Question #fbe14

1 Answer
Apr 8, 2017

#"1.8% NaCl"#


The trick here is to realize that a solution's mass by mass percent concentration, #"% m/m"#, expresses the number of grams of solute present for every #"100 g"# of solution.

The mass of the solution will be equal to the sum of the mass of the solute and of the mass of the solvent

#"mass of solution = mass of solute + mass of solvent"#

In your case, you will have

#"mass of solution" = "4.6 g" + "250 g" = "254.6 g"#

Now, you know that this solution contains #"4.6 g"# of sodium chloride, the solute, in #"254.6 g"# of solution. Your goal now is to figure out the number of grams of solute present in #"100 g"# of solution.

As you know, solutions are homogeneous mixtures, which implies that they have the same composition throughout.

This allows you to use the known composition of the solution as a conversion factor

#100 color(red)(cancel(color(black)("g solution"))) * overbrace("4.6 g NaCl"/(254.6 color(red)(cancel(color(black)("g solution")))))^(color(blue)("the composition of the solution")) = "1.807 g NaCl"#

You can thus say that the solution's mass by mass percent concentration is equal to

#color(darkgreen)(ul(color(black)("% m/m = 1.8% NaCl")))#

The answer is rounded to two sig figs, the number of sig figs you have for the mass of sodium chloride and for the mass of water.