Question

Question #fbe14

Answer 1

`"1.8% NaCl"`

Explanation:

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.