# Dilution Equation With Low Concentration Diluent - (Jun/09/2015 )

I am currently working on a dilution and need some help.  Normally I use the C1V1=C2V2 equation when the diluent is DI water or something with no concentration.

However, I am working with trying to dilute down a sample with a concentration of say, 900ng/mL.  The diluent I am using has a concentration of 20ng/mL.  Is there an equation that I could use to do a 1:5 dilution of the sample using the diluent?  I don't think I can use the C1V1=C2V2 because of the 20ng/mL diluent would throw off the end result and it wouldn't be a true 1:5 dilution.

Any help is appreciated.

Thank you.

It's simple really, you would need to solve with two equations.

(C0V0 + C1V1) = C2V2

V0+V1=V2

C0 = 900 ng/ml

C1= 20 ng/ml

C2 = desired concentration

V2 = desired volume

Your variables are V0 and V1.

So you have:

V1 = V2 - V0

and

C0V0 +C1(V2-V0) = C2V2

So:

C0V0 + C1V2 - C1V0 = C2V2

(C0-C1)V0 = C2V2-C1V2

...Which eventually results in:

V0 = (C2-C1)V2 / (C0-C1)

and then

V1 = V2 - V0

Example:

You want 5 ml of a 100 ng/ul solution.

V0 = (100-20)*5 / (900-20)

so

V0 = 0.454 ml

and then

V1 = 4.545 ml

Double-check:

0.454 ml * 900 ng/ml = 408.6 ng

4.545 ml * 20 ng/ml = 90.9 ng

Total = 408.6 + 90.9 = 499,5 ng

499,5 ng / 5 ml = 99,9 ng/ml ~= 100 ng/ml (0.1 lost to approximation).

-r.rosati-