A solution of $Ba(N{O}_3{)}_2$ from an evaporator contains $30\mathrm{.}6$lbBa$\frac{(N{O}_3{)}_2}{100}lb{H}_{2}O$ and goes to a crystallizer where the solution is cooled and $Ba(NO3)$ z crystallizes. On cooling, $10\%$ of the original water present evaporates. For a feed solution of $250lb$ total, calculate the following:

a$)$ Make a sketch of the process.

b$)$ Give a complete basis.

c$)$ Give the degree of freedom analysis.

d$)$ The yield of crystals if the solution is cooled to $290K,$ where the solubility is $8\mathrm{.}6lbBa\frac{(N{O}_3{)}_2}{100}lb$ total water.

e$)$ The yield if cooled instead to $283K,$ where the solubility is $7$kgBa$\frac{(N{O}_3{)}_2}{100}kg$ total water.