How many milliliters o a 0.2% solution o a skin test antigen must be used to prepare 4 mL o a solution containing 0.04 mg/mL o the antigen?

0.08 mL

Explanation:

The solution of the skin test has a concentration of 0.2% (w/v), which means that there are 0.2 g of the antigen per 100 mL of the solution. If a new solution will be done using it, then this solution will be diluted, and the mass of the antigen added must be the same in the volume taken and at the diluted solution.

The mass is the concentration (in g/mL) multiplied by the volume of the solution (in mL), so, if m is the mass, C the concentration, V the volume, 1 the initial solution, and 2 the diluted:

m1 = m2

C1*V1 = C2*V2

Where

C1 = 0.2 g/100 mL = 0.002 g/mL

V1 = ?

C2 = 0.04 mg/mL = 0.00004 g/mL

V2 = 4 mL

0.002*V1 = 0.00004*4

V1 = 0.08 mL