Which of the following plots of $\ln k$ versus $\frac{1}{T}$ is consistent with the Arrhenius equation?

Solution & Explanation

\textbf{Answer:} (C) a straight line of negative slope \textbf{Solution:} The Arrhenius equation is $k=A{e}^{-E_a/RT}$. Taking the natural log: $\ln k=\ln A-\frac{E_a}{R}\cdot \frac{1}{T}$. This is a straight line in $\ln k$ vs $\frac{1}{T}$ with intercept $\ln A$ and slope $-\frac{E_a}{R}$. Since $E_a$ and $R$ are positive, the slope is negative, so the line falls as $\frac{1}{T}$ increases. The plot showing a straight line of negative slope is consistent with the Arrhenius equation.