Based on data in Table 8.2 , estimate (within \(30 \mathrm{~kJ} / \mathrm{mol}\) ) the lattice energy for (a) LiBr, (b) CsBr, (c) \(\mathrm{CaCl}_{2}\)

The Born-Lande equation allows us to calculate the lattice energy, which is given by: \[E_l = -\frac{N_AMz^+z^-e^2}{4\pi \epsilon_0r_0}(1-\frac{1}{n})\] Where: - \(E_l\) is the lattice energy - \(N_A\) is Avogadro's number (approximately \(6.022\times10^{23}\) mol⁻¹) - \(M\) is the Madelung constant, a dimensionless constant specific to the crystal structure - \(z^+\) and \(z^-\) are the charges of the positive and negative ions, respectively - \(e\) is the elementary charge (approximately \(1.602\times10^{-19}\) C) - \(\epsilon_0\) is the vacuum permittivity constant (approximately \(8.854\times10^{-12}\) C²/(N·m²)) - \(r_0\) is the sum of the ionic radii of the positive and negative ions - \(n\) is the Born exponent, typically in the range of 5-12, depending on the compound.

From Table 8.2 of the given problem, extract the values of Madelung constant (M), charges of the ions (z⁺ and z⁻), ionic radii (r₀), and the Born exponent (n) for LiBr, CsBr, and CaCl2.

Using the data extracted in Step 2, plug the values for LiBr into the Born-Lande equation and calculate the lattice energy for LiBr: \[E_l = -\frac{N_AMz^+z^-e^2}{4\pi \epsilon_0r_0}(1-\frac{1}{n})\]

Using the data extracted in Step 2, plug the values for CsBr into the Born-Lande equation and calculate the lattice energy for CsBr: \[E_l = -\frac{N_AMz^+z^-e^2}{4\pi \epsilon_0r_0}(1-\frac{1}{n})\]

Using the data extracted in Step 2, plug the values for CaCl2 into the Born-Lande equation and calculate the lattice energy for CaCl2: \[E_l = -\frac{N_AMz^+z^-e^2}{4\pi \epsilon_0r_0}(1-\frac{1}{n})\] Once you have completed Steps 3-5, you will have estimated the lattice energy for LiBr, CsBr, and CaCl2 within 30 kJ/mol.