Question

Suppose you prepared a Vitamin C stock solution by dissolving 500 mg of ascorbic acid in 60 mL distilled water.

To create solution A, you need to have the following concentrations: 50 mg, 75 mg, 100 mg and 500 mg.

You take 10 mL of the 500 mg concentration stock solution, how much water will you need to dilute to have a 50 mg concentration? How about 75? 100? 500?

Answer 1

When 500 g of a Vitamin C is dissolved in 60 mL of distilled water, the concentration of the solution is:

$\rho = \frac{m}{V} = \frac{500\text{ mg}}{60·10^{-3}\text{ L}} = 8.333·10^3$ mg/L.

In order to prepare a solution with the concentration $\rho$ = 50 mg/L from 10 mL aliquot of the stock solution, one needs to bring the total volume to:

$\rho_{stock} ·10\text{mL} = \rho_{50}·V$

$V = \frac{\rho_{stock}·10}{\rho_{50}} = \frac{8.333·10^4}{50} = 1.667·10^3$ mL.

Therefore, the volume of water needed to dilute the 10 mL aliquot is:

$V_w = 1667 - 10 = 1657$ mL.

Analogically, for the solution with the concentration of 75 mg/L:

$V_w = \frac{8.333·10^4}{75} - 10 = 1101$ mL,

for the solution with the concentration of 100 mg/L:

$V_w = \frac{8.333·10^4}{100} - 10 = 823$ mL,

and for the solution with the concentration of 500 mg/L:

$V_w = \frac{8.333·10^4}{500} - 10 = 157$ mL.

Answer: 1657 mL , 1101 mL, 823 mL and 157 mL of water will be needed to dilute 10 mL of stock solution prepared by dissolving 500 mg of Vitamin C in 60 mL of water in order to prepare the solutions of the concentrations equal to 50 mg, 75 mg, 100 mg and 500 mg, respectively. Remark: 1mg/L in mass/volume terms can be called parts per million, or ppm.