How do you find the enthalpy change for a given reaction?
Step 1 Calculate $q_\text{solution}$. To do so, you have to have in mind that the mass of the solution is aproximatly equals to $100\ \mathrm{ml}$ of $\ce{HCl}$ plus the mass of $\ce{Mg}$.

\begin{align*}
   q_\text{solution}&amp;=100.5\ \mathrm g\cdot4.20\ \frac{\mathrm J}{\mathrm{mol\cdot K}}\cdot\left(318.0\ \mathrm K-295.4\ \mathrm K\right)\\
   &amp;=9.54\cdot 10^3\ \mathrm J
  \end{align*}
Step 2 Calculate $q_\mathrm{rxn}$

\begin{align*}
 q_\mathrm{rxn} + q_\text{solution} &amp;=0\\
 q_\mathrm{rxn} + 9.54\cdot 10^3\ \mathrm J &amp;= 0
\end{align*}
Step 3 Calculate the value of $\Delta H$ per mole.

\begin{align*}
 \Delta H&amp;= \left(\frac{-9.54\cdot 10^3\ \mathrm J}{0.500\ \mathrm g\ \text{of}\ \ce{Mg}}\right)\left(\frac{24.31\ \mathrm g\ \text{of}\ \ce{Mg}}{1\ \mathrm{mol}\ \text{of}\ \ce{Mg}}\right)\\
 &amp;= -4.64 \cdot 10^5\ \frac{\mathrm J}{\mathrm{mol}}\ \text{of}\ \ce{Mg}
\end{align*}