Chem 3411 Solution Set 5 - Mindanao State University - Iligan Institute Of Technology - 2010 Page 5
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14CHEM 3411, Fall 2010
Solution Set 5
3
Exercise 5.13b pg 201
Given
◦
Predict the ideal solubility of lead (M
= 207.2 g/ mol) in bismuth (M
= 208.98 g/ mol) at T = 280
C given
w,Pb
w,Bi
◦
1
that its melting point is T
= 327
C and its enthalpy of fusion is 5.2 kJ mol
.
f
In terms of given variables, this is written:
M
= 207.2 g/ mol
w,Pb
M
= 208.98 g/ mol
w,Bi
◦
T = 280
C
◦
T
= 327
C
f
1
∆
H = 5.2 kJ mol
fus
Find
The ideal solubility of lead.
Strategy
For this problem we’ll use the equation for ideal solubility (eq 5.37 on pg 172)
(
)
∆
H
1
1
fus
ln χ
=
B
R
T
T
f
Solving for χ
, the solubility of the solute, which is χ
in this case gives
B
Pb
[
(
)]
∆
H
1
1
fus
χ
= exp
Pb
R
T
T
f
We can simply substitute the given values into the expression for χ
after temperatures have been converted from
Pb
Celsius to Kelvin.
◦
T = 280
C = 553 K
◦
T
= 327
C = 600 K
f
[
(
)]
∆
H
1
1
fus
χ
= exp
Pb
R
T
T
f
[
(
)]
$ $
J $ $
5.2 × 10
1
3
mol
1
1
= = exp
$
$ $ $
8.3145 J ¨ ¨ ¨
1
1
600 K
553 K
K
mol
= 0.9152
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