concentration solution

Question

You have 330ul of stock at a concentration of 10mg/ul. How do you make 500ml of 10ng/ml out of the stock solution? My answer is 5x10 to power of -8ml added to the needed amount of ml of water. Is this correct?

Answer 1

Hello Alec

First we need to ensure the units for the initial concentration matches the units of the final concentration.

Initial concentration (C_i) = 10 mg / uL --> need to convert to ng / mL. 1 mg = 10⁶ ng and 1 mL = 10³ uL

C_i = 10 mg / uL x (10⁶ ng / 1 mg) = 1 x 10⁷ ng / uL

Convert denominator unit from uL to mL.

1 x 10⁷ ng / uL x (10³ uL / 1 mL) = 1 x 10¹⁰ ng / mL

Next, we can use the dilution equation to determine how much of the stock solution is needed.

C_i V_i = C_f V_f

Solve for V_i, you get

V_i = C_f V_f / C_i

= (10 ng / mL x 500 mL) / 1 x 10¹⁰ ng / mL

= 5 x 10^-7 mL