Question 1
Multiple choiceMedium1 markThe following standard enthalpy changes are given for a Born–Haber cycle for MgCl₂(s). The chloride electron-affinity step occurs twice. Which value and interpretation of the final step are consistent with the cycle?
| Process | ΔH° / kJ mol⁻¹ |
|---|---|
| Mg(s) → Mg(g) | +148 |
| Mg(g) → Mg⁺(g) + e⁻ | +738 |
| Mg⁺(g) → Mg²⁺(g) + e⁻ | +1451 |
| Cl₂(g) → 2Cl(g) | +243 |
| Cl(g) + e⁻ → Cl⁻(g) | −349 |
| Mg(s) + Cl₂(g) → MgCl₂(s) | −642 |
| Mg²⁺(g) + 2Cl⁻(g) → MgCl₂(s) | ? |
Show answer and explanation
Answer: B. The enthalpy changes around the cycle sum to the standard enthalpy of formation: 148 + 738 + 1451 + 243 + 2(−349) + ΔH_latt = −642, so ΔH_latt = −2524 kJ mol⁻¹. The negative value means energy is released as gaseous ions form MgCl₂(s).
A: counts only one electron-affinity step, giving −2873 kJ mol⁻¹.
C: omits the second ionization energy, giving −1073 kJ mol⁻¹.
D: reverses the sign of the lattice step, making formation from gaseous ions endothermic.
Remember: the enthalpy changes around a complete Hess cycle sum to zero.