# What is the mole fraction of #"Na"_2"SO"_4# in a solution which is #11.5%# by weight #"Na"_2"SO"_4# ?

##### 1 Answer

#### Explanation:

Your starting point here will be the solution's percent concentration by mass.

Your solution is said to have a percent concentration by mass of

To make the calculations easier, let's pick a sample of this solution that has a mass of exactly

#overbrace("mass of water")^(color(blue)("mass solvent")) = overbrace("100.0 g")^(color(blue)("mass solution")) - overbrace("11.5 g")^(color(blue)("mass solute"))#

#"mass of water = 88.5 g"#

Now, use the **molar mass** of water to convert the mass to *moles*.

#88.5 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "4.9126 moles H"_2"O"#

Do the same for sodium sulfate, i.e. use its **molar mass** to convert the mass to *moles*.

#11.5 color(red)(cancel(color(black)("g"))) * ("1 mole Na"_2"SO"_4)/(142.04color(red)(cancel(color(black)("g")))) = "0.08096 moles Na"_2"SO"_4#

To find the **mole fraction** of sodium sulfate, **total number of moles** present in the solution.

#chi_ ("Na"_ 2"SO"_ 4) = (0.08096 color(red)(cancel(color(black)("moles"))))/((4.9126 + 0.08096)color(red)(cancel(color(black)("moles")))) = color(darkgreen)(ul(color(black)(0.0162)))#

The answer is rounded to three **sig figs**.