$$ CuO_{s}+H_{2}O_{l} = Cu^{+2}_{aq} + 2OH^{-}_{aq}\:\:\:\:\:\:\:\:\:\:K_{sp}+2.2\times 10^{-21} \tag{1} $$
$$ 2OH^{-}\:_{aq} + 2H^{+}\:_{aq} = 2H_{2}O_{1}\:\:\:\:\:\:\:\:\:\:\:\:\:K=(1/K_{w})^{2}=1\times 10^{28} \tag{2} $$
$$ CuO_{s} + 2H^{+}\:_{aq} = Cu^{+2}\:_{aq} + H_{2}O_{l}\:\:\:\:\:\:\:\:\:K_{l} = K_{sp}/K_{w}^{2} = 2.2\times 10^{7} \tag{3} $$

$$ Fe^{+3}\:_{aq}\:+\: e^{-} = Fe^{+2}\:_{aq}\:\:\:\:\:\:\:\:\:\:E^{\circ} = 0.77\:V; \sim0.68 V in\:aq. \:H_{2}SO_{4} \tag{9} $$

$$ CuS_{s}+ 2Fe^{+3}\:_{aq} = Cu^{+2}\:_{aq} + 2Fe^{+2}\:_{aq} + S_{s} \tag{10} $$

$$ 2Fe^{+2}\:_{aq}+1/20_{2}\:_{g}+2H^{+}\:_{aq}=2Fe^{+3}\:_{ag}+H_{2}O_{l} \tag{11} $$

(By thiobacillus ferrooxidans)

$$ S_{s}\;+\:3/20_{2g}\:+\:H_{2}O_{l}\:=\:H_{2}SO_{4}\:_{aq} \tag{12} $$

$$ Cu_{2}S_ {s}\:+\:2Fe^{+3}\:_{aq}\: =\: Cu^{+2}\:_{aq}\:+\: 2Fe^{+2}\;_{aq}\:+\: CuS_{s} \tag{13} $$

$$ E\:=\:E^{\circ}\:-\:\frac{2.303RT}{F}log\frac{a_{Fe+2}}{a_{Fe+3}} \tag{14} $$

$$ pH\:=\:pK_{a}\:+\:log\frac{a_{A-}}{a_{HA}} \tag{15} $$

$$ Au^{+}\:_{aq}\:+\:e^{-}\:=\:Au_{s}\:\:\:\:\:\:\:\:\:\:E^{\circ}\:=\:1.69\:V \tag{16} $$

$$ Au^{+3}\:_{aq}\:+\:3e^{-}\:=\:Au\:_{s}\:\:\:\:\:\:\:\:\:\:E^{\circ}\:=\:1.41\:V \tag{17} $$

$$ O_{2\:g}\:+\:4H^{+}\:_{aq}\:+\:4e^{-}\:=\:2H_{2}O\:_{l}\:\:\:\:\:\:\:\:\:\:E^{\circ}\:=\:1.23\:V \tag{18} $$

$$2Au_{s}\:+\:4CN^{-}\:_{aq}\:+\:O_{2}\:_{g}\:+\:2H_{2}O\:_{l}\:=\:2[Au(CN)_{2}]^{-}\:+\:H_{2}O_{2}\:_{aq}\:+\:2OH^{-}\:_{aq} \tag{19} $$

$$ HCN_{aq}\:=\:H^{+}\:_{aq}\:+\:CN^{-}\:_{aq}\:\:\:\:\:\:\:\:\:\:K_{a}\:=\:5.25\:\times\:10^{-10};\:pK_{a}\:=\:9.28 \tag{20} $$

$$ HCN_{aq}\:=\:HCN_{g}\:\:\:\:\:\:\:\:\:\:K\:=\:0.1 \tag{21} $$

In basic solution:

$$ Al(OH)_{3}\:_{s}\:+\:OH^{-}\:=\:[Al(OH)_{4}]^{-}\:_{aq} \tag{22} $$

$$ Al(O)OH\:_{s}\:+\:H_{2}O_{l}\:+\:OH^{-}\:_{aq}\:=\:[Al(OH)_{4}]^{-}\:_{aq}\tag{23} $$

$$ 0.5\text{Al}_2O_{3s} + 1.5\text{H}_{2\text{O}_l} + \text{OH}^-{}_{\text{aq}} = [\text{Al}(\text{OH}_4)]^-{}_{\text{aq}}\tag{24} $$

In acid solution:

$$ Al(OH)_{3}\:_{s}\:+\:3H^{+}\:_{aq}\:=\:Al^{+3}\:_{aq}\:+3H_{2}O\:_{l}\tag{25} $$

$$ Al(O)OH\:_{s}\:+\:3H^{+}\:_{aq}\:=\:Al^{+3}\:_{aq}\:+\:2H_{2}O\:_{l}\tag{26} $$

$$ 0.5Al_{2}O_{3}\:_{s}\:+\:3H^{+}\:_{aq}\:=\:Al^{+3}\:_{aq}\:+\:1.5H_{2}O\:_{l}\tag{27} $$

$$ 2Al(OH)_{3}\:_{s}\:=Al_{2}O\:_{3}\:_{s}+3H_{2}0\;_{g}\;\;\;\;\;\Delta H^{\circ}=186\text{ kJ/mol} \tag{28} $$

$$ 2\:[Al(H_{2}0)_{6}]Cl_{3}\:=\:Al_{2}O_{3s}\:+\:6HCl_{g}\:+\:9H_{2}O_{g}\;\;\;\;\;\Delta H^{\circ}=959\text{ kJ/mol} \tag{29} $$

$$ = 1.44\%\: CuFeS_{2} \tag{1} $$

$$ P = N p \rho N^3D^5 (Watts)\tag{1} $$

$$\begin{equation}\rho = fluid \:density  (kg/m^3)\end{equation}$$

$$ kg \:m^{-3} \times \:sec^{-3} \times \:m^5 = kg \:m \:sec^{-2} m\:sec^{-1} = N\: m \:sec^{-1} = J \:sec^1 = Watt\tag{4} $$

$${equation}Np=\frac{P}{N^3D^5\rho}\tag{4} $$

$$P \propto\rho N^3D^5 \tag{4} $$

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