Question

A pharmacy intern is asked to prepare 3 L of a 30% w/v solution. T he pharmacy stocks the active ingredient in 8-ounce bottles of 70% w/v strength. How many bottles will be needed as the source of the active ingredient?

Answer 1

Answer: The number of bottles that will be needed are 6

Explanation:

We are given:

Amount of solution, the intern is asked to prepare = 3 L = 3000 mL   (Conversion factor:  1 L = 1000 mL)

Strength of solution needed = 30 % (w/v)

This means that in 100 mL of solution, the solute present is 30 grams

So, in 3000 mL of solution, the solute present will be = $\frac{30}{100}\times 3000=900g$

Active ingredient present in 1 bottle = 8 ounce of 70 % (w/v)

Conversion factor used: 1 ounce = 29.57 mL

So, $8ounce\times \frac{29.57mL}{1ounce}=236.6mL$

Amount of active ingredient present in 1 bottle = $236.6\times \frac{70}{100}=165.6g$

To calculate the number of bottles, we need to divide the total amount of solution needed by the amount of active ingredient present in 1 bottle, we get:

$\text{Number of bottles}=\frac{\text{Amount of solution to prepare}}{\text{Amount of active ingredient in 1 bottle}}$

Putting values in above equation, we get:

$\text{Number of bottles}=\frac{900g}{165.6g}\\\\\text{Number of bottles}=5.43\approx 6$

Hence, the number of bottles that will be needed are 6