Question #865b5

In order to find the solution's percent concentration by mass, `"% m/m"`, you must find the number of grams of solute present for every `"100 g"` of the solution.

You know that a sample of this solution contains `"5 g"` of the solute dissolved in `"50 mL = 50 cm"^3` of the solvent.

I will assume that the pure solvent has a density of `"0.7 g cm"^(-3) = "0.7 g mL"^(-1)`, which means that the `"50-mL"` sample has a mass of

`50 color(red)(cancel(color(black)("mL"))) * "0.7 g"/(1color(red)(cancel(color(black)("mL")))) = "35 g"`

So, the sample contains `"5 g"` of the solute in

`"5 g + 35 g = 40 g"`

of the solution, which means that `"100 g"` of this solution will contain

`100 color(red)(cancel(color(black)("g solution"))) * "5 g solute"/(40color(red)(cancel(color(black)("g solution")))) = "12.5 g solute"`

Therefore, you can say that the solution's percent concentration by mass is equal to

`color(darkgreen)(ul(color(black)("% m/m = 12.5%")))`

I'll leave the answer rounded to three sig figs, but keep in mind that you should report the answer as

`"% m/m = 10%"`

because you have only one significant figure for your values.