Nernst equation and electrolysis

Let's say we have a stable solution of 
$\mathrm{A}\_{\left(\mathrm{aq}\right)}^{2+}$
and $\mathrm{C}\_{\left(\mathrm{aq}\right)}^{+}$
, with their respective counter-ions.


The associated redox reactions are:


$\mathrm{A}\_{\left(\mathrm{aq}\right)}^{2+}+\mathrm{e}^{-}\rightleftharpoons\mathrm{A}\_{\left(\mathrm{aq}\right)}^{+}\qquad\mathcal{E}\_{\mathrm{A}\_{\left(\mathrm{aq}\right)}^{2+}/\mathrm{A}\_{\left(\mathrm{aq}\right)}^{+}}^{\circ}$


$\mathrm{C}\_{\left(\mathrm{aq}\right)}^{2+}+\mathrm{e}^{-}\rightleftharpoons\mathrm{C}\_{\left(\mathrm{aq}\right)}^{+}\qquad\mathcal{E}\_{\mathrm{C}\_{\left(\mathrm{aq}\right)}^{2+}/\mathrm{C}\_{\left(\mathrm{aq}\right)}^{+}}^{\circ}$


where $\mathcal{E}\_{\mathrm{A}\_{\left(\mathrm{aq}\right)}^{2+}/\mathrm{A}\_{\left(\mathrm{aq}\right)}^{+}}^{\circ}<\mathcal{E}\_{\mathrm{C}\_{\left(\mathrm{aq}\right)}^{2+}/\mathrm{C}\_{\left(\mathrm{aq}\right)}^{+}}^{\circ}$
, since no reaction between $\mathrm{A}\_{\left(\mathrm{aq}\right)}^{2+}$
and $\mathrm{C}\_{\left(\mathrm{aq}\right)}^{+}$
is occurring. 


The questions are:


1. Provided that neither $\mathrm{A}\_{\left(\mathrm{aq}\right)}^{+}$
nor $\mathrm{C}\_{\left(\mathrm{aq}\right)}^{2+}$
are present in the solution, how can we determine, form the Nernst equation, the $\mathcal{E}$ needed to start the electrolysis process 
$\mathrm{A}\_{\left(\mathrm{aq}\right)}^{2+}+\mathrm{C}\_{\left(\mathrm{aq}\right)}^{+}\rightleftharpoons\mathrm{A}\_{\left(\mathrm{aq}\right)}^{ +}+\mathrm{C}\_{\left(\mathrm{aq}\right)}^{2+}$?
2. **In other words, how can the Nernst equation deal with activities that are equal to zero?**


Thanks in advance!




The Nernst equation only technically applies when the system is in electrochemical equilibrium—when there's no net current flow, but there's actually an exchange current. A system in which the reaction can only happen in one direction because there are no products wouldn't apply. Source: Electrochemical Dictionary; Bard, A. J.; Inzelt, G.; Scholz, F., Eds.; Springer Berlin Heidelberg: Berlin, Heidelberg, 2008.


What I'm not sure about is the validity of ∆G values calculated from $∆G=∆G°+RT\ln Q$ at the limits where the system is all products or all reactants. ±∞ don't seem to be meaningful values, but the system should quickly move away from these boundary values, even if only by a small amount. These chemical thermodynamics methods are well-behaved when near equilibrium, but well away from equilibrium, they can produce invalid results.


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$$\mathrm{A}\_{\left(\mathrm{aq}\right)}^{2+}+\mathrm{C}\_{\left(\mathrm{aq}\right)}^{+}\rightleftharpoons\mathrm{A}\_{\left(\mathrm{aq}\right)}^{ +}+\mathrm{C}\_{\left(\mathrm{aq}\right)}^{2+}$$
If you don't have $\mathrm{A}\_{\left(\mathrm{aq}\right)}^{+}$ or $\mathrm{C}\_{\left(\mathrm{aq}\right)}^{2+}$ you must be having atleast $\mathrm{A}\_{\left(\mathrm{aq}\right)}^{2+}$ or $\mathrm{C}\_{\left(\mathrm{aq}\right)}^{+}$, the reactants to produce the products when there is no product the case is:
$$\mathcal{E}=\mathcal{E}^\circ-\frac{\mathcal{R}T}{\mathcal{\nu F}}\ln{\frac{[\mathrm{A}\_{\left(\mathrm{aq}\right)}^{ +}][\mathrm{C}\_{\left(\mathrm{aq}\right)}^{2+}]}{[\mathrm{A}\_{\left(\mathrm{aq}\right)}^{ 2+}][\mathrm{C}\_{\left(\mathrm{aq}\right)}^{+}]}}$$
when the $\ln$ term is zero, the $\mathcal{E}\to\infty$ implying an instantaneous reaction which requires no external force, also implies by the Le'Chatelirer's principe but note that when even a slightest amount of product is created the tendency to procees forward decreases until it reaches the equilibrium where the reaction attains the equilibrium.


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