Question

MgO crystallizes as rock-salt structure with unit cell length 2.12 Å. From the electrostatic model, the calculated lattice energy in kJ mol$^{-1}$ (rounded off to the nearest integer) is ________.
(Given:} $N_A = 6.022 \times 10^{23}$ mol$^{-1}$, $M = 1.748$, $\varepsilon_0 = 8.854 \times 10^{-12}$ J$^{-1}$C$^2$m$^{-1}$, charge on electron $= 1.602 \times 10^{-19}$ C{)

Hint:

Higher ionic charges and smaller ionic radii increase lattice energy (directly proportional to $z^+z^-/r_0$).

Answer 1

Correct Answer: 6150

Step 1: Formula for lattice energy.
\[ U = -\frac{N_A M z^+ z^- e^2}{4\pi \varepsilon_0 r_0} \] For MgO, $z^+ = z^- = 2$, and $r_0 = 2.12 \times 10^{-10}$ m. Step 2: Substitute values.
\[ U = -\frac{(6.022 \times 10^{23})(1.748)(4)(1.602 \times 10^{-19})^2} {4\pi (8.854 \times 10^{-12})(2.12 \times 10^{-10})} \] Step 3: Simplify.
\[ U = -3.90 \times 10^6 \, \text{J mol}^{-1} = -3900 \, \text{kJ mol}^{-1} \] Step 4: Conclusion.
The lattice energy of MgO ≈ 3900 kJ mol$^{-1$}.