Answer:
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
Considering the definition of dilution, 0.08 mL of a 0.2% solution of a skin test antigen must be used to prepare 4 mL of a solution containing 0.04 mg/mL of the antigen.
First of all, you have to know that when it is desired to prepare a less concentrated solution from a more concentrated one, it is called dilution.
Dilution is the process of reducing the concentration of solute in solution, which is accomplished by simply adding more solvent to the solution at the same amount of solute.
In a dilution the amount of solute does not change, but as more solvent is added, the concentration of the solute decreases, as the volume (and weight) of the solution increases.
A dilution is mathematically expressed as:
Ci×Vi = Cf×Vf
where
In this case, you know:
Replacing in the definition of dilution:
0.002 [tex]\frac{g}{mL}[/tex] × Vi= 0.00004 [tex]\frac{g}{mL}[/tex]× 4 mL
Solving:
[tex]Vi=\frac{0.00004 \frac{g}{mL}x4 mL}{0.002\frac{g}{mL} }[/tex]
Vi= 0.08 mL
In summary, 0.08 mL of a 0.2% solution of a skin test antigen must be used to prepare 4 mL of a solution containing 0.04 mg/mL of the antigen.
Learn more about dilution:
