Magnesium chloride is produced industrially by reaction of the elements according to…

CHEMISTRY · Multi-part · A Level · Chemistry · Thermodynamics · Thermodynamics

Problem

Magnesium chloride is produced industrially by reaction of the elements according to the equation Mg(s)+Cl2(g)⟶MgCl2(s)\mathrm{Mg(s) + Cl_2(g) \longrightarrow MgCl_2(s)} Selected standard enthalpy data are given below. • Enthalpy of formation, ΔHf∘(MgCl2(s))=−644 kJ mol−1\Delta H_f^\circ(\mathrm{MgCl_2(s)}) = -644\,\text{kJ mol}^{-1} • Sublimation energy of Mg(s)\mathrm{Mg(s)}: +150 kJ mol−1+150\,\text{kJ mol}^{-1} • First ionization energy of Mg(g)\mathrm{Mg(g)}: +738 kJ mol−1+738\,\text{kJ mol}^{-1} • Second ionization energy of Mg+(g)\mathrm{Mg^+(g)}: +1 451 kJ mol−1+1\,451\,\text{kJ mol}^{-1} • Bond dissociation energy of Cl2(g)\mathrm{Cl_2(g)} (per mole of Cl2\mathrm{Cl_2}): +243 kJ+243\,\text{kJ} • Electron affinity of Cl(g)\mathrm{Cl(g)}: −349 kJ mol−1-349\,\text{kJ mol}^{-1} Assume all values refer to 298 K298\,\text{K} and 1 bar1\,\text{bar}. (a) Write the balanced chemical equation that defines ΔHf∘(MgCl2(s))\Delta H_f^\circ(\mathrm{MgCl_2(s)}). (b) List a logically ordered sequence of thermochemical steps that convert the reactants in their standard states to MgCl2(s)\mathrm{MgCl_2(s)}. For each step, write the corresponding chemical process and associate the appropriate enthalpy value (including its sign). (c) Using the information in part (b), calculate the lattice enthalpy ΔHlattice\Delta H_{\text{lattice}} of MgCl2(s)\mathrm{MgCl_2(s)} in kJ mol−1\text{kJ mol}^{-1}. Show all algebraic steps leading to your answer. (d) Explain why the lattice enthalpy you calculated is exothermic, and predict qualitatively whether the lattice enthalpy for MgF2(s)\mathrm{MgF_2(s)} would be more or less negative. Support your prediction with relevant ionic-size and charge arguments.

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