Weak single-celled acids
For the weak single-celled acids ' is in progress dissociation according to balanced reaction :
,
s éväläžnou konstantou < math >K,</math> which is defined like :
![{\displaystyle K=\ frac{[\ mathrm{A}^{-}]\ cdot[\ mathrm{H}_{3}\ mathrm{O}^{+}]}{[\ mathrm{HA}]\ cdot[\ mathrm{H}_{2}\ mathrm{O}]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a9bf3d7b69e33661f0a2edb5fecad71986030c6)
.
necessary to calculate the pH use other method than at pH strong acids and bases#Strong single-celled strong acids acids , because in weak acids can't to consider dissociation for complete .
On the contrary we assume that :
- acid dissociates very little difference _ between
![{\displaystyle [\ mathrm{HA}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4009e39aa4b44355328594be1d682b4412c0949)
and 
( i.e. ![{\displaystyle [\ mathrm{A}^{-}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/527e4e5358ecb93745d4351d9c8fec2d0a402815)
) we neglect , and therefore ![{\displaystyle [\ mathrm{HA}]\ approxc_{\ mathrm{HA}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1be77d87f49588dc0e76483d2ee5ae73ed3dabe5)
;
- dissociation acid is the only one source oxonium of cations in the system , that is according to ratios fabric amount chemical equation
![{\displaystyle [\ mathrm{H}_{3}\ mathrm{O}^{+}]=[\ mathrm{A}^{-}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0cf121d45ec849532cbe6c7bf404a169eb8ebfc2)
.
Because you can concentration water to consider for constant , the so - called dissociative constant ![{\displaystyle K_{A}=K\ cdot[\ mathrm{H}_{2}\ mathrm{O}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/99fbd8b998ec39a5df1168581474122b5be9b7f0)
whose value is for each acid tabulated . We are getting thus :
![{\displaystyle K_{A}=\ frac{[\ mathrm{A}^{-}]\ cdot[\ mathrm{H}_{3}\ mathrm{O}^{+}]}{[\ mathrm{HA}]}</math>.Accordingtoassumptionswesubstitute<math>[\ mathrm{H}_{3}\ mathrm{O}^{+}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1261d8d890a6027df20e2ae1f9657f5f423669f6)
after and after and expression concentration oxonium cations we get :
![{\displaystyle [\ mathrm{H}_{3}\ mathrm{O}^{+}]^{2}=K_{A}\ cdot[\ mathrm{HA}]=K_{A}\ cdotc_{\ mathrm{HA}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1a9ef00ac1fa3f1b7245d1ec2572b635ffcc29ca)
.
root ( concentration is always positive number ), we logarithmize both parties equation and multiply by 
:
![{\displaystyle -\log \ [\ mathrm{H}_{3}\ mathrm{O}^{+}]=-\log \ sqrt{K_{A}\ cdotc_{\ mathrm{HA}}}=-\log \ (K_{A}\ cdotc_{\ mathrm{HA}})^{\ frac{1}{2}}=-\ frac{1}{2}\log \ (K_{A}\ cdotc_{\ mathrm{HA}})=-\ frac{1}{2}(\log K_{A}+\log c_{\ mathrm{HA}})=-\ frac{1}{2}\log K_{A}-\ frac{1}{2}\log c_{\ mathrm{HA}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/72e2d2e0e79ae43100815cd4c6a8cf1713d6ece8)
.
For "
" (by analogy with pH) the symbol 
was used . If we know dissociative constant or her negative decadent logarithm , we calculate the pH according to formulas :
.
For the weak single-celled principles is ongoing dissociation according to balanced equation :
,
s tabelovanou Dissociation konstantou 
which is defined like :
![{\displaystyle K_{B}=\ frac{[\ mathrm{B}^{+}]\ cdot[\ mathrm{OH}^{-}]}{[\ mathrm{BOH}]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/63054b468e8c3a1821f9e8efc704dcc69894d2aa)
.
