Equation de la réaction de l'acide avec l'eau
\(\ce{CH3COOH + H2O <--> CH3COO- + H3O+}\)
Expression de la constante d'équilibre
\(K = \dfrac{[\ce{CH3COO-}]_f×[\ce{H3O+}]_f}{[\ce{CH3COOH}]_f}\)
Tableau d'avancement
|
Av. |
\(\ce{CH3COOH}\) |
\(\ce{+}\) |
\(\ce{H2O}\) |
\(\ce{<-->}\) |
\(\ce{CH3COO-}\) |
\(\ce{H3O+}\) |
| État initial |
\(x = 0\) |
\(n_0(\ce{CH3COOH})\) |
|
Solvant (excès) |
|
\(0\) |
\(0\) |
| État final |
\(x = x_f\) |
\(n_f(\ce{CH3COOH}) = n_i(\ce{CH3COOH}) - x_f\) |
|
Solvant (excès) |
|
\(n_f(\ce{CH3COO-}) = x_f\) |
\(n_f(\ce{H3O+}) = x_f\) |
Relation entre \(x_f\) et le \(pH\)
D'après le tableau d'avancement \(n_f(\ce{H3O+}) = x_f\)
D'où \([\ce{H3O+}]_f = \dfrac{x_f}{V}\)
Or \([\ce{H3O+}] = 10^{-pH}\)
Donc \(\dfrac{x_f}{V} = 10^{-pH_f}\)
Concentration des différentes espèces dans l'état final en fonction du \(pH\)
\(\begin{align}
[\ce{CH3COO-}]_f &= \dfrac{x_f}{V} \\
&= 10^{-pH_f} \\
\end{align}\)
\(\begin{align}
[\ce{H3O+}]_f &= \dfrac{x_f}{V} \\
&= 10^{-pH_f}
\end{align}\)
\(\begin{align}
[\ce{CH3COOH}]_f &= \dfrac{n_f(\ce{CH3COOH})}{V} \\
&= \dfrac{n_i(\ce{CH3COOH})}{V} - \dfrac{x_f}{V} \\
&= C_i - 10^{-pH_f}
\end{align}\)
Bilan
\(\begin{align}
K &= \dfrac{[\ce{CH3COO-}]_f×[\ce{H3O+}]_f}{[\ce{CH3COOH}]_f} \\
&= \dfrac{10^{-pH_f} × 10^{-pH_f}} {C_i - 10^{-pH_f}} \\
&= \pu{1,8E-4}
\end{align}\)
