To determine whether the reaction can occur using the activity series, we need to look at the reactivity of the metals involved.
In the given reaction:
\[ \text{HgCl}_2 + \text{Al} \rightarrow \text{AlCl}_3 + \text{Hg} \]
We have aluminum (Al) and mercury (Hg). According to the activity series of metals, aluminum is more reactive than mercury. This means that aluminum can displace mercury from its compound (mercury(II) chloride in this case).
Since aluminum is more reactive and can displace mercury from mercury(II) chloride, the reaction can indeed occur.
Thus, the answer is Yes, the reaction can occur.
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