Question

A 4.33 g sample of a laboratory solution contains 1.32 g of acid. What is the concentration of the solution as a mass percentage?

Answer 1

`30.5%`

Explanation:

A solution's percent concentration by mass, `"% m/m"`, tells you how many grams of solute, which in your case is an unknown acid, are present in `"100 g"` of solution.

`color(blue)(|bar(ul(color(white)(a/a)"% m/m" = "grams of solute / 100 g of solution"color(white)(a/a)|)))`

As you know, a solution contains a solute and a solvent, which more often than not is water. This means that a solution's `"% m/m"` concentration tells you how many grams of solute and grams of solvent must be mixed to get `"100 g"` of solution.

In your case, you know that you get `"1.32 g"` of acid in `"4.33 g"` of solution. To find the solution's percent concentration by mass, use this as a conversion factor to figure out how many grams of solute you'd get in `"100 g"` of solution

`100 color(red)(cancel(color(black)("g solution"))) * overbrace("1.32 g acid"/(4.33color(red)(cancel(color(black)("g solution")))))^(color(purple)("given to you")) = "30.5 g acid"`

Since `"100 g"` of this solution contain `"30.5 g"` of acid, it follows that the percent concentration by mass is

`"% m/m" = color(green)(|bar(ul(color(white)(a/a)color(black)("30.5% acid")color(white)(a/a)|)))`

The answer is rounded to three sig figs.

Notice that this is equivalent to dividing the mass of solute by the total mass of the solution and multiplying by `100`

`"% m/m" = (1.32 color(red)(cancel(color(black)("g acid"))))/(4.33color(red)(cancel(color(black)("g solution")))) * 100 = color(green)(|bar(ul(color(white)(a/a)color(black)("30.5% acid")color(white)(a/a)|)))`

As mentioned before, you can use the solution's percent concentration by mass to say that `"100 g"` of solution will contain

`"30.5 g acid"" "` and`" " "100 g " - " 30.5 g" = "69.5 g water"`

In other words, you can make this solution by adding `"30.5 g"` of acid for every `"69.5 g"` of water, which of course gets you `"30.5 g"` of acid per `"100 g"` of solution.