5.5 Moniarvoisten protolyyttien ja suolaliuosten pH

5.31

$CO_3^{2-}\left(aq\right)+H_2O\left(l\right)\xrightleftharpoons[]{}HCO_3^-\left(aq\right)+OH^-\left(aq\right)$
$pK_b=3{,}68$
$K_b=0{,}0002089...$
$\left[OH^-\right]=\frac{\left[HCO_3^-\right]K_b}{\left[CO_3^{2-}\right]}=\frac{0{,}20\cdot0{,}0002089...}{0{,}20}=K_b$

$HCO_3^-\left(aq\right)+H_2O\left(l\right)\xrightleftharpoons[]{}H_2CO_3\left(aq\right)+OH^-\left(aq\right)$
$pK_b=7{,}63$
$K_b=2{,}34422...\cdot10^{-8}$
$\left[OH^-\right]=\frac{\left[H_2CO_3\right]K_b}{\left[HCO_3^-\right]}=\frac{0{,}20\cdot2{,}34422...\cdot10^{-8}}{0{,}20}=K_b$

$\left[OH^-\right]=0{,}0002089...+2{,}34422...\cdot10^{-8}$
$pOH=3{,}67995...$
$pH=14-pOH=10{,}32$

$\begin{array}{l|l} &CO_3^{2-}&H_2O&HCO_3^-&OH^-\\ \hline c_{alku}&0{,}20&-&0&0\\ muutos&-x&-&+x&+x\\ c_{tasap}&0{,}20-x&-&x&x \end{array}$
$0{,}0002089...=\frac{x^2}{0{,}20-x}$
$x=0{,}00636$
$\left[CO_3^{2-}\right]=0{,}19364$

$\left[OH^-\right]=\frac{\left[HCO_3^-\right]K_b}{\left[CO_3^{2-}\right]}=\frac{0{,}00636\cdot0{,}0002089...}{0{,}19364}=6{,}8612...\cdot10^{-6}$

$\begin{array}{l|l} &HCO_3^-&H_2O&H_2CO_3&OH^-\\ \hline c_{alku}&0{,}00636&-&0&0{,}00636\\ muutos&-x&-&+x&+x\\ c_{tasap}&0{,}00636-x&-&x&0{,}00636+x \end{array}$
$2{,}34422...\cdot10^{-8}=\frac{x^2}{0{,}00636-x}$
$x=2{,}3442\cdot10^{-8}$

$\left[HCO_3^-\right]=0{,}0063623$

$\left[OH^-\right]=\frac{\left[H_2CO_3\right]K_b}{\left[HCO_3^-\right]}=\frac{\left(2{,}34422...\cdot10^{-8}\right)^2}{0{,}0063623}=4{,}43141\cdot10^{-11}$
$pOH=-\lg\left[OH^-\right]=-\lg\left(6{,}8612506...\right)=13{,}0636$