The solubility, $S,$ of $K_{2}S{O}_4$ is given as grams $K_{2}S{O}_4$ per $100\mathrm{.}0g$ of $H_{2}O($that is$,$ the number of grams of $K_{2}S{O}_4$ that will dissolve in $100\mathrm{.}0g$ of $H_{2}O$ to form a saturated solution$).$ The experimental data are:

$\backslash$table$[[\frac{T}{}C,20,40,60,80,100],[S,9\mathrm{.}8,14\mathrm{.}2,18\mathrm{.}3,21\mathrm{.}6,25\mathrm{.}9]]$

a$.$ On graph paper, plot the solubility $($ordinate$)$ versus the temperature $($abscissa$).$ Follow the points outlined in your lab manual on plotting data. Use your graph to answer the questions below.

b$.$ Determine the mass of $K_{2}S{O}_4$ that will dissolve in $225\mathrm{.}0g$ of $H_{2}O$ to form a saturated solution at $70\mathrm{.}0C.$

c$.$ Determine the temperature at which $67\mathrm{.}5g{K}_{2}S{O}_4$ will dissolve in $540\mathrm{.}0g{H}_{2}O$ to form a saturated solution.

d$.$ Determine the mass of $K_{2}S{O}_4$ that will crystallize when $444\mathrm{.}0g$ of a saturated solution at $100\mathrm{.}0C$ is cooled to form a saturated solution at $20\mathrm{.}0C.$

e$.$ Determine the mathematical equation that describes $\text{'}S\text{'}$ as a function of $\text{'}T\text{'}.$