Title: The Dilutions Equation: C1V1 = C2V2
Course: BTEC-1100-301-302-303-F21 > Section: Module 1 - Calculations and Measurements

A very useful equation for calculating dilutions is C_1V_1=C_2V_2

C_1 = the concentration of your stock solution

V_1 = the volume of the stock solution you will use

C_2 = the concentration you want after dilution

V_2 = the volume of the final diluted solution

Example 1:

You have a stock solution of 20% SDS. You need 500 mL of 5% SDS. How much of the 20% SDS stock do you need?

We can solve this using the dilutions equation,  C_1V_1=C_2V_2

C_1 = the concentration of your stock solution = 20%

V_1 = the volume of the stock solution you will use = what we want to figure out

C_2 = the concentration you want after dilution = 5%

V_2 = the volume of the final diluted solution = 500 mL

Plugging in the values, we have

20% V_1 = 5% (500 mL)

V_1 = 5% (500 mL) / 20%

V_1 = 125 mL

To make the 5% solution, you’d take 125 mL of 20% stock, and add dH2O to a total volume of 500 mL.

Example 2:

You have a stock solution of 100 mg/mL ampicillin. You need 10 mL of 1 mg/mL ampicillin. How much of the 100 mg/mL ampicillin stock do you need?

We can solve this using the dilutions equation,  C_1V_1=C_2V_2

C_1 = the concentration of your stock solution = 100 mg/mL

V_1 = the volume of the stock solution you will use = what we want to figure out

C_2 = the concentration you want after dilution = 1 mg/mL

V_2 = the volume of the final diluted solution = 10 mL

Plugging in the values, we have

100 mg/mL V_1 = 1 mg/mL (10 mL)

V_1 = 1 mg/mL (10 mL) / 100 mg/mL

V_1 = 0.1 mL = 100 μL

To make the 1 mg/mL  solution, you’d take 100 μL of 100 mg/mL stock, and add dH2O to a total volume of 10 mL.

Example 3:

If you take 200 mL of 1 M NaCl, and dilute it with dH2O to a total volume of 500 mL, what is the final concentration of NaCl in the dilution?

We can solve this using the dilutions equation,  C_1V_1=C_2V_2

C_1 = the concentration of your stock solution = 1 M

V_1 = the volume of the stock solution you will use = 200 mL

C_2 = the concentration after dilution = what we are solving for

V_2 = the volume of the final diluted solution = 500 mL

Plugging in the values, we have

1 M (200 mL) = C_2 (500 mL)

C_2 = 1 M (200 mL) / 500 mL

C_2 = 0.4 M

The final concentration of NaCl in this dilution is 0.4 M.