Уравнение Гендерсона — Хассельбаха

Определение константы кислотности

${\displaystyle K_{\mathrm {a} }=\mathrm {\frac {[H^{+}][A^{-}]}{[HA]}} }$

Прологарифмируем равенство:

${\displaystyle \lg K_{\mathrm {a} }=\lg \left(\mathrm {\frac {[H^{+}][A^{-}]}{[HA]}} \right)}$

${\displaystyle \lg K_{\mathrm {a} }=\lg[H^{+}]+\lg \left(\mathrm {\frac {[A^{-}]}{[HA]}} \right)}$

${\displaystyle -\mathrm {p} K_{\mathrm {a} }=-{\ce {pH}}+\lg \left(\mathrm {\frac {[A^{-}]}{[HA]}} \right)}$

${\displaystyle {\ce {pH}}=\mathrm {p} K_{\mathrm {a} }+\lg \left(\mathrm {\frac {[A^{-}]}{[HA]}} \right)}$

${\displaystyle C}$ - исходная молярная концентрация

${\displaystyle \alpha \approx {\sqrt {K_{a} \over C}}}$ — степень диссоциации

Для слабой кислоты	Для слабого основания
${\displaystyle {\ce {HA}}}$ ${\displaystyle {\ce {<=>}}}$ ${\displaystyle {\ce {A^-}}}$ ${\displaystyle {\ce {+}}}$ ${\displaystyle {\ce {H^+}}}$ ${\displaystyle \mathrm {C-C\alpha } }$ ${\displaystyle \mathrm {C\alpha } }$ ${\displaystyle \mathrm {C\alpha } }$	${\displaystyle {\ce {MOH}}}$ ${\displaystyle {\ce {<=>}}}$ ${\displaystyle {\ce {M^+}}}$ ${\displaystyle {\ce {+}}}$ ${\displaystyle {\ce {OH^-}}}$ ${\displaystyle \mathrm {C-C\alpha } }$ ${\displaystyle \mathrm {C\alpha } }$ ${\displaystyle \mathrm {C\alpha } }$
${\displaystyle \mathrm {pH} ={-\lg \left(\mathrm {K_{a}} \right)-\lg(\mathrm {C} ) \over 2}}$	${\displaystyle \mathrm {pOH} ={-\lg \left(\mathrm {K_{b}} \right)-\lg(\mathrm {C} ) \over 2}}$

${\displaystyle [H^{+}]=\mathrm {\alpha C} }$

${\displaystyle {\ce {pH}}=-\lg \left(\mathrm {\alpha C} \right)=-\lg \left(\mathrm {{\sqrt {K_{a} \over C}}C} \right)=-\lg \left(\mathrm {\sqrt {K_{a}C}} \right)={-\lg \left(\mathrm {K_{a}} \right)-\lg(\mathrm {C} ) \over 2}}$