What you are given
- Reagent (optional): HCl
- I have (stock): 12 M
- I need (target): 1 M
- Final volume: 100 mL
Formula: C₁ · V₁ = C₂ · V₂
Dilutions
How do you calculate a dilution?
Use C1V1 = C2V2. Rearranged for the volume of stock you need: V1 = (C2 x V2) / C1. Measure that volume of stock, then top up to the final volume, rather than adding the final volume of diluent to it.
Worked example
Every number below is computed by the calculator, not typed in
The working
- Solve for stock volume:
V₁ = (C₂ · V₂) / C₁ - Substitute:
V₁ = (1 M · 100 mL) / (12 M)=8.333 mL - Diluent:
V₂ − V₁=91.67 mL
Measure 8.333 mL of 12 M HCl and dilute to 100 mL total volume.
What each symbol means
- C₁: stock concentration (M)
- V₁: stock volume to take (mL)
- C₂: target concentration (M)
- V₂: final volume (mL)
A printable one-page version is on the formula sheet.
Where this usually goes wrong
- Adding V2 of diluent to V1 of stock instead of topping up to V2 total. The final volume is the target, not the amount of water.
- Mixing units between C1 and C2, for example a stock in M and a target in mM. Convert one before dividing.
- For concentrated acids, adding water to acid instead of acid to water. Always the acid into the water.
Try it yourself
Two problems, with the working revealed
Problem 1 Simple dilution
Work out the volume of stock to take and the volume of diluent to add.
- Reagent (optional): NaCl
- I have (stock): 4.5 M
- I need (target): 750 mM
- Final volume: 100 mL
Show the answer and the working
Measure 16.67 mL of 4.5 M NaCl and dilute to 100 mL total volume.
- Solve for stock volume:
V₁ = (C₂ · V₂) / C₁ - Substitute:
V₁ = (0.75 M · 100 mL) / (4.5 M)=16.67 mL - Diluent:
V₂ − V₁=83.33 mL
Open this in the calculator to change the numbers.
Problem 2 Simple dilution
Work out the volume of stock to take and the volume of diluent to add.
- Reagent (optional): HCl
- I have (stock): 10 M
- I need (target): 1 M
- Final volume: 300 mL
Show the answer and the working
Measure 30 mL of 10 M HCl and dilute to 300 mL total volume.
- Solve for stock volume:
V₁ = (C₂ · V₂) / C₁ - Substitute:
V₁ = (1 M · 300 mL) / (10 M)=30 mL - Diluent:
V₂ − V₁=270 mL
Open this in the calculator to change the numbers.
Do it with your own numbers.
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