Question

What would be the final volume of a 10.4% (m/v) solution made from 5.00 g of solute?

Answer 1

`"48.1 mL"`

Explanation:

The idea here is that a solution's mass by volume percent concentration, `"m/v %"`, tells you the number of grams of solute present in exactly `"100 mL"` of the solution.

In your case, the solution is said to have a mass by volume percent concentration of `10.4%`, which implies that every `"100 mL"` of this solution contain `"10.4 g"` of solute.

Now, you know that your target solution must contain `"5.00 g"` of solute, so you can determine the volume of the solution by using the mass by volume percent concentration as a conversion factor.

`5.00 color(red)(cancel(color(black)("g solute"))) * "100 mL solution"/(10.4color(red)(cancel(color(black)("g solute")))) = color(darkgreen)(ul(color(black)("48.1 mL solution")))`

The answer is rounded to three sig figs, the number of sig figs you have for your values.

So, in order to make this `"10.4% m/v"` solution, you need to dissolve `"5.00 g"` of solute in enough water to get the total volume of the solution to `"48.1 mL"`.