Final answer:
To prepare 400 mL of a 5% w/v solution, 20 grams of the drug are required. This is calculated using a proportional relationship based on the definition that a 5% w/v solution contains 5 grams of solute per 100 mL of solution.
Step-by-step explanation:
The question asks how many grams of a drug are needed to prepare a 400 mL solution at a 5% w/v (weight/volume) concentration. In a 5% w/v solution, 5 grams of solute (in this case, the drug) is present in every 100 mL of solution.
To find the mass of the drug required for 400 mL of solution, we use a simple proportion, w/v-percent formula:
- 5 grams drug / 100 mL solution = x grams drug / 400 mL solution
By solving the proportion, we calculate the following:
- x = (5 grams drug \(\times\) 400 mL solution) / 100 mL solution
x = 20 grams drug
Therefore, 20 grams of the drug are needed to prepare 400 mL of a 5% w/v solution.