Question

In the van 't Hoff Equation $\frac{dlnK}{dT}=\frac{\Delta H^{\circ }}{R{T}^2}$
Which are the following statements is true?

• A. The slope of the graph when $lnK$ is plotted vs $\frac{1}{T}$ increases and then decreases
• B. The slope of the graph when $lnK$ is plotted vs $\frac{1}{T}$ is positive throughout
• C. When $\frac{dlnK}{dT}<0$, the reaction is endothermic
• D. When $\frac{dlnK}{dT}<0$, the reaction is exothermic

Answer 1

The correct option is D When $\frac{dlnK}{dT}<0$, the reaction is exothermic

In van 't Hoff's Equation
$\frac{dlnK}{dT}=\frac{\Delta H^{\circ }}{R{T}^2}$
or, $lnK=\frac{-\Delta H^{\circ }}{R}\frac{1}{T}+C$
This is a linear equation so the slope is constant throughout.
The slope of the graph would depend on the sign of $\Delta H$ and it can be negative or positive if the reaction is endothermic or exothermic respectively.