$($a$)$ Write all reactions and equations for a closed carbonate system except for the charge balance

equation.

$($b$)$ Derive the equation for $log[H_{2}C{O}_3^{**}]$ as a function of $[H^{+}],C_T,K_{a1},$ and $K_{a2}.$

$($c$)$ Simply and rewrite the equation in Part $($b$)$ using $pH,log{C}_T,p{K}_{a1},$ and $\frac{?}{?}$ or $p{K}_{a2}$ if $pHp{K}_{a1}p{K}_{a2}pH>p{K}_{a2}pH.$ Draw the

equation $on$ a grid paper.

$(d)$ Repeat Part $(c)ifpHis$ between $p{K}_{a1}$ and $p{K}_{a2}.$

$(e)$ Repeat Part $(c)ifpH>p{K}_{a2}.$