mole fraction and mass percent

Question

The mole fraction of ammonium phosphate, (NH₄)₃PO₄, in an aqueous solution is 2.28×10^-2 .

The percent by mass of ammonium phosphate in the solution is __%.

Answer 1

Okay, first if the mole fraction of ammonium phosphate is 0.0228, then the rest is water. So, the mole fraction of water is 1 - 0.0228 or 0.9772 .

But we want % by mass. So lets find the masses assuming we have a 1 mole sample.

for water 0.9772 x 18.00 = 17.59 g and for AP it is .0228 x 149.09 = 3.399 g

Now percent by mass is 3.399 / (3.399 + 17.59) = .1619 or 16.19%

Note: The answer might need to be round to 3 significant figures.