Solution, Solute and Solvent Problem 2

Let Mass of water in solution $= xg$
$\Rightarrow$ Mass of $KNO_3 = \left(100-x\right)g$

Initially , i.e at $80^oC$ ,
Solubility in $100g$ of water $= 169g$

$\Rightarrow$ Solubility in $xg$ of water $= 1.69x$

$\Rightarrow 100-x = 1.69x$
$\Rightarrow$ Mass of Water $= x = 37.174g$
$\Rightarrow$ Mass of $KNO_3$ (Initially) $= 100-x = 62.825g$

Now, It is important to note that the mass of water is not going to change when the solution is cooled.But, the $KNO_3$ will precipitate.

Hence, When the solution is cooled to $20^oC$ ,
Mass of Water is still = $37.174g$

Thus, At $20^oC$ ,
we now have to check the solubility in $37.174g$ of water,
Solubility in $37.174g$ water $= \frac{31.6}{100}\times 37.174 = 11.747g$

Hence, This should be the amount of $KNO_3$ dissolved in the solution finally .

To find out the amount precipitated,
we subtract this final amount of $KNO_3$ from the initial amount of $KNO_3$ .

Finally,
Mass of $KNO_3$ precipitated $= 62.825g-11.747g \approx \boxed{51g}$