Final answer:
To make a dilution containing 0.5 mg of drug in each 100 mg of powder, approximately 50.2513 mg of additional diluent must be added to the contents of one capsule.
Step-by-step explanation:
To find out how much additional diluent must be added to the contents of one capsule, we can use the concept of dilution.
First, let's calculate the amount of drug in one capsule:
Each capsule contains 12.5 mg of drug, so in 100 capsules, there would be 12.5 mg x 100 = 1250 mg of drug.
Next, let's calculate the total amount of powder in one capsule:
Each capsule contains 12.5 mg of drug and 37.5 mg of diluent, so the total amount of powder in one capsule is 12.5 mg + 37.5 mg = 50 mg.
Now, we can calculate the dilution that is required:
We want a dilution that contains 0.5 mg of drug in each 100 mg of powder. This means that for every 100 mg of powder, we want 0.5 mg of drug. So, the ratio of drug to powder in the dilution is 0.5 mg : 100 mg = 1 : 200.
To make the dilution, we need to add additional diluent to the contents of one capsule. Since we want a 1 : 200 ratio of drug to powder in the dilution, we need to add diluent in a ratio of 199 : 200. This means that for every 199 parts of diluent, we add 200 parts of the contents of one capsule. Therefore, to find out how much additional diluent must be added, we can set up the following proportion:
199 parts of diluent / x = 200 parts of contents of one capsule / 50 mg
Cross-multiplying, we get:
199x = 200 * 50
Simplifying, we find:
x = (200 * 50) / 199
Calculating this, we get:
x ≈ 50.2513 mg
Therefore, approximately 50.2513 mg 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.