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

1 Answer
Apr 9, 2018

Answer:

#"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.