An electrolyte can be electrolysed by a voltage higher than the reverse reaction’s cell potential, while conducting a current in the process. But what happens at the electrodes when the applied voltage is below this cell potential, such as below 1.23 V for water or 4.07 V for NaCl? Does the reverse reaction occur simultaneously, or is the electrolyte unable to conduct a current with such a low voltage at all?
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Electrolysing water is NOT required for it to conduct electricity. Water ionizes into $\ce{H+}$ and $\ce{OH-}$. Pure water will contain $10^{-7}\ \mathrm{M}$ of either ion at room temperature at equilibrium. This will result in $18\ \mathrm{M\Omega\ cm}$ of resistivity. If and when potentials above the electrolysis potential is applied, the local pH around the electrodes will change and more ions will be created.
$\ce{NaCl}$ dissociates as soon as it is dissolved in water. The $\ce{Na+}$ and $\ce{Cl-}$ ions created in the solution carry current and increase the conductivity.
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$\begingroup$ I think the OP also wants to know what will happen to the water or NaCl outside the window. In short, in water, you'll evolve $\ce{H2}$ or $\ce{O2}$ at the electrodes, or $\ce{Na(s)}$ or $\ce{Cl2}$ with $\ce{NaCl}$ depending on oxidizing or reducing conditions. $\endgroup$ Apr 30 '15 at 15:56
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$\begingroup$ What happens when these ions meet the electrode? How does the current continue from the ions to the electrode if the potential is not enough to add/remove electrons from the ions? $\endgroup$ May 3 '15 at 23:38
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$\begingroup$ The concept appears related to chemistry.stackexchange.com/questions/278/… , but neither did answers under that question fully explain the very nature of current in electrolyte and particularly at the metal-electrolyte boundary. $\endgroup$ May 3 '15 at 23:44
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$\begingroup$ @kadabrium in that case the system will act as a pure capacitor. It will charge until the voltage is fully screened and then the current will drop to zero asymptotically. At DC voltage, there will not be a sustained current without redox reactions $\endgroup$ May 4 '15 at 5:23