What you are given
- Label concentration (%w/w): 37
- Density (g/mL): 1.19
- Molar mass (g/mol): 36.46
- Target concentration: 1 M
- Final volume: 100 mL
Formula: M = 10·%·ρ / MW ; C₁V₁ = C₂V₂
Dilutions
How do you dilute a concentrated acid from its label?
First convert the label to molarity: C = (10 x %w/w x density) / molar mass. Then use C1V1 = C2V2 for the aliquot. Always add the acid to the water.
Worked example
Every number below is computed by the calculator, not typed in
The working
- Derive Stock molarity:
M = (10 · %w/w · ρ) / MW - Substitute label:
M = (10 · 37 · 1.19) / 36.46=12.08 M - Solve for Aliquot:
V₁ = (C₂ · V₂) / C₁ - Substitute:
V₁ = (1 M · 100 mL) / (12.08 M)=8.281 mL - Diluent:
V₂ − V₁=91.72 mL
Measure 8.281 mL of the 37% stock (≈ 12.08 M) and dilute to 100 mL total.
What each symbol means
- C₁: Stock molarity (mol/L)
- %w/w: Label percent weight per weight (%)
- ρ: Density (g/mL)
- MW: Molar mass of pure solute (g/mol)
A printable one-page version is on the formula sheet.
Where this usually goes wrong
- Using the percentage directly as a concentration without the density term.
- Adding water to concentrated acid. The heat of dilution can boil and spit.
- Using the molar mass of the solution rather than of the pure acid.
Try it yourself
Two problems, with the working revealed
Problem 1 Acid / base dilution
Work out the stock molarity, the acid aliquot, and the water volume.
- Label concentration (%w/w): 25
- Density (g/mL): 1.84
- Molar mass (g/mol): 98.08
- Target concentration: 3 M
- Final volume: 250 mL
Show the answer and the working
Measure 159.9 mL of the 25% stock (≈ 4.69 M) and dilute to 250 mL total.
- Derive Stock molarity:
M = (10 · %w/w · ρ) / MW - Substitute label:
M = (10 · 25 · 1.84) / 98.08=4.69 M - Solve for Aliquot:
V₁ = (C₂ · V₂) / C₁ - Substitute:
V₁ = (3 M · 250 mL) / (4.69 M)=159.9 mL - Diluent:
V₂ − V₁=90.09 mL
Open this in the calculator to change the numbers.
Problem 2 Acid / base dilution
Work out the stock molarity, the acid aliquot, and the water volume.
- Label concentration (%w/w): 75
- Density (g/mL): 1.19
- Molar mass (g/mol): 36.46
- Target concentration: 1 M
- Final volume: 100 mL
Show the answer and the working
Measure 4.085 mL of the 75% stock (≈ 24.48 M) and dilute to 100 mL total.
- Derive Stock molarity:
M = (10 · %w/w · ρ) / MW - Substitute label:
M = (10 · 75 · 1.19) / 36.46=24.48 M - Solve for Aliquot:
V₁ = (C₂ · V₂) / C₁ - Substitute:
V₁ = (1 M · 100 mL) / (24.48 M)=4.085 mL - Diluent:
V₂ − V₁=95.91 mL
Open this in the calculator to change the numbers.
Do it with your own numbers.
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