What you are given
- Percent: 0.9
- Molar mass (optional): 58.44
Formula: %w/v · 10 = g/L
Concentration
How do you convert a percent solution to molarity?
%w/v x 10 gives grams per litre, and dividing that by the molar mass gives molarity. For %w/w you also need the solution density, because a percentage by weight is not a percentage by volume.
Worked example
Every number below is computed by the calculator, not typed in
The working
- %w/v → g/L (× 10):
c (g/L) = %w/v · 10=9 g/L - g/L → M (÷ MW):
M = c(g/L) / MW=0.154 M
0.9% w/v = 9 g/L = 0.154 M.
What each symbol means
- c: Mass per volume (g/L)
- %w/v: Percent weight per volume (%)
A printable one-page version is on the formula sheet.
Where this usually goes wrong
- Treating %w/w as %w/v for a concentrated reagent. For 37% HCl at density 1.19, the difference is 19%.
- Forgetting the factor of 10 between percent and g/L. 0.9% w/v is 9 g/L, not 0.9 g/L.
- Using %v/v for a solid, which has no meaning.
Try it yourself
Two problems, with the working revealed
Problem 1 % concentration
Convert the percentage to grams per litre and to molarity.
- Percent: 25
- Basis: % w/w
- Molar mass (optional): 36.46
- Density (for w/w): 1.19
Show the answer and the working
25% w/w = 297.5 g/L = 8.16 M.
- %w/w → %w/v (× ρ):
%w/v = %w/w · ρ=29.75% w/v - %w/v → g/L (× 10):
c (g/L) = %w/v · 10 = %w/w · 10 · ρ=297.5 g/L - g/L → M (÷ MW):
M = c(g/L) / MW=8.16 M
Open this in the calculator to change the numbers.
Problem 2 % concentration
Convert the percentage to grams per litre and to molarity.
- Percent: 0.75
- Molar mass (optional): 58.44
Show the answer and the working
0.75% w/v = 7.5 g/L = 0.1283 M.
- %w/v → g/L (× 10):
c (g/L) = %w/v · 10=7.5 g/L - g/L → M (÷ MW):
M = c(g/L) / MW=0.1283 M
Open this in the calculator to change the numbers.
Do it with your own numbers.
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