find the overall dilution ratio and the total amount of water added

Question

A 24% w/v stock solution of NaCl is diluted with water according to a 1:10 dilution ratio, then again by a 5:6 dilution ratio.
a) Determine the overall dilution ratio (in lowest terms) performed:
b) If there is 84 g of NaCl in the final diluted solution, determine the total amount of water added to the stock solution to perform the dilutions:

mL

Answer 1

a)  1:10 x 5:6 = 5:60 = 1:12 overall dilution ratio

 

b) 24% w/v = 24 g/100 ml soln

24g/100 ml = 84 g/x ml and x = 350 ml original solution to have 84 g

Based on a 12 fold dilution factor... 350 ml/12 = 29.2 ml of original solution diluted to 350 ml

Water added = 350 ml - 29.2 ml = 320.8 ml = 321 ml (to 2 significant figures)