5.4 Two weak acids

3.1 Degree of Ionization (Dissociation)

5.1 Strong acid
5.2 Weak acid
5.3 Strong Acid + Weak Acid
5.4 Two weak acids
5.5 Dibasic and polyprotic weak acids

6.1 Salts of weak acid + strong base
6.2 Salt of weak base + strong acid
6.3 Salt of weak acid and weak base

7.1 Acidic buffer
7.2 Basic buffer
7.3 Salt buffer

8.1 Calculating Solubility of a salt

For two weak acids $HA$ and $HB$ with concentrations ${C_1}$ and ${C_2}$ and dissociation constants ${K_{{a_1}}}$ & ${K_{{a_2}}}$,

$$HA \rightleftharpoons {{\text{H}}^ + }{\text{ + }}{{\text{A}}^ - }$$

${C_1}(1 - {\alpha _1})$ ${C_1}{\alpha _1} + {C_2}{\alpha _2}$ ${C_1}{\alpha _1}$

$$HB\rightleftharpoons {{\text{H}}^ + }{\text{ + }}{{\text{B}}^ - }$$

${C_2}(1 - {\alpha _2})$ ${C_1}{\alpha _1} + {C_2}{\alpha _2}$ ${C_2}{\alpha _2}$

$${K_{{a_1}}}{\text{ = }}\frac{{\left[ {{H^ + }} \right]\left[ {{A^ - }} \right]}}{{\left[ {HA} \right]}}{\text{ = }}\frac{{({C_1}{\alpha _1} + {C_2}{\alpha _2}){C_1}{\alpha _1}}}{{{C_1}(1 - {\alpha _1})}}{\text{ }}$$

$${K_{{a_2}}}{\text{ = }}\frac{{\left[ {{H^ + }} \right]\left[ {{B^ - }} \right]}}{{\left[ {HB} \right]}}{\text{ = }}\frac{{({C_1}{\alpha _1} + {C_2}{\alpha _2}){C_2}{\alpha _2}}}{{{C_2}(1 - {\alpha _2})}}{\text{ }}$$

Just like previous case, these two equation can be solved for the values of ${\alpha _1}$ and ${\alpha _2}$ from where $\left[ {{H^ + }} \right]$ can be calculated and finally the $pH$ can be found out.