Chem 3411 Solution Set 5 - Mindanao State University - Iligan Institute Of Technology - 2010 Page 4
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14CHEM 3411, Fall 2010
Solution Set 5
where ∆T is the quantity by which the freezing point is decreased, b is the molality of solute, and K
is an empirical
f
1
constant (K
= 1.86 K kg mol
for water as found in Table 5.2).
f
We know molality is given by moles of solute over mass of solvent.
n
b
b =
M
H
O
2
n
b
=
n
M
H
O
w,H
O
2
2
$ $ $
$
$ $ $
Π
n
M
H 2 O
w,H 2 O
RT ρ
H 2 O
=
$
$ $ $
$ $ $
n
M
H
O
w,H
O
2
2
Π
=
RT ρ
H
O
2
where in the second equation we’ve calculated the mass of water from the moles of water solvent and in the third
expression we’ve used the expression for n
calculated earlier.
b
Inserting this expression for b into the freezing point depression equation gives
K
Π
f
∆T
=
RT ρ
H
O
2
$ $
kg $ $
¨ ¨
1.86 K & &
1
× 99.0 × 10
3
mol
Pa
=
$
$ $ $
¨
¨ ¨
Pa¨ ¨
kg ¨ ¨
8.3145 ¨ ¨
mol 1 × 288 & & K1.000 × 10
& &
3
1
3
3
m
K
m
= 0.076899 K
◦
= 0.076899
C
(as we’re only looking at a change, Kelvin and Celsius are the same)
∗
∗
With ∆T we know the the freezing point is given by T
= T
∆T where T
is the original freezing point, which
f
f
f
∗
◦
for water is T
= 0.000
C.
f
∗
T
= T
∆T
f
f
◦
◦
= 0.000
C
0.076899
C
◦
=
0.076899
C
Solution
◦
T
=
0.0769
C
f
4
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