Question

A solution is made by dissolving 3.60g of sodium chloride to a final volume of 115mL solution. What is the weight/volume % of the solute?

Answer 1

`3.13%`

Explanation:

The idea here is that a solution's mass by volume percent concentration, `"% m/v"`, sometimes called weight by volume, tells you how many grams of solute you get per `"100 mL"` of solution.

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

This means that in order to determine a solution's mass by volume percent concentration, all you have to do is figure out how many grams of solute you have in `"100 mL"` of solution.

In your case, you know that you're dissolving `"3.60 g"` of sodium chloride, `"NaCl"`, which is your solute, to get a final volume of `"115 mL"` of solution.

Right from the start, you can say that the solution's mass by volume percent concentration will be lower than `3.60%` because `"100 mL"` will contain less than `"360 g"` of sodium chloride.

More specifically, `"100 mL"` of solution will contain

`100 color(red)(cancel(color(black)("mL solution"))) * "3.60 g NaCl"/(115color(red)(cancel(color(black)("mL solution")))) = "3.13 g NaCl"`

So, if `"100 mL"` of solution contain `"3.13 g"` of solute, it follows that the solution's `"% m/v"` will be

`color(green)(|bar(ul(color(white)(a/a)color(black)("% m/v " = " 3.13 %")color(white)(a/a)|)))`

The answer is rounded to three sig figs.