Mole Fraction
The concentration of a solution refers to the amount of solute in a given amount of solvent. There are many ways to express, quantatively, the concentration of a solution. Some solution properties depend on the relative amounts of all the solution components in terms of moles. The mole fraction of a solution component Xi is the fraction of moles of component i of the total number of moles of all components in solution.
moles of component i |
||
Xi |
= |
------------------------ |
total moles of solution |
Lets work through an example problem that will illustrate this concept.
Example problem
What is the mole fraction of each component in a solution in which 3.57 g of sodium chloride, NaCl, is dissolved in 25.0 g of water?
Solution
First, convert from mass of NaCl to moles of NaCl.
1 mole NaCl |
||||
3.57 g NaCl |
x |
--------------------- |
= |
0.0611 mole NaCl |
58.44 g NaCl |
Next, convert from mass of water to moles of water.
1 mole H2O |
||||
25.0 g H2O |
x |
--------------------- |
= |
1.39 mole H2O |
18.02 g H2O |
Substitute these two quantities into the defining equation for mole fraction.
0.0611 mol NaCl |
||||
XNaCl |
= |
-------------------- |
= |
0.0421 |
(0.0611 + 1.39) mol solution |
|
1.39 mole H2O |
||||
Xwater |
= |
-------------------- |
= |
0.958 |
(0.0611 + 1.39) mol solution |
Note that within the limits of the significant figures that XNaCl + Xwater = 1. The sum of the mole fractions for a solution will equal 1. In our example above, after we have calculated one mole fraction we could have subtracted it from 1 to obtain the other.