PH of salts

When we talk about the pH of salts, we mean the pH of aqueous solutions of soluble salts. Such salts dissociate in solution according to Eq

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{BA} + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{B}^{+} + \mathrm{A}^{-} + \mathrm{H}_2\mathrm{O},}

Where $\mathrm {BA}$ is a salt of an acid $\mathrm {HA}$ and policies $\mathrm {B(OH)} ,$ which arises, for example, by neutralisation according to the equation

$\mathrm {HA} +\mathrm {BOH} \rightarrow \mathrm {BA} +\mathrm {H} _{2}\mathrm {O} .$

pH of salts of strong acids and strong bases[edit | edit source]

In the case of a salt of a strong acid and a strong base, we consider that

Cation $\mathrm {B} ^{+}$ — because it is strong — it will remain dissociated:

$\mathrm {B} ^{+}+\mathrm {H} _{2}\mathrm {O} \rightarrow \mathrm {B} ^{+}+\mathrm {H} _{2}\mathrm {O}$

Anion $\mathrm {A} ^{-}$ — because it is strong — it will also remain dissociated:

$\mathrm {A} ^{-}+\mathrm {H} _{2}\mathrm {O} \rightarrow \mathrm {A} ^{-}+\mathrm {H} _{2}\mathrm {O}$

Therefore, not one of the salt ions will react with the water molecules and the only source $\mathrm {H} _{3}\mathrm {O} ^{+}$ and $\mathrm {OH} ^{-}$ will be the autoprotolysis of water itself. I mean

$\mathrm {pH} =-\log \ [\mathrm {H} _{3}\mathrm {O} ^{+}]=-\log \ [\mathrm {OH} ^{-}]=-\log {\sqrt {K_{w}}}={\frac {1}{2}}\mathrm {p} K_{w}$

and at 25 °C the pH will be equal to 7.

pH of salts of weak acids and strong bases[edit | edit source]

In the case of a salt of a weak acid and a strong base, we consider that

cation $\mathrm {B} ^{+}$ — because it is strong — it will remain dissociated: $\mathrm {B} ^{+}+\mathrm {H} _{2}\mathrm {O} \rightarrow \mathrm {B} ^{+}+\mathrm {H} _{2}\mathrm {O}$
anion $\mathrm {A} ^{-}$ — because it is weak — it will react with water, i.e. undergo so-called hydrolysis, according to the equation: $\mathrm {A} ^{-}+\mathrm {H} _{2}\mathrm {O} \rightleftharpoons \mathrm {HA} +\mathrm {OH} ^{-}$
will hydrolyze very few anions, the amount of hydrolyzed anions will be negligible, i.e
$c_{\mathrm {BA} }-[\mathrm {A} ^{-}]\approx 0,$ ,or otherwise Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{A}^{-}] \approx c_{\mathrm{BA}}}
the only source Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{OH}^{-}} is the above-mentioned hydrolysis reaction, we neglect other sources of hydroxide anions and oxonium cations, i.e. the amount Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{HA}} and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{OH}^{-}} will be the same according to her equation.

The above hydrolysis reaction has an equilibrium constant

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K = \frac{[\mathrm{HA}] \cdot [\mathrm{OH}^{-}]}{[\mathrm{A}^{-}] \cdot [\mathrm{H}_2\mathrm{O}]}.}

We will consider the concentration of water in water as constant and introduce a new constant, the so-called hydrolytic constant:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,A} = [\mathrm{H}_2\mathrm{O}] \cdot K = \frac{[\mathrm{HA}] \cdot [\mathrm{OH}^{-}]}{[\mathrm{A}^{-}]}}

If we adjust the (slightly imprecise) notation of water in chemical equations, it will be easier to see that the hydrolysis equation is de facto just the opposite equation to dissociation:

dissociation: Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{HA} \rightarrow \mathrm{H}^{+} + \mathrm{A}^{-},}
hydrolysis: Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{A}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{HA}.}

It is therefore natural that the hydrolytic constant Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,A}} and the dissociation constant Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_A} they will be related:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,A} \cdot K_A = \frac{[\mathrm{HA}] \cdot [\mathrm{OH}^{-}]}{[\mathrm{A}^{-}]} \cdot \frac{[\mathrm{A}^{-}] \cdot [\mathrm{H}_3\mathrm{O}^{+}]}{[\mathrm{HA}]} = [\mathrm{OH}^{-}] \cdot [\mathrm{H}_3\mathrm{O}^{+}] = K_w}

For a constant Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,A}} so we get the formula

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,A} = \frac{K_w}{K_A}.}

If to the definition of the hydrolytic constant Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,A}} we substitute forFailed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{HA}]} according to our assumptionsFailed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{OH}^{-}],} and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_{\mathrm{BA}}} for Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{A}^{-}]} we will get

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,A} \cdot [\mathrm{A}^{-}] = K_{h,A} \cdot c_{\mathrm{BA}} = [\mathrm{OH}^{-}]^{2}.}

