Final answer:
The binding energy per mole for potassium chloride is calculated using Coulomb's law and considering the Madelung constant. The result is approximately 644 kJ/mol.
Step-by-step explanation:
To calculate the binding energy per mole for potassium chloride (KCl), we use Coulomb's law of electrostatic attraction between oppositely charged ions. The formula for lattice energy (U) in an ionic crystal is given by:
U = (k * Q1 * Q2) / r0
where k is the Coulomb's constant (8.99 x 109 Nm2/C2), Q1 and Q2 are the charges on the ions (+1 and -1 e for K+ and Cl-), and r0 is the nearest neighbour distance.
The Madelung constant (α), which accounts for the geometry of the crystal lattice, is given as 1.64, and the charge on an ion is 1.6 x 10-19C. The nearest neighbour distance (r0) for KCl is 3.14 x 10-10 m (3.14 Å). To find U per mole, we use Avogadro's number (6.022 x 1023/mol) to convert the energy per ion pair to energy per mole. Hence, the binding energy per mole is calculated as follows:
U per ion pair = (k * Q1 * Q2 * α) / r0
= (8.99 x 109 Nm2/C2 * (1.6 x 10-19C)2 * 1.64) / (3.14 x 10-10 m)
= -1.069 x 10-19J/ion pair
To convert this energy to kJ/mol:
U per mole = U per ion pair * Avogadro's number
= (-1.069 x 10-19J/ion pair) * (6.022 x 1023/mol)
= -643.9618 kJ/mol
The negative sign indicates that energy is released when the ions form a solid lattice, meaning the process is exothermic. Therefore, the binding energy per mole for potassium chloride is approximately 644 kJ/mol.