# Electrolysis of dilute and concentrated sodium chloride and the Nernst equation

Interested to know if there is a critical concentration at which $\ce{Cl-}$ will oxidise over $\ce{H2O}$ and if this can be determined using the Nernst equation.

That is, obviously if $[\ce{Cl-}]>3.0\ \mathrm{mol/l}$ then it will oxidise, but if $[\ce{Cl-}]<1.0\ \mathrm{mol/l}$ it will not, since

\begin{alignat}{2} \ce{2H2O(l) \;&<=> 4H+(aq) + O2(g) +4e-}\quad&&E^\circ=-1.23\ \mathrm V\\[6pt] \ce{2Cl- (aq) \;&<=> Cl2(g) + 2e-}\quad&&E^\circ=-1.36\ \mathrm V \end{alignat}

However, in attempting to use the Nernst equation to determine the exact concentration at which $\ce{Cl-}$ will oxidise over $\ce{H2O}$, I get an obviously incorrect number,

\begin{align} 1.23\ \mathrm V&=E^\circ-\frac{2.569\times10^{-2}\ \mathrm V}{2}\ln\left( {\frac{\left[\ce{Cl- (aq)}\right]^2}{\left[\ce{Cl2(g)}\right]}}\right)\\ \frac{0.13\times2}{2.569\times10^{-2}}&=\ln\left[\ce{Cl- (aq)}\right]^2\\ \ln\left[\ce{Cl- (aq)}\right]&=\frac{0.13}{2.569\times10^{-2}}\\ \left[\ce{Cl- (aq)}\right]&=\mathrm e^\frac{0.13}{2.569\times10^{-2}}\\ &=157.643\gg3 \end{align}

In this above relationship, I have set the $E$ value to that of $\ce{H2O}$'s reduction potential to determine the concentration of chlorine ions required to get the same voltage. But obviously my number is too large!

• The problem with your approach is that the Nernst equation is defined: $$E=E^\circ - \dfrac{RT}{nF}\ln Q$$ and the reaction quotient $Q$ can only be defined for complete reactions, not just half reactions. You need to define a reduction half reaction for your system - $\left(\ce{2H+ + 2e- -> H2}\right)$ might be convenient. However, then you have additional species to worry about in $Q$. – Ben Norris May 17 '16 at 12:33
• You actually get the same result when you consider the reduction of water with each of the above-mentioned oxidation equations. Is taking a theoretical approach here invalid as it does not consider practical phenomena such as overvoltage, which would increase the 1.23 V value to make the required chlorine concentration smaller? – Pravin Singh May 18 '16 at 3:19