Problem $2$ In Homework $3,$ you have worked with the aluminum$-$hydroxide coordination $logC-pH$ diagram for coagulation$-$flocculation water treatment, which is shown below. $($c$)$ pts$]$ The envelop curve is Total$(Al),$ which is the sum of $A{l}^{3+},Al(OH{)}^{2+},Al(OH{)}_2^{+},Al(OH{)}_3,$ and

$Al(OH{)}_4^{-}.$ Because Total$($Al$)$ varies with pH $,$ the concentration of most species can be presented as a function

of $H^{+},$ with other constants in the expression.

For example, $[Al(OH{)}^{2+}]=*{}_1{K}_{sp}\frac{[H^{+}{]}^2}{K^3}.$

Please derive $A{l}^{3+}$ and $Al(OH{)}_4^{-}$using $H^{+}$and the constants: $K_{sp},{?}^{*}{}_i,$ and $K_w.$ Show your process. $($d$)[4$pts$]$ If citric acid $($see the structure below$)$ is added into the solution, do you expect the dissolved total Al to

be higher or lower? Why?

$($a$)[8$pts$]$ Please assign the four chemicals to A thru D$.$ For clarity, write the letters right below the four chemicals rather than indicate in the diagram

$A{l}^{3+},Al(OH{)}_2^{+},Al(OH{)}_3,Al(OH{)}_4^{-}$

$($b$),[7pts]$ If $27m\frac{g}{L}$ of $A{l}^{3+}$ is added for water treatment at pH $7,$ how much $Al(OH{)}_3$ solid will form? The atomic weight for $Al,O,$ and H are $27,16,$ and $1,$ respectively. The $logC-pH$ diagram uses $mo\frac{l}{L}$ as the unit on the $y$ axis, which uses the $log$ scale.

$($c$),)[16$pts$]$ The envelop curve is Total$($Al$),$ which is the sum of Al$3+,$ Al$($OH$)2+$

$,$ Al$($OH$)2$

$+$

$,$ Al$($OH$)3,$ and

Al$($OH$)4$

$$

$.$ Because Total$($Al$)$ varies with pH$,$ the concentration of most species can be presented as a function

of $[$H$+$

$],$ with other constants in the expression.

For example, $[$Al$($OH$)2+$

$]=*\backslash$beta $1$Ksp$[$H$+$

$]$

$2$

$/$Kw

$3$

$.$

Please derive $[$Al$3+]$ and $[$Al$($OH$)4$

$$

$]$ using $[$H$+$

$]$ and the constants: Ksp$,*\backslash$beta i$,$ and Kw$.$ Show your process

$($d$),4$pts$]$ If citric acid $($see the structure below$)$ is added into the solution, do you expect the dissolved total Al to

be higher or lower? Why?