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

C_{f} x V_{f} = C_{S} x V_{S}

C_{f}: Concentration of diluted solution

V_{f}: Volume of diluted solution

C_{S}: Concentration of stock solution

V_{S}: 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

C_{f}: 1 X

V_{f}: 100 ml

C_{S}: 10 X

V_{S}: ? ml (to be calculated)

Formula: C_{f} x V_{f} = C_{S} x V_{S}

Place all values in formula:

1 x 100 = 10 x V_{S}

${V}_{s}=\frac{1x100}{10}$

V_{S} = 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

C_{f}: 1 mM

V_{f}: 100 ml

C_{S}: 0.5 M

V_{S}: ? 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:

C_{f}: 1 mM

V_{f}: 100 ml

C_{S}: 500 mM

V_{S}: ? ml (to be calculated)

Place all values in formula:

Cf x Vf = CS x VS

1 x 100 = 500 x VS

${V}_{S}=\frac{1x100}{500}$

V_{S} = 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 volume 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.

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