Conversion of Concentration Units Problems
Conversion of Molality to Mole Fraction
What is the mole fraction of each component in a 0.500 m aqueous solution of NaCl?
From the definition of molality we know that this solution contains 0.500 mol of NaCl
in 1.00 kg of water. So let's assume we have enough solution to contain 0.500 mol
NaCl. This means that the solution will have 1.00 kg of water, convert this to moles.
1 mol H2O
1.00 x 10 g
H2O
3
x
--------------------- =
55.6 mol H2O
18.0 g H2O
0.500 mol NaCl
XNaCl
= -------------------- =
0.00891
(0.500 + 55.6) mol
solution
55.6 mole H2O
Xwater
=
--------------------
=
0.99109
(0.500 + 55.6) mol
solution
Conversion of Molality to Mass Percent
What is the mass percentage of NaCl in a 0.500 m aqueous solution of NaCl?
Again assume that you have enough solution, that it contains 0.500 mol NaCl and therefore
1.00 x 103 g of water. Convert 0.500 mol of NaCl into mass.
0.500 mol NaCl
x
58.44 g NaCl
---------------1 mole NaCl
=
29.22 g NaCl
29.22 g NaCl x 100
mass %
NaCl
2.84 %
= ----------------------------- =
(29.22 + 1.00 x 103) g
soln
1
Conversion of Mole Fraction to Molality
What is the molality of NaCl in an aqueous solution in which the mole fraction of NaCl
is 0.100?
Let's assume we have 1.00 mol of solution. This means that the solution will contain
0.100 mol of NaCl and 0.900 mol of water. Convert 0.900 mole of water to kilograms.
0.900 mol H2O
x
18.0 g H2O
---------------1 mole H2O
=
16.2 g H2O
0.100 mol NaCl
molality
6.17 m
= ----------------------------- =
0.0162 kg solvent
Conversion of Molarity to Molality
What is the molality of NaCl in an aqueous solution which 4.20 M? The density of the
solution is 1.05 x 103 g/L.
Let's assume we have 1.00 L of solution. This means that the solution will contain
4.20 mol of NaCl. Convert this to mass.
4.20 mol NaCl
x
58.44 g NaCl
---------------1 mole NaCl
=
245 g NaCl
Subtract this from the mass of one liter of solution (obtained from the density) to
obtain the mass of water.
mass water = 1050 g solution - 245 g NaCl = 805 g water
4.20 mol NaCl
molality
5.22 m
= ----------------------------- =
0.805 kg solvent
2
Conversion of Molality to Molarity
What is the molarity of NaCl in an aqueous solution which 4.50m. The density of the
solution is 1.050 g/mL (1.050 x 103 g/L)
Let's assume we have enough solution to contain 4.50 mol NaCl, which means that we
will have 1.00 kg of water. Convert 4.20 mol of NaCl to mass.
4.50 mol NaCl
x
58.44 g NaCl
---------------1 mole NaCl
=
263 g NaCl
Add the mass of NaCl and the mass of water to obtain the mass of solution.
mass solution = 1000 g water + 263 g NaCl = 1263 g solution
Next use the density to calculate the volume of solution.
volume
1.26 x 103 g
= ----------------------------- =
1.05 x 103 g/L
1.203 L
4.50 mol NaCl
molarity
3.74 M
= ----------------------------- =
1.203 L
3