When we express the dependence of the concentration of oxonium cations on the concentration of hydroxide anions from the definition of the ionic product of water Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_w} , we obtain

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}]^{2} = \frac{K_w^2}{[\mathrm{OH}^{-}]^{2}} = \frac{K_w^2}{K_{h,A} \cdot c_{\mathrm{BA}}} = \frac{K_w^2}{\frac{K_w}{K_A} \cdot c_{\mathrm{BA}}} = \frac{K_w^2 \cdot K_A}{K_w \cdot c_{\mathrm{BA}}} = \frac{K_w \cdot K_A}{c_{\mathrm{BA}}}}

We take the square root (concentrations are always positive), logarithmize and multiply by −1:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\log [\mathrm{H}_3\mathrm{O}^{+}] = -\log \sqrt{\frac{K_w \cdot K_A}{c_{\mathrm{BA}}}} = -\log \frac{K_w^{\frac{1}{2}} \cdot K_A^{\frac{1}{2}}}{c_{\mathrm{BA}}^{\frac{1}{2}}} = \frac{1}{2} \log c_{\mathrm{BA}} - \frac{1}{2} \log K_w - \frac{1}{2} \log K_A = \frac{1}{2} \log c_{\mathrm{BA}} + \frac{1}{2} \mathrm{p}K_w + \frac{1}{2} \mathrm{p}K_A}

At 25 °C we get the formula Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{pH} = 7 + \frac{1}{2} \log c_{\mathrm{BA}} + \frac{1}{2} \mathrm{p}K_A}

The resulting pH will be alkaline . This is due to the fact that the anion of the acid draws hydrons from the system.

The pH of a salt of a strong acid and a weak base[edit | edit source]

In the case of a salt of a strong acid and a weak base, we consider that

cation Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{B}^{+}} —because it is weak — it will hydrolyse according to the reaction

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{B}^{+} + 2\ \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{BOH} + \mathrm{H}_3\mathrm{O}^{+}}

anion Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{A}^{-}} — because it is strong — it will not hydrolyse, that is

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{A}^{-} + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{A}^{-} + \mathrm{H}_2\mathrm{O}}

will hydrolyze very few cations, and the amount of hydrolyzed cations will thus be negligible, i.e
Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_{\mathrm{BA}} - [\mathrm{B}^{+}] \approx 0} , or not Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_{\mathrm{BA}} \approx [\mathrm{B}^{+}]}
hydrolysis of cations is the only source of oxonium cations, we neglect other sources, so according to the hydrolysis equation Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}^{+}] = [\mathrm{BOH}]}

For hydrolysis, we introduce a hydrolytic constantFailed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,B} = K \cdot [\mathrm{H}_2\mathrm{O}]^{2}} like

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,B} = \frac{[\mathrm{H}_3\mathrm{O}^{+}] \cdot [\mathrm{BOH}] }{ [\mathrm{B}^{+}] },}

for which it can again be proved to hold Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,B} \cdot K_B = K_w.}

According to the assumptions, we substitute in the hydrolytic constant Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_{\mathrm{BA}}} za Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B^{+}} and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}^{+}]} for Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{BOH}]} :

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{B}^{+}] \cdot K_{h,B} = c_{\mathrm{BA}} \cdot K_{h,B} = [\mathrm{H}_3\mathrm{O}^{+}]^{2}}

We take the square root (concentrations are always positive numbers), logarithmize and multiply by −1:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\log\ [\mathrm{H}_3\mathrm{O}^{+}] = \frac{1}{2} \left(-\log c_{\mathrm{BA}} - \log K_{h,B} \right) = \frac{1}{2} \left(-\log c_{\mathrm{BA}} - \log \frac{K_w}{K_B} \right)}

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\log\ [\mathrm{H}_3\mathrm{O}^{+}] = \frac{1}{2} \left(- \log c_{\mathrm{BA}} + \log K_B - \log K_w \right) = \frac{1}{2} \left(\mathrm{p}K_w - \mathrm{p}K_B - \log c_{\mathrm{BA}} \right)}

So at 25 °C we get the formula:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{pH} = 7 - \frac{1}{2} \mathrm{p}K_B - \frac{1}{2} \log c_{\mathrm{BA}}}

The resulting pH will be acidic . This is because the base cation adds hydrons to the system.

pH of salts of weak acids and weak bases[edit | edit source]

In the case of a salt of a weak acid and a weak base, we consider that

Cation Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{B}^{+}} will hydrolyse according to Eq

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{B}^{+} + 2\ \mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{BOH} + \mathrm{H}_3\mathrm{O}^{+}}

anion Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{A}^{-}} will react with the resulting oxonium cations and then possibly further hydrolyse according to the equation

