Solution Dilution Formula For Lab Stock Solutions
By The Calcumatix Team Reviewed by Calcumatix Editorial Review 4 min read
Quick Answer
The solution dilution formula is C1V1 = C2V2, where C is concentration and V is volume. Rearrange to find any missing value, so to dilute a 2 M stock to 0.5 M in 100 mL, V1 = (0.5 x 100) / 2 = 25 mL of stock topped up to 100 mL. Always add solvent to the stock.
The solution dilution formula helps prepare a lower concentration from a stronger stock solution. This is lab solution dilution, not ownership or equity dilution. The method assumes the amount of solute stays the same while solvent is added to reach the final volume. This guide supports the Percentage Dilution Calculator because both use the C1V1 equals C2V2 relationship.
What Does The Solution Dilution Formula Mean?
The dilution formula states that the amount of solute before dilution equals the amount of solute after dilution. You start with a stock solution, take a measured volume, then add solvent until the final solution reaches the target concentration and volume.
The formula is written as C1V1 = C2V2. C1 is stock concentration. V1 is stock volume used. C2 is target concentration. V2 is final solution volume. The concentration units must match, and the volume units must match.
Khan Academy describes dilution with the same M1V1 = M2V2 relationship for molarity and volume. The C version is the same structure, but C can stand for any compatible concentration unit.
How Do You Solve For Stock Volume?
To find how much stock solution to use, rearrange C1V1 = C2V2 for V1: V1 = (C2 × V2) ÷ C1.
This is the most common lab use. You know the stock concentration, the target concentration, and the final volume. The unknown is the volume of stock solution to pipette or measure before adding solvent.
- Write C1, C2, and V2.
- Put C1 and C2 in the same concentration unit.
- Put V2 in the final volume unit you want.
- Substitute values into V1 = C2V2 ÷ C1.
- Calculate V1.
- Add solvent until the total volume equals V2.
Never add the solvent volume first unless the procedure asks for it. Usually, you measure V1 of stock, then bring the solution up to the final volume mark.
Worked example. Prepare 100 mL of 2 M solution from a 10 M stock solution. Find the stock volume.
V1 = (C2 × V2) ÷ C1 = (2 × 100) ÷ 10. 2 × 100 = 200. 200 ÷ 10 = 20. Result: use 20 mL of 10 M stock solution, then add solvent to make 100 mL total, rounded to the nearest mL.
The solvent added is not always 80 mL exactly in careful volumetric work. The correct lab step is to add solvent to the final mark because mixing can change volume slightly.
How Do You Solve For Final Concentration?
To find the final concentration, rearrange the same formula for C2: C2 = (C1 × V1) ÷ V2.
Example: C1 = 10 M, V1 = 15 mL, V2 = 100 mL. C2 = (10 × 15) ÷ 100 = 150 ÷ 100 = 1.5. Result: the final concentration is 1.5 M, rounded to one decimal place.
This version is useful when a lab note says how much stock was used and asks what concentration the final solution has.
What Unit Checks Prevent Dilution Errors?
Unit checks prevent most dilution mistakes. Concentrations must match before you divide. For example, do not use 10 M for C1 and 2 mM for C2 without converting one value. Volumes must also match, such as mL with mL or L with L.
If C1 is in M and C2 is in M, the concentration units cancel cleanly. If V2 is in mL, V1 will come out in mL. If V2 is in L, V1 will come out in L. That consistency is one reason the formula is easy to use in lab prep.
When Does C1V1 = C2V2 Not Apply?
C1V1 = C2V2 works for simple dilution where the amount of solute remains the same. It does not handle reactions, precipitation, evaporation, serial dilution mistakes, or changes in solute amount. It also does not replace a safety data sheet or a lab procedure.
The formula assumes the stock concentration is known and the solution mixes evenly. If the stock label is old, the solute is unstable, or the final solution reacts with solvent, the simple dilution result may not describe the true concentration.
How Does This Relate To Percentage Dilution?
Percentage dilution can use the same structure when both concentrations are percent values on the same basis. For example, a 10% w/v stock diluted to 2% w/v follows C1V1 = C2V2. A 10% w/w stock and a 2% w/v target should not be mixed in one calculation without a valid conversion.
State the percent convention before using the formula. w/w% compares mass with mass. v/v% compares volume with volume. w/v% compares mass with volume. The dilution equation works only when the concentration basis stays compatible. See the Percentage By Weight Calculator and Percentage Of Volume Calculator for related conversions.
Sources And Notes For Solution Dilution
Frequently asked questions
Is C1V1 C2V2 the same as M1V1 M2V2?
C1V1 = C2V2 and M1V1 = M2V2 use the same dilution idea. M is used when concentration is molarity, while C can represent a compatible concentration unit.
Do I add 80 mL of water to make 100 mL total?
In careful volumetric work, measure the stock volume first, then add solvent to the final volume mark. Do not assume the solvent volume equals final volume minus stock volume in every lab setup.
Can I use percent concentrations in the dilution formula?
You can use percent concentrations if both percent values use the same basis, such as w/v% with w/v%. Do not mix w/w%, v/v%, and w/v% without conversion.
What if the stock concentration is lower than the target?
A lower stock concentration cannot make a higher target concentration by dilution. Dilution only lowers concentration by adding solvent without adding more solute.
Does the formula work for serial dilutions?
The formula can be applied one step at a time in a serial dilution. Treat the output of one step as the stock solution for the next step.