For a triprotic system, the fractional composition equations are:

${}_{H_{3}A}=\frac{[H^{+}{]}^3}{D},{}_{H_2{A}^{-}}=\frac{K_1[H^{+}{]}^2}{D},{}_{H{A}^{2-}}=\frac{K_1{K}_2[H^{+}]}{D},{}_{A^{3-}}=\frac{K_1{K}_2{K}_3}{D}$

where $D=[H^{+}{]}^3+K_1[H^{+}{]}^2+K_1{K}_2[H^{+}]+K_1{K}_2{K}_3$

a$.$ pts$.)$ Use the systematic treatment of equilibrium to prove that ${}_{H3A}$ is correct.

b$.(6$ pts$.)$ Using Microsoft Excel, make a graph of fractional composition vs$.pH$ for all four forms of tyrosine $($overlay each curve onto one graph$).$ Your graph should start at $pH=0\mathrm{.}00$ and end at $pH=13\mathrm{.}00$ and increase in increments of $0\mathrm{.}20pH$ units. Email your Excel sheet to Dr$.$ McKenzie before the due date of this exam.