5.112 Principles Of Chemical Science Worksheet With Answers - Problem Set #4 Solutions - 2011 Page 3
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16Problem set #4 solutions for 5.112, Fall 2011
Page 3 of 16
Question 5 (out of 6 points)
Consider KF, which has an ionic bond. The bond length is 2.17 x 10 -10 m or 217 pm.
(a) Calculate the energy (in kJ/mol) required to dissociate the KF molecule into the ions K +
and F - .
+
-1
This energy is the Coulomb energy of interaction between the ions of K
and F
:
Q
Q
1
2
ΔE
=
ε
coulombic
4π
r
0
(
)
(
)
2
( )
( )
-19
23
-1
1
1
1.602 x 10
C
6.022 x10
mol
=
(
)
(
)
−12
−1
−1
2
-10
4π 8.854 x 10
C
J
m
2.17 x 10
m
-1
2
-1
= 6.40 x 10
= 640113 J mol
kJ mol
2
-1
The energy required to dissociate KF into its ions is 6.40 x 10
kJ mol
. The energy is positive
because we are going from molecule to ions (up on the energy scale).
(b) The energy required to dissociate KF into neutral atoms is 498 kJ/mol. Given that the first
ionization energy for K is 419 kJ/mol, calculate the electron affinity (in kJ/mol) for F.
We can calculate the electron affinity for F by using the following equation:
Q
Q
[
]
1
2
ΔE
− IE
ε
=
(K) - EA(F)
d
1
4π
R
0
We are given the ΔE
-1
(498 kJ mol
). We calculated the coulomb interaction energy in part (a) (640
d
-1
-1
kJ mol
) and we are given IE
for potassium (419 kJ mol
), so we can calculate the electron
1
affinity for F by substitution into the above equation:
Q
Q
[
]
1
2
ΔE
− IE
=
ε
(K)-EA(F)
d
1
4π
r
0
⎡
⎤
-1
2
-1
-1
498 kJ mol
= 6.40 x 10
kJ mol
- 419 kJ mol
-EA(F)
⎣
⎦
-1
2
-1
-1
− 6.40 x 10
+ 419 kJ mol
EA(F)=498 kJ mol
kJ mol
-1
= 277 kJ mol
-1
-1
The electron affinity for F is 277 kJ mol
. (The electron affinity is actually 328 kJ mol
). Since this
method is an approximation, the agreement is reasonable.
Question 6 (out of 6 points)
-10
Consider the SrO molecule that has an ionic bond length of 1.54 x 10
m.
-1
+2
-2
a) Calculate the energy in kJ mol
required to dissociate SrO into its ions Sr
and O
. Treat
the ions as point charges.
The energy the question asked for is the ΔE
, which can be calculated from the following
coulomb
equation:
(
)
(
)
( )
2
2
-19
23
-1
2
1.602176 x 10
C
6.02214 x 10
mol
2
e
ΔE
=
=
(
)
(
)
4 πε
4 π 8.85419 x 10
coloumb
-12
2
-1
-1
-10
r
C
J
m
1.54 x 10
m
0
-14
2
-1
6.183456 x 10
C
mol
=
-20
2
-1
1.713482 x 10
C
J
= 3.60871 x 10
6
-1
J mol
= 3.61 x 10
3
-1
kJ mol
+2
-2
3
-1
The energy required to dissociate SrO into its ions Sr
and O
is 3.61 x 10
kJ mol
.
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