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Step 1:I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Write the lattice energy equation
The lattice energy equation for $$\mathrm{MgCl}_{2}(s)$$ can be represented as:
\mathrm{Mg}^{2 +}(g) + 2\mathrm{Cl}^{-}(g) \rightarrow \mathrm{MgCl}_{2}(s)
Step 3:: Identify the given thermochemical data
- Formation reaction: $$\mathrm{Mg}(g) + 2\mathrm{Cl}(g) \rightarrow \mathrm{MgCl}_{2}(s)$$, $$\Delta H = -642 \mathrm{~kJ/mol}
- Chlorine electron affinity: \mathrm{Cl}(g) + e^{-} \rightarrow \mathrm{Cl}^{-}(g), \Delta H = - 337 \mathrm{~kJ/mol}
Step 4:: Calculate lattice energy using Hess's Law
\text{Lattice Energy} = -\Delta H_{\text{formation}} - \Delta H_{\text{ionization}} - 2\Delta H_{\text{electron affinity}}
Rearrange the formation equation to solve for lattice energy:
Step 5:: Substitute the values
\text{Lattice Energy} = -(-642) - (+2188) - 2(-337)
Step 6:: Calculate the lattice energy
\text{Lattice Energy} = -872 \mathrm{~kJ/mol}
\text{Lattice Energy} = + 642 - 2188 + 674
Final Answer
The lattice energy of \mathrm{MgCl}_{2}(s) is - 872 \mathrm{~kJ/mol}.
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