Chapter 9, Problem 9.48P

a)

Interpretation Introduction

Interpretation:

The equations are to be written to find the $\text{pH}\text{of}\text{Al}{\left({\text{ClO}}_{\text{4}}\right)}_{\text{3}}$ at formal concentration F.

To write the equations to find the $\text{pH}\text{of}\text{Al}{\left({\text{ClO}}_{\text{4}}\right)}_{\text{3}}$ at formal concentration F

Concept Introduction:

Mass balance: Mass balance can be defined as the amount of all species that is present in a solution having a specific atom that should be same as the quantity of that atom that is given to the solution.

Charge balance: Charge balance can be defined as the sum of all positive ions present in solution will be same as the sum of all negative ions present in the solution.

Explanation of Solution

Equilibria:

${\text{β}}_{\text{1}}\text{=}\frac{\left[{\text{AlOH}}^{\text{2+}}\right]\left[{\text{H}}^{\text{+}}\right]}{\left[{\text{Al}}^{\text{3+}}\right]}\text{(1)}$

${\text{β}}_{\text{2}}\text{=}\frac{\left[{\text{Al(OH)}}_{\text{2}}{}^{\text{+}}\right]{\left[{\text{H}}^{\text{+}}\right]}^{\text{2}}}{\left[{\text{Al}}^{\text{3+}}\right]}\text{(2)}$

${\text{β}}_{\text{3}}\text{=}\frac{\left[{\text{Al(OH)}}_{\text{3(aq)}}\right]{\left[{\text{H}}^{\text{+}}\right]}^{\text{3}}}{\left[{\text{Al}}^{\text{3+}}\right]}\text{(3)}$

${\text{β}}_{\text{4}}\text{=}\frac{\left[\text{Al}{\left(\text{OH}\right)}_{\text{4}}{}^{\text{-}}\right]{\left[{\text{H}}^{\text{+}}\right]}^{\text{4}}}{\left[{\text{Al}}^{\text{3+}}\right]}\text{(4)}$

${\text{K}}_{\text{22}}\text{=}\frac{\left[{\text{Al}}_{\text{2}}{\left(\text{OH}\right)}_{\text{2}}{}^{\text{4+}}\right]{\left[{\text{H}}^{\text{+}}\right]}^{\text{2}}}{{\left[{\text{Al}}^{\text{3+}}\right]}^{\text{2}}}\text{(5)}$

${\text{K}}_{\text{43}}\text{=}\frac{\left[{\text{Al}}_{\text{3}}{\left(\text{OH}\right)}^{\text{5+}}{}_{\text{4}}\right]{\left[{\text{H}}^{\text{+}}\right]}_{\text{4}}}{{\left[{\text{Al}}^{\text{3+}}\right]}^{\text{3}}}\text{(6)}$

${\text{K}}_{\text{w}}\text{=}\left[{\text{H}}^{\text{+}}\right]\left[{\text{OH}}^{\text{-}}\right]\text{(7)}$

Charge balance:

$\begin{array}{l}\text{3}\left[{\text{Al}}^{\text{3+}}\right]\text{+2}\left[{\text{AlOH}}^{\text{2+}}\right]\text{+}\left[\text{Al}{\left(\text{OH}\right)}_{\text{2}}{}^{\text{+}}\right]\text{+4}\left[{\text{Al}}_{\text{2}}{\left(\text{OH}\right)}_{\text{2}}{}^{\text{4+}}\right]\text{+}\\ \text{5}\left[{\text{Al}}_{\text{3}}{\left(\text{OH}\right)}_{\text{4}}{}^{\text{5+}}\right]\text{+}\left[{\text{H}}^{\text{+}}\right]\text{=}\left[\text{Al}{\left(\text{OH}\right)}_{\text{4}}{}^{\text{-}}\right]\text{=}\left[{\text{OH}}^{\text{-}}\right]\text{+}\left[{\text{ClO}}_{\text{4}}{}^{\text{-}}\right]\text{(8)}\end{array}$

Mass balances: $\text{3F=}\left[{\text{ClO}}_{\text{4}}{}^{\text{-}}\right]\text{(9)}$

$\begin{array}{l}\text{F=}\left[{\text{Al}}^{\text{3+}}\right]\text{+}\left[{\text{AlOH}}^{\text{2+}}\right]\text{+2}\left[{\text{Al}}_{\text{2}}{\left(\text{OH}\right)}^{\text{4+}}{}_{\text{2}}\right]\text{+}\\ \left[\text{Al}{\left(\text{OH}\right)}_{\text{3(aq)}}\right]\text{+}\left[\text{Al}{\left(\text{OH}\right)}_{\text{4}}{}^{\text{-}}\right]\text{+3}\left[\text{Al}{\left(\text{OH}\right)}^{\text{5+}}{}_{\text{4}}\right]\text{(10)}\end{array}$

b)

Interpretation Introduction

Interpretation:

The explanations has to be to find the $\text{pH}\text{of}\text{Al}{\left({\text{ClO}}_{\text{4}}\right)}_{\text{3}}$ and concentration if all the values are known for equilibrium constant and formal concentration

To give explanations to find the $\text{pH}\text{of}\text{Al}{\left({\text{ClO}}_{\text{4}}\right)}_{\text{3}}$ concentration if all the values are known for equilibrium constant and formal concentration

Explanation of Solution

Upon solving the 10 equations along with their unknowns the $\text{pH}\text{of}\text{Al}{\left({\text{ClO}}_{\text{4}}\right)}_{\text{3}}$ and the concentration if all the values are known for equilibrium constant and formal concentration can be solved.

The required constants and formulas are entered in the cells in the spreadsheets and the values are calculated.