Example 5.14b: A More Challenging Problem Using Hess’s Law

Aluminum chloride can be formed from its elements:

[i]
\(\ce{2Al(s)}\)\(\ce{ + }\)\(\ce{3Cl2(g)}\)\(\ce{->}\)\(\ce{2AlCl3(s)}\)\(\ce{ }\)       \(ΔH°\) \( = \)?

Use the reactions here to determine the \(ΔH°\) for reaction (i):

[ii]
\(\ce{HCl(g)}\)\(\ce{->}\)\(\ce{HCl(aq)}\)\(\ce{ }\)       \(ΔH°_{\mathrm{ii}} = - 74.8\ \mathrm{kJ}\)

[iii]
\(\ce{H2(g)}\)\(\ce{ + }\)\(\ce{Cl2(g)}\)\(\ce{->}\)\(\ce{2HCl(g)}\)\(\ce{ }\)       \(ΔH°_{\mathrm{iii}}\)\( = - 185\ \mathrm{kJ}\)

[iv]
\(\ce{AlCl3(aq)}\)\(\ce{->}\)\(\ce{AlCl3(s)}\)\(\ce{ }\)       \(ΔH°_{\mathrm{iv}}\)\( = + 323\ \frac{\mathrm{kJ}}{\mathrm{mol}}\)

[v]
\(\ce{2Al(s)}\)\(\ce{ + }\)\(\ce{6HCl(aq)}\)\(\ce{->}\)\(\ce{2AlCl3(aq)}\)\(\ce{ + }\)\(\ce{3H2(g)}\)\(\ce{ }\)       \(ΔH°_{\mathrm{v}} = - 1049\ \mathrm{kJ}\)