Cas d'un corps dissocié
Dans le cas d'un électrolyte de type {A}_{m}^{{z}_{A}}{B}_{n}^{{z}_{B}}, totalement dissocié (X=1) , le potentiel chimique s'écrit :
En terme de sursaturation on obtient donc :
soit
Sursaturation | en activité |
---|---|
rapport de sursaturation | S_{i,a}=\frac{a_{\pm, {A_{m}^{z_A}B_{n}^{z_B}}}} {a_{\pm, {A_{m}^{z_A}B_{n}^{z_B}}}^{eq}} |
sursaturation relative | \sigma_{i,a}=S-1 |
sursaturation absolue | \Delta C_{i,a}={a_{\pm, {A_{m}^{z_A}B_{n}^{z_B}}}} - {a_{\pm, {A_{m}^{z_A}B_{n}^{z_B}}}^{eq}} |
Comme {a}_{±,{A}_{m}^{{z}_{A}}{B}_{n}^{{z}_{B}}}={\left({a}_{{A}^{{z}_{A}}}^{m}{a}_{{B}^{{z}_{B}}}^{n}\right)}^{\frac{1}{m+n}} et {\gamma }_{±,,{A}_{m}^{{z}_{A}}{B}_{n}^{{z}_{B}}}={\left({\gamma }_{{A}^{{z}_{A}}}^{m}{\gamma }_{{B}^{{z}_{B}}}^{n}\right)}^{\frac{1}{m+n}}
on obtient {a}_{±,{A}_{m}^{{z}_{A}}{B}_{n}^{{z}_{B}}}={\left({\gamma }_{{A}^{{z}_{A}}}^{m}{C}_{{A}^{{z}_{A}}}^{m}{\gamma }_{{B}^{{z}_{B}}}^{n}{C}_{{B}^{{z}_{B}}}^{n}\right)}^{\frac{1}{m+n}}={\left({\gamma }_{±,{A}_{m}^{{z}_{A}}{B}_{n}^{{z}_{B}}}^{\left(m+n\right)}{C}_{{A}^{{z}_{A}}}^{m}{C}_{{B}^{{z}_{B}}}^{n}\right)}^{\frac{1}{m+n}}={\gamma }_{±,{A}_{m}^{{z}_{A}}{B}_{n}^{{z}_{B}}}{\left({C}_{{A}^{{z}_{A}}}^{m}{C}_{{B}^{{z}_{B}}}^{n}\right)}^{\frac{1}{m+n}}
et à l'équilibre {a}_{±,{A}_{m}^{{z}_{A}}{B}_{n}^{{z}_{B}}}^{\mathrm{eq}}={\left({\gamma }_{{A}^{{z}_{A}}}^{\mathrm{eq}m}{C}_{{A}^{{z}_{A}}}^{\mathrm{eq}m}{\gamma }_{{B}^{{z}_{B}}}^{\mathrm{eq}n}{C}_{{B}^{{z}_{B}}}^{\mathrm{eq}n}\right)}^{\frac{1}{m+n}}={\left({\gamma }_{±,{A}_{m}^{{z}_{A}}{B}_{n}^{{z}_{B}}}^{\left(\mathrm{eq}m+n\right)}{C}_{{A}^{{z}_{A}}}^{\mathrm{eq}m}{C}_{{B}^{{z}_{B}}}^{\mathrm{eq}n}\right)}^{\frac{1}{m+n}}={\gamma }_{±,{A}_{m}^{{z}_{A}}{B}_{n}^{{z}_{B}}}^{\mathrm{eq}}{\left({C}_{{A}^{{z}_{A}}}^{\mathrm{eq}m}{C}_{{B}^{{z}_{B}}}^{\mathrm{eq}n}\right)}^{\frac{1}{m+n}}
Sursaturation | en concentration |
---|---|
rapport de sursaturation | S_{i,a}= \frac{\gamma_{\pm,{A_{m}^{z_A}B_{n}^{z_B}}}\left( C_{A^{z_A}}^m C_{B^{z_B}}^n \right)^{\frac{1}{m+n}}} {\gamma_{\pm,{A_{m}^{z_A}B_{n}^{z_B}}}^eq \left( C_{A^{z_A}}^{eq, m} C_{B^{z_B}}^{eq, n} \right)^{\frac{1}{m+n}}} |
sursaturation relative | \sigma_{i,a}=S-1 |
sursaturation absolue | \Delta C_{i,a}=\gamma_{\pm,{A_{m}^{z_A}B_{n}^{z_B}}}\left( C_{A^{z_A}}^m C_{B^{z_B}}^n \right)^{\frac{1} {m+n}} -\gamma_{\pm,{A_{m}^{z_A}B_{n}^{z_B}}}^{eq} \left( C_{A^{z_A}}^{eq, m} C_{B^{z_B}}^{eq, n} \right)^{\frac{1}{m+n}} |