Question

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

Answer 1

`0.0162`

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 `11.5%`, which means that for every `"100.0 g"` of this solution, you get `"11.5 g"` of sodium sulfate, the solute.

To make the calculations easier, let's pick a sample of this solution that has a mass of exactly `"100.0 g"`. Since you know how many grams of sodium sulfate it contains, you can calculate the mass of water present in the sample.

`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, `chi_ ("Na"_ 2"SO"_ 4)`, you must divide the number of moles of sodium sulfate by the 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.