Calculate the magnitude of the cohesive energy of potassium iodide (KI). The ionic radii of K+ and I−, are 152 pm and 206 pm, respectively. Assume the Born exponent n is 10. Assume a Madelung constant of 1.7. Please report your answer in kJ/mol or how to calculate it.
To calculate the magnitude of the cohesive energy of potassium iodide (KI), you can use the Born-Lande equation:
E = (k * M / (n-1)) * (z1 * z2 / d) * [1 - (1.7 * (r1 + r2) / d)]
Where:
E is the cohesive energy
k is a constant (9 × 10^9 N·m^2/C^2)
M is the Madelung constant
n is the Born exponent (in this case, 10)
z1 and z2 are the charges of the ions (K+ and I-, respectively)
d is the distance between the ions (sum of their ionic radii, r1 + r2)
Now, let's go through the steps to calculate the cohesive energy of KI:
Step 1: Convert the ionic radii from picometers (pm) to meters (m):
r1 = 152 pm = 152 × 10^-12 m
r2 = 206 pm = 206 × 10^-12 m
Step 2: Calculate the distance between the ions (d):
d = r1 + r2
Step 3: Calculate the cohesive energy (E):
E = (k * M / (n-1)) * (z1 * z2 / d) * [1 - (1.7 * (r1 + r2) / d)]
In this case, z1 = +1 (for K+) and z2 = -1 (for I-). The Madelung constant for potassium iodide is given as 1.7.
Plug in all the values to calculate the cohesive energy.