Consider a system of the pesticide Calcium Arsenate $(CaHAs{O}_4*7H_{2}O)$ completely

dissolved in pure water to reach a total concentration of $[CaHAs{O}_4{]}_T=6*{10}^{-6}M($we

will ignore the $7$ molecules of water$).$

The Recipe is $[CaHAs{O}_4{]}_T=6*{10}^{-6}M$ and pure water.

The species in the system are:

$(H_{2}O),H^{+},O{H}^{-},C{a}^{2+},H_{3}As{O}_4,H_{2}As{O}_4^{-},HAs{O}_4^{2-},As{O}_4^{3-}$

For the dissolved arsenate $($ignoring the possibility of the arsenate $As(5)$ being

reduced to arsenite: $As(3)$ the following reactions are of relevance:

$H_{3}As{O}_4=H_{2}As{O}_4^{-}+H^{+},K_1={10}^{-2\mathrm{.}3}$

$H_{2}As{O}_4^{-}=HAs{O}_4^{2-}+H^{+},K_2={10}^{-7\mathrm{.}16}$

$HAs{O}_4^{2-}=As{O}_4^{3-}+H^{+},K_3={10}^{-11\mathrm{.}65}$

$($a$)$ Construct a tableau for the system. Hint: consider whether $CaHAs{O}_4$ act as an

acid or a base.

$($b$)$ Write all the mole balance equations and the mass law equations for the problem

as defined by the tableau.

$($c$)$ Verify that the mole balance equations satisfy the condition of electro$-$neutrality

$($charge balance$).$

$($d$)$ Write the alkalinity expression and determine the alkalinity of the system.

$($e$)$ Sketch a graphical solution in a $logC$ vs$.pH$ diagram.

$($f$)$ Calculate $pH$ and the concentration of all relevant species using the algebraic

equations from $($b$)$ and the approximation method. Use assumptions to simplify the

equations. Calculate an updated value of the dominant arsenate specie based on the

calculated arsenate species concentrations and the mole balance equation for total

arsenate. Report all results using scientific notation and $3$ decimals $($except for $pH).$

Important: Verify the validity of all your assumptions! $($such as omitting species

from mole balance equations by assuming low concentrations$).$