Question

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

Answer 1

`"3.13% w/v NaCl"`

Explanation:

A solution's weight by volume percent concentration, `"% w/v"`, sometimes called mass by volume percent concentration, `"% m/v"`, is simply a measure of the mass of solute present in `"100 mL"` of solution.

This implies that in order to determine a solution's weight by volume percent concentration, all you have to do is to figure out the number of grams of solute you get for every `"100 mL"` of solution.

In your case, you know that you have `"3.60 g"` of sodium chloride dissolved in enough water to make for `"115 mL"` 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 as a conversion factor to scale the mass of the solute to a volume of `"100 mL"` of solution.

In other words, you will have

`100 color(red)(cancel(color(black)("mL solution"))) * overbrace("3.60 g NaCl"/(115color(red)(cancel(color(black)("mL solution")))))^(color(blue)("known composition")) = "3.13 g NaCl"`

Since this represents the mass of solute present in `"100 mL"` of solution, you can say the solution has a weight by volume percent concentration of

`color(darkgreen)(ul(color(black)("% w/v = 3.13% NaCl")))`

The answer is rounded to three sig figs.