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

##### 1 Answer

#### Explanation:

The solution's **mass by volume percent concentration**,

In your case, the solution is said to have a mass by volume percent concentration of

#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

#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

#"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

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

The answer is rounded to one **significant figure**.