Question

How many milliliters of a 1:2000 drug "i" solution and a 7% drug "i" solution mixed would make 120ml of a 3.5% solution of drug "i"?

Answer 1

To solve this problem, let us say that:

x = volume of 1:2000 drug "i" solution

y = volume of 7% drug "i" solution

Assuming volume additive, then this forms:

x + y = 120 mL

x = 120 – y                    ---> 1

 

1:2000 also refers to 0.0005 concentrations and 7% also refers to 0.07 concentrations. By doing a component balance:

0.0005 x + 0.07 y = 0.035 (120 mL)

0.0005 x + 0.07 y = 4.2

Substituting equation 1 into this derived equation to get an equation in terms of y:

0.0005 (120 – y) + 0.07 y = 4.2

0.06 – 0.0005 y + 0.07 y = 4.2

0.0695 y = 4.14

y = 59.568 mL = 59.57 mL

 

From equation 1, x would be:

x = 120 - 59.57

x = 60.43 mL

 

Answers:

59.57 mL of 1:2000 drug "i" solution

60.43 mL of 7% drug "i" solution