Gce Model Questions Vol1 2024 Chemistry Question 24

Using the Born-Lande equation\n\n\[\nU = -\frac{N_A M z^+ z^- e^2}{4\pi\varepsilon_0 r_0}\left(1-\frac{1}{n}\right)\n\]\n\nestimate the lattice energy of solid NaCl. Given: Madelung constant \(M = 1.7476\), ionic charges \(|z^+| = |z^-| = 1\), inter‑ionic distance \(r_0 = 2.82\;\text{Å}\), Born exponent \(n = 9\), and \(e^2/(4\pi\varepsilon_0) = 2.307\times10^{-28}\;\text{J·m}\).\n\nThen, using a Born‑Haber cycle, calculate the enthalpy of solution \(\Delta H_{\text{sol}}\) for NaCl, given the following data (all per mole): sublimation of Na(s) \(+108\;\text{kJ}\), ionisation energy of Na \(+496\;\text{kJ}\), half the bond dissociation energy of \(\mathrm{Cl_2}\) \(+121\;\text{kJ}\), hydration enthalpies \(\Delta H_{\text{hyd}}(\mathrm{Na^+}) = -406\;\text{kJ}\), \(\Delta H_{\text{hyd}}(\mathrm{Cl^-}) = -363\;\text{kJ}\). Assume the lattice energy you calculated is the only other term. Provide both the lattice energy (in kJ mol\(^{-1}\)) and \(\Delta H_{\text{sol}}\) (in kJ mol\(^{-1}\)).