What is the energy of a bond formed between a potassium (K+) cation and an iodide (I−) anion? The ionic radii of K+ and I−, are 152 pm and 206 pm, respectively. Assume the Born exponent n is 10. Please report your answer in joules.
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To calculate the energy of a bond between a potassium cation (K+) and an iodide anion (I-), we can use the Born-Lande equation:
E = (k * (z1 * z2 * e^2)) / (r * n)
Where:
E = Energy of the ionic bond
k = Coulomb's constant (8.99 * 10^9 J*m/C^2)
z1 and z2 = charges of the ions (in this case, +1 for K+ and -1 for I-)
e = elementary charge (1.6 * 10^-19 C)
r = distance between the centers of the two ions
n = Born exponent
In this case, we need to convert the ionic radii of K+ and I- from picometers (pm) to meters (m) before calculating the energy.
Given:
Ionic radius of K+ = 152 pm = 152 * 10^-12 m
Ionic radius of I- = 206 pm = 206 * 10^-12 m
n = 10
Now we can substitute these values into the equation to find the energy:
E = (8.99 * 10^9 J*m/C^2) * ((+1) * (-1) * (1.6 * 10^-19 C)^2) / ((152 * 10^-12 m + 206 * 10^-12 m) * 10)
Simplifying:
E = (8.99 * 10^9 J*m/C^2) * (-1.6 * 10^-19 C)^2 / (358 * 10^-12 m * 10)
E = (8.99 * 10^9 J*m/C^2) * (2.56 * 10^-38 C^2) / (3.58 * 10^-9 m)
E = (8.99 * 2.56)/(3.58) * 10^-29 J
E ≈ 6.4478 * 10^-29 J
Therefore, the energy of the bond formed between K+ and I- is approximately 6.4478 * 10^-29 joules.