Pragya tested the solubility of four different substances at different temperatures and collected the data as given below (results are given in the following table,as grams of substance dissolved in $100 \,g$ of water to form a saturated solution).

Substance Dissolved	$283 \,K$	$293 \,K$	$313 \,K$	$333 \,K$	$353 \,K$
Potassium nitrate	$21$	$32$	$62$	$106$	$167$
Sodium chloride	$36$	$36$	$36$	$37$	$37$
Potassium chloride	$35$	$35$	$40$	$46$	$54$
Ammonium chloride	$24$	$37$	$41$	$55$	$66$

$(a)$ What mass of potassium nitrate would be needed to produce a saturated solution of potassium nitrate in $50 \,g$ of water at $313 \,K$?
$(b)$ Pragya makes a saturated solution of potassium chloride in water at $353 \,K$ and leaves the solution to cool at room temperature. What would she observe as the solution cools? Explain.