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Sparked off by Is sea water more conductive than pure water because "electrical current is transported by the ions in solution"?

This question really belongs on chemistry.SE, which is still in area 51.

While answering this question, I realised that there was a flaw in the standard logic for these situations.

Let's take $NaNO_3$ solution in water, and compare it with pure water (same size cell). (I'm not taking $NaCl$ for a reason*).

In both cases, we have nearly the same(~7) PH and pOH, right? So concentrations of $H^+$ and $OH^-$ are the same, and thus contribution of these ions to the overall conductance/conductivity is the same. These ions both migrate to the electrodes, get reduces/oxidised, and emit/absorb electrons, facilitating passage of current.

OK. Now, let's consider the $Na^+$ and $NO_3^-$ ions. Yes, they migrate as well. But, they don't get redoxed (the water ions are preferentially redoxed). So, all I see happening here is a buildup of charges on either electrode, which will stop once equilibrium is attained. This buildup of charges cannot migrate to the outside circuit like a capacitor, as it cannot translate to electrons. But, these ions still make a significant contribution to the net conductance by Kohlrausch law.

So how does a general good neutral electrolyte help water conduct electricity? I feel that it should conduct electricity at the same rate as water; but by Kohlrausch law, it clearly doesn't. And anyways, I've always heard that impure water conducts electricity better.

*$NaCl$ has the issue of overvoltage of $O_2$, causing oxidation to of $Cl_2$, which complicates the situation. The $Cl^-$, being able to get oxidised, facilitate current and thus don't serve as a good example here.

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On a related note, please consider supporting the area51 chemistry proposal. –  Manishearth Mar 4 '12 at 3:13
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FYI, "This question really belongs on chemistry.SE" means "This question is off topic," and in general we (mods) will act accordingly. However, I happen to disagree that this particular question really belongs on a hypothetical chemistry site; yes, it could go there, but it's also physics-related enough that it's appropriate here. (Conductance = E&M, equilibrium = stat mech) I just wanted to mention (in case you didn't know) that the presence or absence of another SE site on a particular topic has no bearing on whether a question on that topic is appropriate here or not. –  David Z Mar 4 '12 at 4:06
    
@DavidZaslavsky Yep, I know, otherwise I wouldn't have asked it here(I wasn't too sure of its on-topicness, so I kept the hatnote). But, if there was a chemistry site, wouldn't this have been migrated? (its on-topic, but I doubt conductance of solutions is dealt with in physics as much as chemistry--so its more appropriate there). I do realise that the meaning of on-topic won't change, though. Unless an overlapping site is created (I think that theoreticalphysics.SE must've changed the definition of on topic, right?) –  Manishearth Mar 4 '12 at 4:19
    
Nah, I probably wouldn't have migrated it even if there was a chemistry site. First we decide if the question is on topic or not, and only if it is off topic do we consider migration. The existence of theoreticalphysics.SE doesn't change the scope of what is on topic on this site at all. –  David Z Mar 4 '12 at 7:52
    
What happens when the $Na^+$ ion meets an electron at the elektrode? And in my opinion, this is a very relevant physics question! –  Bernhard Mar 4 '12 at 8:07
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1 Answer 1

if the electrolyte is not removed you will indeed get a buildup that will stop conduction (assuming there is no conventive or other mixing within your cell). However bearing in mind that 1 amp is $10^{-5}$ (ish) moles of electrons per second it will take a while.

In your example sodium gets reduced at the cathode then reacts with the water to produce hydrogen and sodium hydroxide. If it was silver nitrate the silver would be plated on the cathode and removed from solution.

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Aah right. 1/96500 tiny.. Yeah, I know about the plating. A quick and dirty order of magnitude calculation reveals that it will take $\approx 10^7 s$ which can range from a few months to a few years. Any idea how the charge distributes itself? Will there be a charge gradient, or will almost all of it stick to the plates? –  Manishearth Mar 4 '12 at 8:36
    
That's a good question, and I must admit I have no idea how the charge would be distributed. Google, Google, Google, bing! www2.bren.ucsb.edu/~dturney/port/papers/… –  John Rennie Mar 4 '12 at 10:36
    
If the Na+ and NO3- ions aren't going to be redoxed, won't they just diffuse back throughout the water, and serve as a catalyst for further conduction? They're not all going to stick around the plates. –  Peter Shor Mar 4 '12 at 13:33
    
I just realised that this doesn't answer the full question--By kohlrausch law, the nitrate contributes significantly to conductivity. But here, I can't see why.. I see how sodium contributes. :/ –  Manishearth May 6 '12 at 15:59
    
Rejected! How will I live with the shame :-) Actually I don't see the problem. Both Na and NO3 are mobile and contribute to the conductivity, though the NO3 is a lot less mobile than Na because it's bigger. Anyhow, what does this have to do with the charge separation in an unstirred tank? Can you elaborate on what you see as the problem? –  John Rennie May 6 '12 at 17:40
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