Question

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

Answer 1

`"5 mg mL"^(-1)`

Explanation:

The solution's mass by volume percent concentration, `"m/v %"`, tells you the number of grams of solute present for every `"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 `"0.5 g"` of solute for every `"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 `"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

`"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 `"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.