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
Mar 15, 2018

Answer:

#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.