Question

A drug is commercially available in capsules each containing 12.5 mg of drug and 37.5 mg of diluent. How many milligrams of additional diluent must be added to the contents of one capsule to make a dilution containing 0.5 mg of drug in each 100 mg of powder

Answer 1

Answer:

2450 mg

Explanation:

From the given information:

The total weight of the capsule = 12.5 mg + 37.5 mg

= 50 mg

The percentage of drug in each capsule = $\dfrac{12.5}{50} \times 100$

= 25%

= 0.25

To make 0.5 mg of drug in each  100 mg of powder after dilution;

Then, the drug percent in each capsule after dilution is:

$=\dfrac{0.5}{100}\times 100$

= 0.5%

= 0.005

Suppose (p) mg represent the amount that is added to the diluent in the given capsule. Then;

The total amount is = (50 + p) mg

Since the amount of the drug = 12.5 mg

Then the concentration  $=\dfrac{12.5}{50 + x}$ which needs to be equal to the needed concentration that is diluted.

i.e.

$\dfrac{12.5}{50 + x} = 0.005$

By cross multiply;

(50 + x) 0.005 = 12.5

(50 × 0.005) + (0.005x) = 12.5

0.25 + 0.005x = 12.5

0.005x = 12.5 - 0.25

0.005x = 12.25

x = 12.25 / 0.005

x = 2450 mg

Thus, there is a need for an additional 2450 mg to make a dilution that compass 0.5 mg of drug in 100 mg powder.