The data below show the temperature variation of the equilibrium constant of the reaction $\mathrm{Ag}_2 \mathrm{CO}_3(\mathrm{~s}) \rightleftharpoons \mathrm{Ag}_2 \mathrm{O}(\mathrm{s})+\mathrm{CO}_2(\mathrm{~g})$. Calculate the standard reaction enthalpy of the decomposition.
$\begin{array}{lllll}T / \mathrm{K} & 350 & 400 & 450 & 500 \\ K & 3.98 \times 10^{-4} & 1.41 \times 10^{-2} & 1.86 \times 10^{-1} & 1.48\end{array}$
We draw up the following table:
$\begin{array}{lllll}T / \mathrm{K} & 350 & 400 & 450 & 500 \\ \left(10^3 \mathrm{~K}\right) / T & 2.86 & 2.50 & 2.22 & 2.00 \\ -\ln K & 7.83 & 4.26 & 1.68 & -0.39\end{array}$
These points are plotted in Fig. 6.9. The slope of the graph is $+9.6 \times 10^3$, so
$$
\Delta_{\mathrm{r}} H^{\ominus}=\left(+9.6 \times 10^3 \mathrm{~K}\right) \times R=+80 \mathrm{~kJ} \mathrm{~mol}^{-1}
$$