Molality is a concentration unit defined as the ratio of the numbers of moles of solute to the mass of the solvent in kilograms:
m
=
mol\;solute
kg\;solvent
Since these units are computed using only masses and molar amounts, they do not vary with temperature and, thus, are better suited for applications requiring temperature-independent concentrations, including several colligative properties, as will be described in this chapter module.
Example 1
Calculating Mole Fraction and Molality
The antifreeze in most automobile radiators is a mixture of equal volumes of ethylene glycol and water, with minor amounts of other additives that prevent corrosion. What are the (a) mole fraction and (b) molality of ethylene glycol, C2H4(OH)2, in a solution prepared from 2.22 × 103 g of ethylene glycol and 2.00 × 103 g of water (approximately 2 L of glycol and 2 L of water)?
Solution
(a) The mole fraction of ethylene glycol may be computed by first deriving molar amounts of both solution components and then substituting these amounts into the unit definition.
mol\;C
2
H
4
(
OH
)
2
=
2220
g
×
1
mol\;C
2
H
4
(
OH
)
2
62.07
g\;C
2
H
4
(
OH
)
2
=
35.8
mol\;C
2
H
4
(
OH
)
2
mol\;H
2
O
=
2000
g
×
1
mol\;H
2
O
18.02
g\;H
2
O
=
11.1
mol\;H
2
O
X
ethylene\;glycol
=
35.8
mol\;C
2
H
4
(
OH
)
2
(
35.8
+
11.1
)
mol\;total
=
0.763
Notice that mole fraction is a dimensionless property, being the ratio of properties with identical units (moles).
Answers & Comments
Answer:
Molality is a concentration unit defined as the ratio of the numbers of moles of solute to the mass of the solvent in kilograms:
m
=
mol\;solute
kg\;solvent
Since these units are computed using only masses and molar amounts, they do not vary with temperature and, thus, are better suited for applications requiring temperature-independent concentrations, including several colligative properties, as will be described in this chapter module.
Example 1
Calculating Mole Fraction and Molality
The antifreeze in most automobile radiators is a mixture of equal volumes of ethylene glycol and water, with minor amounts of other additives that prevent corrosion. What are the (a) mole fraction and (b) molality of ethylene glycol, C2H4(OH)2, in a solution prepared from 2.22 × 103 g of ethylene glycol and 2.00 × 103 g of water (approximately 2 L of glycol and 2 L of water)?
Solution
(a) The mole fraction of ethylene glycol may be computed by first deriving molar amounts of both solution components and then substituting these amounts into the unit definition.
mol\;C
2
H
4
(
OH
)
2
=
2220
g
×
1
mol\;C
2
H
4
(
OH
)
2
62.07
g\;C
2
H
4
(
OH
)
2
=
35.8
mol\;C
2
H
4
(
OH
)
2
mol\;H
2
O
=
2000
g
×
1
mol\;H
2
O
18.02
g\;H
2
O
=
11.1
mol\;H
2
O
X
ethylene\;glycol
=
35.8
mol\;C
2
H
4
(
OH
)
2
(
35.8
+
11.1
)
mol\;total
=
0.763
Notice that mole fraction is a dimensionless property, being the ratio of properties with identical units (moles).
Explanation: