# If a solution is 0.5% (w/v), how many mg/ml is that?

Apr 9, 2018

${\text{5 mg mL}}^{- 1}$

#### Explanation:

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

In your case, the solution is said to have a mass by volume percent concentration of 0.5%, which means that you get $\text{0.5 g}$ of solute for every $\text{100 mL}$ of the solution.

color(blue)(0.5)color(darkorange)(%) quad "m/v" = color(blue)("0.5 g") quad "solute per" quad color(darkorange)("100 mL") quad "of the solution"

You can thus say that $\text{1 mL}$ of this solution will contain

1 color(red)(cancel(color(black)("mL solution"))) * "0.5 g solute"/(100color(red)(cancel(color(black)("mL solution")))) = "0.005 g solute"

To convert this to milligrams, use the fact that

$\text{1 g" = 10^3 quad "mg}$

You will end up with

0.005 color(red)(cancel(color(black)("g"))) * (10^3 quad "mg")/(1color(red)(cancel(color(black)("g")))) = "5 mg"

Since this represents the number of milligrams of solute present for every $\text{1 mL}$ of the solution, you can say that the solution has a concentration of

"concentration" = color(darkgreen)(ul(color(black)("5 mg mL"^(-1))))

The answer is rounded to one significant figure.