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{A}^{-} + \mathrm{H}_3\mathrm{O}^{+} \rightleftharpoons \mathrm{HA} + \mathrm{H}_2\mathrm{O}}

both ions will hydrolyse in negligible amounts, ie

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_{\mathrm{BA}} \approx [\mathrm{B}^{+}] \approx [\mathrm{A}^{-}]}

there is no other source of hydroxide anions and oxonium cations in the system, therefore
- oxonium cations formed by hydrolysis of the basecation Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{B}^{+}} we markFailed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O} ^{+}]_{\mathrm{B}}} and according to the chemical equation of hydrolysis it applies to them Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle . [\mathrm{H}_3\mathrm{O}^{+}]_{\mathrm{B}} = [\mathrm{BOH}]. }
- oxonium cations destroyed by acid anion hydrolysisFailed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{A}^{-}]} we mark Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle . [\mathrm{H}_3\mathrm{O}^{+}]_{\mathrm{A}}} and according to the chemical equation of hydrolysis it applies to them Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}^{+}]_{\mathrm{A}} = [\mathrm{HA}]}

the equilibrium concentration of oxonium cations is calculated as the difference between the concentration of oxonium cations formed by the hydrolysis of the base cation and the concentration of oxonium cations consumed by the hydrolysis of the acid anion , i.e.

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf [\mathrm{H}_3\mathrm{O}^{+}] = [\mathrm{H}_3\mathrm{O}^{+}]_{\mathrm{B}} - [\mathrm{H}_3\mathrm{O}^{+}]_{\mathrm{A}}}

For the hydrolysis of the cation, we have the hydrolysis constant:Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_{h,B} = \frac{K_w}{K_B} = \frac{[\mathrm{H}_3\mathrm{O}^{+}] \cdot [\mathrm{BOH}]}{[\mathrm{B}^{+}]}}

and for the hydrolysis of the anion it is better to express the concentration of oxonium cations using another constant describing the equilibrium, namely the dissociation constant:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_A = \frac{[\mathrm{H}_3\mathrm{O}^{+}] \cdot [\mathrm{A}^{-}]}{[\mathrm{HA}]}}

By adding the penultimate assumption to the last assumption, we get

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}^{+}] = [\mathrm{BOH}] - [\mathrm{HA}].}

We express Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{BOH}]} and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{HA}]} from the equations for the equilibrium constants:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}^{+}] = \frac{K_w \cdot [\mathrm{B}^{+}]}{K_B \cdot [\mathrm{H}_3\mathrm{O}^{+}]} - \frac{[\mathrm{H}_3\mathrm{O}^{+}] \cdot [\mathrm{A}^{-}] }{K_A}}

We will edit:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}^{+}] + \frac{[\mathrm{H}_3\mathrm{O}^{+}] \cdot [\mathrm{A}^{-}] }{K_A} = [\mathrm{H}_3\mathrm{O}^{+}] \left(1 + \frac{[\mathrm{A}^{-}]}{K_A} \right) = \frac{K_w \cdot [\mathrm{B}^{+}]}{K_B \cdot [\mathrm{H}_3\mathrm{O}^{+}]} }

We express the concentration of oxonium cations:

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}^{+}]^{2} = \frac{ \frac{K_w \cdot [\mathrm{B}^{+}]}{K_B} }{ 1 + \frac{ [\mathrm{A}^{-}] }{ K_A } } = \frac{ \frac{K_w \cdot [\mathrm{B}^{+}]}{K_B} }{ \frac{ K_A + [\mathrm{A}^{-}] }{ K_A } } = \frac{ K_w \cdot [\mathrm{B}^{+}] \cdot K_A }{ K_B \cdot (K_A + [\mathrm{A}^{-}]) }}

Because it is Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{A}^{-}] \gg K_A,} we can Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K_A} neglect the denominator and approximate the formula to

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}^{+}]^{2} = \frac{ K_w \cdot [\mathrm{B}^{+}] \cdot K_A }{ K_B \cdot [\mathrm{A}^{-}] }}

By supplementing Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_{\mathrm{BA}}} by assumptions we get

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [\mathrm{H}_3\mathrm{O}^{+}]^{2} = \frac{ K_w \cdot c_{\mathrm{BA}} \cdot K_A }{ K_B \cdot c_{\mathrm{BA}} } = \frac{ K_W \cdot K_A }{ K_B }}

We take the square root (these are positive constants), take the logarithm, multiply by −1 and get

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\log\ [\mathrm{H}_\mathrm{O}^{+}] = -\frac{1}{2} \log K_w -\frac{1}{2} \log K_A + \frac{1}{2} \log K_B = \frac{1}{2} (\mathrm{p}K_w + \mathrm{p}K_A - \mathrm{p}K_B)}

Thus, the pH of the salt of a weak acid and a weak base (after approximation) does not depend on the concentration of the salt .

At 25 °C we get

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{pH} = 7 + \frac{1}{2} \mathrm{p}K_A - \frac{1}{2} \mathrm{p}K_B}

Links[edit | edit source]

References[edit | edit source]

BERKA, Antonín – FETL, Ladislav – NĚMEC, Ivan. Practitioner's Guide to Quantitative Analytical Chemistry.. 1. edition. SNTL, 1985. 228 pp. pp. 56–66.

recommended literature[edit | edit source]