# How many grams of solute are in "2.5 L" of a solution which is "20% w/v" ?

Nov 29, 2017

$\text{500 g}$

#### Explanation:

A solution's mass by volume percent concentration, $\text{% m/v}$, is a measure of the number of grams of solute present for every $\text{100 mL}$ of the solution.

So if you take exactly $\text{100 mL}$ of a given solution, the number of grams of solute present in that sample will give you the solution's mass by volume percent concentration and vice versa.

In your case, the solution is $\text{20% m/v}$, which means that it contains $\text{20 g}$ of solute for every $\text{100 mL}$ of the solution.

color(blue)(20)color(red)(%)"m/v" " " implies " " color(blue)("20 g") color(white)(.)"solute in"color(white)(.)color(red)("100 mL")color(white)(.)"of solution"

You can thus say that your sample contains

$2.5 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{L solution"))) * (10^3color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("L")))) * "20 g solute"/(100color(red)(cancel(color(black)("mL solution")))) = color(darkgreen)(ul(color(black)("500 g solute}}}}$

The answer is rounded to one significant figure, the number of sig figs you have for the solution's mass by volume percent concentration.