A solution of `KCl` has a density of `1.69 g mL^(-1)` and is 67% by weight. Find the denisty of the solution if it is diluted so that the percentage by weight of `KCl` in the diluted solution is 30%`

Explanation

Let the volume of the KCl solution be 100 mL,
Weight of KCl solution `= 100 xx 1.69 = 169g`
100g of solution contains = 67 g of KCl
169 g of solution `= (67)/(100) xx 169 = 113.23g`
Let x mL of `H_(2)O` be added
New volume of solution `= (100 + x) mL`
New weight of solution `= (169 + x)g`
(Since x mL of `H_(2)O = x g " of " H_(2)O, d_(H_(2)O) = 1`)
New percentage of the solution = 30%
% by weight `= ("weight of solute " xx 100)/("weight of solution")`
`30 = (113.23)/((169 + x)) xx 100`
`x = 208.43 mL = 208.43 g`
New density `= ("New weight of solution")/("New volume of solution")`
`= ((169 + x))/((100 + x))`
`((169 + 208.43))/((100 + 208.43)) = (377.43)/(308.43)`
`:. d = 1.224`