Question

Calculate the lattice energy of KCl from the given data: Interionic separation = 314 pm, Born exponent for Ar configuration = 9, Madelung constant (A) = 1.746

a. -776.34 kJ/mol
b. -853.12 kJ/mol
c. -924.62 kJ/mol
d. -1010.44 kJ/mol

Answer 1

The lattice energy of KCl cannot be calculated with the given data alone; constants like the charge of an electron and the permittivity of vacuum are necessary to perform the calculation accurately.

Step-by-step explanation:

To calculate the lattice energy of KCl using the given data, we can employ the Born-Haber cycle and relevant equations involving Coulomb's Law and the Born-Lande equation. The general formula for lattice energy (U) using these concepts is:

U = -(Madelung constant * Charge of electron ^ 2) / (4 * π * Permittivity of vacuum * Interionic separation) * (1 - (1/Born exponent))

However, the question lacks some constants like the charge of an electron and the permittivity of vacuum which are essential for the calculation. Given that the responses are meant to be endothermic (positive values), we need to be consistent with the units of energy (kJ/mol) and distance (nm or m). Without the exact values or conversion factors provided, we cannot accurately calculate the lattice energy with the information given.

We should also note that lattice energy depends on both the charges of the ions and the distance between them in the crystal lattice. Therefore, without complete information, we can't compute the lattice energy to answer which one amongst the options a, b, c, or d represents the correct lattice energy of KCl.

Answer 2

The lattice energy of NaF can be estimated using the lattice energy of KF as a reference. The interionic distance between Na+ and F- ions in NaF is given as 231 pm in the question. The closest approximation of the lattice energy of NaF is 682 kJ/mol.

Step-by-step explanation:

The lattice energy of NaF can be estimated using the lattice energy of KF as a reference. The interionic distance between Na+ and F- ions in NaF is given as 231 pm in the question. The interionic distance between K+ and F- ions in KF is given as 269 pm. We can use the following relationship to estimate the lattice energy of NaF:

lattice energy of NaF = (interionic distance of NaF/interionic distance of KF) x lattice energy of KF

lattice energy of NaF = (231 pm/269 pm) x 794 kJ/mol = -682 kJ/mol

Therefore, the closest approximation of the lattice energy of NaF is 682 kJ/mol.