of a plot of $ln K$ against $1/ T$ is positive, about $+ 2.14 \times 1 0^{4} K$
DThe intercept of the plot of $ln K$ against $1/ T$ is about $+ 19.4$

K = 1

when

T = Δ H^{\circ} /Δ S^{\circ} = 178000/161 = 1106 K

, and

K > 1

above it. At

800 K

Δ G^{\circ} = 178000 - 800 \times 161 = + 49200 J mo l^{- 1}

, so

K = 6.13 \times 1 0^{- 4} < 1

. The slope is

- Δ H^{\circ} / R = - 21410 K

, which is negative, so statement C is false. The intercept

Δ S^{\circ} / R = 19.36

is correct.