# Question 53829

Feb 28, 2017

$\text{1.67% m/v}$

#### Explanation:

The idea here is that when a solution undergoes a $1 : 3$ dilution, its final volume increases by a factor of $3$.

This is done by adding enough solvent to ensure that the total volume of the solution increases by a factor of $3$. As a result, the concentration of the solution will decrease by a factor of $3$.

In your case, the starting solution has a $\text{5% m/v}$ concentration and a volume of $\text{250 mL}$. The total volume of the solution after the dilution will be

${V}_{\text{final" = 3 xx "250 mL" = "750 mL}}$

The concentration of the solution after the dilution will be

"% m/v" = "5%"/3 = color(darkgreen)(ul(color(black)(1.67%)))

You can double-check this result by working with the mass of solute present in the solution. In the initial solution, you have

250 color(red)(cancel(color(black)("mL solution"))) * overbrace("5 g NaCl"/(100color(red)(cancel(color(black)("mL solution")))))^(color(blue)("= 5% m/v NaCl")) = "12.5 g NaCl"

Remember, the solution is diluted by adding solvent, so you know for a fact that the diluted solution will contain $\text{12.5 g}$ of sodium chloride.

In order to find the diluted solution's mass by volume percent concentration, you must determine how many grams of solute you have in $\text{100 mL}$ of solution. The diluted solution has a volume of $\text{750 mL}$ and contains $\text{12.5 g}$ of sodium chloride, which means that $\text{100 mL}$ of this solution will contain

100 color(red)(cancel(color(black)("mL solution"))) * "12.5 g NaCl"/(750 color(red)(cancel(color(black)("mL solution")))) = "1.67 g NaCl"#

This means that the mass by volume percent concentration of the diluted solution will be

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{\text{% m/v = 1.67% NaCl}}}}$

I'll leave the answer rounded to three sig figs, but keep in mind that you only have one significant figure for the concentration of the initial solution.