We assume that :
- principle dissociates very little difference _ between
![{\displaystyle [\ mathrm{BOH}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8fe646666322151e70931f2cc68a3e2f35dfb999)
and 
( ie ![{\displaystyle [\ mathrm{B}^{+}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e629664cfb2accea25e103fba6f6ac0f3f38bd2)
) we neglect , and therefore ![{\displaystyle [\ mathrm{BOH}]\ approxc_{\ mathrm{BOH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8b197322b0cfc2669f57f1efd190b9c114e3b792)
;
- dissociation acid is the only one source hydroxides of anions in the system , that is according to ratios fabric amount chemical equation
![{\displaystyle [\ mathrm{OH}^{-}]=[\ mathrm{B}^{+}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93277ac177022cb27782ee4509a520602444af2b)
;
- emergence hydroxides of anions acts decrease oxonium cations according to equation for the ionic product of water :
![{\displaystyle [\ mathrm{H}_{3}\ mathrm{O}^{+}]=\ frac{K_{w}}{[\ mathrm{OH}^{-}]}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38f18dcb26fa632d9fc989ef7ae041d9fd1985f9)
.
Substitution according to assumptions into the definition dissociative constants we get :
![{\displaystyle [\ mathrm{OH}^{-}]^{2}=K_{B}\ cdot[\ mathrm{BOH}]=K_{B}\ cdotc_{\ mathrm{BOH}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2632d8d39b1d2bd30a544354b41c03d9577c110)
.
We square root ( concentration they are always positive numbers ):
![{\displaystyle [\ mathrm{OH}^{-}]=\ sqrt{K_{B}\ cdotc_{\ mathrm{BOH}}}=(K_{B}\ cdotc_{\ mathrm{BOH}})^{\ frac{1}{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e8b1c6871bca1edb0007618c37bcc520a9986e3c)
.
We substitute in the equation for ionic product water :
![{\displaystyle [\ mathrm{H}_{3}\ mathrm{O}^{+}]=\ frac{K_{w}}{(K_{B}\ cdotc_{\ mathrm{BOH}})^{\ frac{1}{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f9ca99f9c134d85524bc303a209d69c26612600d)
.
Zlogaritmujeme a vynaňíme :
![{\displaystyle -\log[\ mathrm{H}_{3}\ mathrm{O}^{+}]=\ frac{1}{2}\log K_{B}+\ frac{1}{2}\log c_{\ mathrm{BOH}}-\log K_{w}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0b4bbae2accce9b08aefac4644ed929d7b00b473)
At 25 °C , we calculate the pH according to formulas
U slabých vícesytných kyselin a zásad je pro přesný výpočet nutné znát disociační konstanty všech disociačních stupňů, sestavit z chemických rovnic soustavu rovnic o několika neznámých a za pomoci základní algebry vyjádřit pH. Toto je pro rutinní výpočty poměrně zdlouhavý proces, proto se pH většinou počítá pouze přibližně, zanedbáním méně preferovaných disociačních stupňů, a použije se pak vzorec pro slabé jednosytné kyseliny. V praxi bývá chyba vzniklá tímto zanedbáním relativně malá, neboť jednotlivé disociační konstanty se od sebe liší zpravidla o několik řádů, takže ovlivnění pH zanedbanými reakcemi bývá málo podstatné.
For weak polyhydric acids and bases, for an accurate calculation it is necessary to know the dissociation constants of all dissociation degrees, to compile a system of equations with several unknowns from the chemical equations, and to express the pH using basic algebra. This is a rather tedious process for routine calculations, so the pH is usually calculated only approximately, neglecting the less preferred dissociation degrees, and then applying the formula for weak monoacids. In practice, the error caused by this neglect is relatively small, as the individual dissociation constants usually differ from each other by several orders of magnitude, so the influence of the neglected reactions on the pH is not significant.
