# 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?

Oct 3, 2014

You will need 0.6 mL of diluent.

You can use the formula

${c}_{1} {V}_{1} = {c}_{2} {V}_{2}$

${c}_{1}$ = 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 × $\text{1 mL"/"2.5 mg}$ = 0.14 mL

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