Chemical Bonding Worksheet With Answers Page 5
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11
12+
-
2.16
Consider a hypothetical X
-Y
ion pair for which the equilibrium interionic spacing and bonding
energy values are 0.35 nm and -6.13 eV, respectively. If it is known that n in Equation 2.11 has a value of 10, using
the results of Problem 2.14, determine explicit expressions for attractive and repulsive energies E
and E
of
A
R
Equations 2.8 and 2.9.
Solution
This problem gives us, for a hy pothetical X + -Y - ion pair, values for r
(0.35 nm ), E
(– 6.13 eV), and n
0
0
(10), and asks t hat we determine explicit expressions for attractive and repulsive energies of Equations 2.8 and 2.9.
In essence, it is necessary to compute the values of A and B in these equations. Expressions for r
and E
in terms
0
0
of n, A, and B were determined in Problem 2.14, which are as follows:
1/(1 - n )
⎛
⎞
A
=
r
⎜
⎟
0
⎝
⎠
nB
A
B
= −
+
E
0
1/(1 - n )
n /(1 - n )
⎛
⎞
⎛
⎞
A
A
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
nB
nB
Thus, we have t wo simultaneous equations with two unknowns (vi z. A and B). Upon substitution of values for r
0
and E
in terms of n, these equations take the forms
0
1/(1 - 10)
-1/9
⎛
⎞
⎛
⎞
A
A
0.35 nm =
⎜
⎟
⎜
⎟
=
10 B
10 B
⎝
⎠
⎝
⎠
and
A
B
− 6.13 eV = −
+
1/(1 − 10)
10 /(1 − 10)
⎛
⎞
⎛
⎞
A
A
⎜
⎟
⎜
⎟
10 B
10 B
⎝
⎠
⎝
⎠
A
B
= −
+
− 1/ 9
− 10 / 9
⎛
⎞
⎛
⎞
A
A
⎜
⎟
⎜
⎟
⎝
10B
⎠
⎝
10B
⎠
We now want t o sol ve t hese t wo equat ions si multaneously for val ues of A and B. Fro m th e first o f th ese two
equations, solving for A/8B leads to
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