Keep amount, volume, units, and final-volume assumptions visible when planning a water-based dilution on paper.
Field diagramA labeled dilution trail
Estimated reading
9 min
Estimated practice
15 min
Equipment
Calculator, paper or spreadsheet, dilution worksheet, and clean labeled water containers only if a supervised water demonstration is performed.
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Objective
By the end, you can:
Distinguish a concentration basis such as molarity from a mass-per-volume basis.
Apply C1V1 = C2V2 only when the stock, target, and final-volume assumptions fit.
Draft a label that preserves identity, concentration, units, date, preparer, and hazards or limitations.
Name the quantity before calculating
Concentration is a ratio, so its numerator and denominator matter. Molarity is amount of substance per final volume, written mol/L; mass concentration might be g/L; a percent can mean mass/mass, volume/volume, or mass/volume. These are not interchangeable labels. Write the basis, units, stock identity, target identity, and final volume before entering numbers. A label saying ‘2’ is not a concentration.
The familiar dilution relationship C1V1 = C2V2 assumes the same solute is conserved and the stated volumes represent the stock aliquot and final solution volume in compatible units. It is a planning equation, not permission to add volumes blindly. For accurate work, follow the volumetric glassware and mixing method specified for the material. This lesson keeps practice to arithmetic and water; it does not authorize chemical preparation.
Worked dilution with explicit assumptions
Suppose a 10 mM stock is to be diluted to 2 mM final concentration and final volume 50 mL. Assuming the stock and target use the same solute and the final volume is set as 50 mL, V1 = (C2 × V2) / C1 = (2 mM × 50 mL) / 10 mM = 10 mL stock. The remaining amount is made up to a final volume of 50 mL, so the nominal added diluent is 40 mL only as a planning figure. If mixing changes volume, the method must use a calibrated final-volume vessel and its instructions.
Carry units through the equation and cancel them visibly.
Record stock lot or source and the calculation version.
Label nominal concentration separately from any later verified concentration.
Worked example
10 mM to 2 mM, 50 mL final
C1 = 10 mM, C2 = 2 mM, V2 = 50 mL. V1 = C2V2/C1 = (2 mM × 50 mL)/(10 mM) = 10 mL.
01Nominal stock aliquot: 10 mL.
02Final-volume instruction: dilute to a final volume of 50 mL; do not assume volumes are additive without method support.
03Paper label: Illustrative calculation only — not a prepared 2 mM solution; hypothetical solute X; target 2 mM; final 50 mL; date; preparer. Label any physical water container plain water.
Materials
Set out what you need.
Dilution worksheet
Calculator with unit annotations
Representative stock and target names
Water-only practice labels
Safety & stop conditions
Pause if the work no longer fits the plan.
Do calculations before handling any material. This lesson does not authorize preparation of hazardous, biological, or unknown solutions.
If a water demonstration is performed, use clean containers and a spill plan; discard or retain it as clearly labeled practice water.
Never infer compatibility, stability, sterility, or safe use from a concentration calculation.
Method
Work through the steps.
01
Define the basis
Write whether the concentration is mol/L, g/L, % v/v, or another basis. Record the stock and target units exactly.
02
Convert compatible units
Convert only where needed so concentration units cancel and volume units agree. Show the conversion instead of relying on a hidden calculator setting.
03
Calculate the stock volume
For a direct dilution, rearrange C1V1 = C2V2 and solve for V1. Check that the result is no larger than the planned final volume.
04
State the final-volume method
Write whether the method calls for making up to a mark, a measured diluent volume, or another validated approach. Do not assume additive volumes.
05
Draft the label
Include identity, nominal concentration and basis, final volume, date, preparer, source/lot, storage or safety instruction if applicable, and the word practice when appropriate.
Checkpoints
Observe, record, investigate.
The concentration basis and units appear in both the calculation and label.
The answer is smaller than the final volume and the stock is more concentrated than the target.
The final-volume assumption is stated rather than hidden in the arithmetic.
The label distinguishes nominal planning from a measured or verified result.
Common mistakes
Correct the process, preserve the record.
mM and M are mixed without conversion.
Convert one unit: 10 mM is 0.010 M. Keep the same concentration unit on both sides when possible.
The learner adds 10 mL stock and 40 mL water and calls the result exactly 50 mL.
Call 40 mL the nominal diluent amount only if the method permits that assumption; otherwise make up to final volume.
A label says ‘2 mM’ with no solute name.
Add the solute identity, basis, final volume, date, preparer, and source information.
A calculation uses the wrong stock concentration.
Read the stock label back into the worksheet and perform a direction check: dilution must reduce concentration.
Practice
Calculation-only dilution sheet
On paper, calculate a dilution from a 10 mM stock to a 2 mM final concentration at 50 mL. Draft a label for the hypothetical solution, naming the hypothetical solute and marking it illustrative calculation only. Any actual water used to practice labeling must be labeled plain water, not 2 mM.
What is conserved in the equation?
What assumption is made about final volume?
Which fields would a second person need to audit your result?
How would you revise the plan if only a 1 mL pipette were available?
