# Preparing Working Solution from Stock Solution by Dilution

If you have a concentrated stock solution of known concentration, you can prepare a working solution of specific concentration and volume by diluting the stock solution.

Use the following formula to calculate the volume of stock solution required to prepare a diluted solution

Cf x Vf = CS x VS

Cf: Concentration of diluted solution
Vf: Volume of diluted solution
CS: Concentration of stock solution
VS: Volume of stock solution

Example: The concentration of stock solution is given in x fold (times) e.g. 10X stock solution

For example, you want to prepare 100 ml of working solution (after dilution) from 10X stock solution
Cf: 1 X
Vf: 100 ml
CS: 10 X
VS: ? ml (to be calculated)

Formula: Cf x Vf = CS x VS

Place all values in formula:
1 x 100 = 10 x VS

VS = 10 ml

So you need to take 10 ml of 10 X stock solution to prepare a 100 ml working (diluted) solution.

How much solvents do you need to add?
The final volume of the working (diluted) solution: 100 ml
The volume of stock solution to be taken: 10 ml
The volume of water to be added: 100 – 10 = 90 ml

So you need to mix 10 ml of 10X stock solution and 90 ml water to obtain 100 ml of working (diluted) solution.

Example: When the concentration of stock solution concentration is given in a concentration unit e.g. 1 M stock solution

For example, you want to prepare 100 ml of 1 mM EDTA solution from 0.5M EDTA solution

Cf: 1 mM
Vf: 100 ml
CS: 0.5 M
VS: ? ml (to be calculated)

Tip: Stock concentration is given in M (molar) and working concentration is given in mM (milliMolar). Convert Stock concentration Molar to millimolar.

1 M = 1000 mM

Now the values are:
Cf: 1 mM
Vf: 100 ml
CS: 500 mM
VS: ? ml (to be calculated)

Place all values in formula:

Cf x Vf = CS x VS

1 x 100 = 500 x VS

VS = 0.2 ml

So you need to take 0.2 ml of 0.5M EDTA solution to prepare 100 ml of 1 mM EDTA  solution.

How many solvents do you need to add?

The final volume of the working solution: 100 ml
The volume of stock solution to be taken: 0.2 ml
The v
olume of water to be added: 100 – 0.2 = 99.8 ml

So you need to mix 0.2 ml of 0.5M EDTA solution and 99.8 ml water to obtain 100 ml of 1 mM EDTA solution. 