How to calculate the activation energy of diffusion of carbon in iron?
Maybe I'm wrong but my calculation has given another result:
\begin{align}
D_{298} &amp;= D_0\cdot\exp\left\{\frac{-Q}{298~\mathrm{K}\cdot\mathcal{R}}\right\}\\
D_{573} &amp;= D_0\cdot\exp\left\{\frac{-Q}{573~\mathrm{K}\cdot\mathcal{R}}\right\}\\
\end{align}

Thus, going through the $\ln$ form, you get 
\begin{align}
\ln\{D_{298}\} &amp;= \ln\{D_0\} - \frac{Q}{298~\mathrm{K}\cdot\mathcal{R}}\\
\ln\{D_{573}\} &amp;= \ln\{D_0\} - \frac{Q}{573~\mathrm{K}\cdot\mathcal{R}}\\
\ln\{D_{298}\} - \ln\{D_{573}\} &amp;= -\frac{Q}{\mathcal{R}}\cdot\left(\frac{1}{298}-\frac{1}{573}\right)
\end{align}

And then I obtained $Q\approx 38~\mathrm{kJ/mol}$.