What is the %m/m of 75.0 g of ethanol dissolved in 500.0 g of water?

1 Answer
Feb 23, 2018

Answer:

#13.0%#

Explanation:

By definition, a solution's percent concentration by mass, #"% m/m"#, tells you the number of grams of solute present for every #"100 g"# of the solution.

This means that if you know the number of grams of ethanol dissolved in exactly #"100 g"# of this solution, you know the solution's percent concentration by mass.

Now, you know that your solution contains #"75.0 g"# of ethanol and #"500.0 g"# of water. The total mass of the solution is equal to

#"75.0 g " + " 500.0 g" = "575.0 g"#

So you can say your #"575.0-g"# sample of this solution contains #"75.0 g"# of ethanol, the solute.

This means that #"100 g"# of this solution will contain

#100 color(red)(cancel(color(black)("g solution"))) * "75.0 g ethanol"/(575.0 color(red)(cancel(color(black)("g solution")))) = "13.043 g ethanol"#

Since this represents the number of grams of ethanol present per #"100 g"# of the solution, you can say that the solution's percent concentration by mass is equal to

#color(darkgreen)(ul(color(black)("% m/m = 13.0% ethanol")))#

The answer is rounded to three sig figs, the number of sig figs you have for the mass of ethanol.