Question

What fraction of water and ethanol should be used to prepare a 4 mg/mL solution of a drug that has the solubility of 0.2 and 24 mg/mL in water and ethanol, respectively? (please explain each step)

Answer 1

We need to prepare a 4 mg/mL solution of a drug. Thus 1 mL of solution will have 4 mg of drug.

Let 1 mL of this solution will have x mL of water. 1-x mL of ethanol will be present.

The drug has the solubility of 0.2 and 24 mg/mL in water and ethanol, respectively.

In x mL of water, the amount of drug present is 0.2 x mg. In (1-x) mL of ethanol, the amount of drug present is 24 (1-x) mg. The total amount of drug is 0.2 x + 24 (1-x) which is equal to 4 mg

Thus we have 0.84 mL water and   mL ethanol.

The fraction of water and ethanol is