If a stock solution of 20.0 g of sugar per 100. ml of solution is available, how much of this stock is needed to prepare 10.0 ml of 5.00 g sugar/ 100. ml solution?

You must use 2.50 mL of the concentrated solution to make 10.0 mL of the dilute solution.

We can use the dilution formula

V_1C_1 = V_2C_2

where

V represents the volumes and

C represents the concentrations

We can rearrange the formula to get

V_2 = V_1 × (C_1/C_2)

V_1 = 10.0 mL; C_1 = 5.00 g/100. mL

V_2 = ?; C_2 = 20.0 g/100. mL

∴ V_2 = 10.0 mL × [(5.00 g/100. mL)/(20.0 g/100. mL)] = 10.0 mL × 0.250

= 2.50 mL