Question #97eda

Your goal here is to figure out the number of grams of sodium chloride, your solute, present in `"100 g"` of this solution.

Since you know that your sample contains `"0.5 g"` of sodium chloride in `"20 g"` of water, you can say that the mass of the solution is equal to

`overbrace("0.5 g")^(color(blue)("mass of solute")) + overbrace("20 g")^(color(blue)("mass of solvent")) = overbrace("20.5 g")^(color(blue)("mass of solution"))`

Now, you know that you have `"0.5 g"` of sodium chloride in `"20.5 g"` of solution, which means that `"100 g"` of this solution will contain

`100 color(red)(cancel(color(black)("g solution"))) * overbrace("0.5 g NaCl"/(20.5color(red)(cancel(color(black)("g solution")))))^(color(blue)("known composition")) = "2.439 g NaCl"`

Since a solution's percent concentration by mass, `"m/m %"`, tells you the number of grams of solute present for every `"100 g"` of solution, you can say that your solution will be

`color(darkgreen)(ul(color(black)("% by mass = 2% NaCl")))`

The answer must be rounded to one significant figure, the number of sig figs you have for your values.