Question

What volume of diluent must I add to 1 mL of a 4 mg/L solution of dexamethasone to get a concentration of 2.5 mg/L? Bonus: What volume of the diluted solution contains 0.35 mg of dexamethasone?

Answer 1

You will need 0.6 mL of diluent.

You can use the formula

`c_1V_1 = c_2V_2`

`c_1` = 4 mg/mL; `V_1` = 1 mL
`c_2` = 2.5 mg/mL; `V_2` = ?

`V_2 = V_1 × c_1/c_2 = "1 mL" × "4 mg/mL"/"2.5 mg/mL"` = 1.6 mL

You started with 1 mL and want 1.6 mL of diluted solution, so you must add
(1.6 -1) mL = 0.6 mL of diluent.

Bonus:

0.35 mg × `"1 mL"/"2.5 mg"` = 0.14 mL

So 0.14 mL of the diluted solution will contain 0.35 mg of dexamethasone.