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

Mar 14, 2018

$\text{48.1 mL}$

Explanation:

The idea here is that a solution's mass by volume percent concentration, $\text{m/v %}$, tells you the number of grams of solute present in exactly $\text{100 mL}$ 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 $\text{100 mL}$ of this solution contain $\text{10.4 g}$ of solute.

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

$5.00 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g solute"))) * "100 mL solution"/(10.4color(red)(cancel(color(black)("g solute")))) = color(darkgreen)(ul(color(black)("48.1 mL solution}}}}$

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

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