Lead-Acid Battery Electric Potential & Lead Sulfate

[isaaclimdc]

How does the amount of lead sulfate on the electrodes of a lead-acid battery affect its electric potential?

The discharge reaction of a lead-acid battery produces amorphous lead (II) sulfate at the electrodes. If I can work out the number of moles of lead sulfate formed, how can I interpret this in terms of electric potential? (i.e. more PbSO4, greater potential?

What about qualitatively and quantitatively?

Also, why does the distance between the electrodes of a battery affect its electric potential?

Can this be explained in terms of chemistry? I know it is because of the internal resistance of the cell, but that is more of a physics-related explanation (Ohm's Law)

Any help is much appreciated,
Isaac

 

[Borek]

Potential depends on the Nernst equation and ohmic drops. Try to write Nernst equation for the battery. Amount of the PbSO₄ on the electrode surface will not modify Nernst equation, it can increase ohmic drop, but your main source of ohmic drop is solution composition (hint: what is the main component of the electrolyte?)

Chemistry vs physics... we are getting dangerously close to the number of devils on the pinhead. There is a solution of strong electrolyte between lead plates. This solution has specific resistance that is a function of its composition. Resistance is then l*ro/A. You may call one part chemistry and second part physics if it makes you feel better, I see world described by universal laws

 

[isaaclimdc]

I have tried the Nernst equation and it does not seem to work in this case, since the number of moles of electrons transferred is the same no matter the quantities. I don't really understand the ohmic drop: how does it depend on the sulfate ions in the electrolyte?

Thanks for your help.

 

[Borek]

Show your Nernst equation, it works for sure.

In general conductivity of the solution is the higher, the higher the concentration of ions present.

 

[isaaclimdc]

Attached is my document for the Nernst equation.. I'm sorry I still don't get how all this applies! Just f.y.i, I'm doing this at high school IB level.. so I'm still quite inexperienced in this field.

Are you also saying that I cannot have a chemical explanation as to why the IR increases? Can I say something about the SO4 ions impeding the flow of current?

 

[Borek]

Take a look at what you have. n refers to the number of electrons exchanged in the redox reaction that takes place in the battery, and as such is constant throughout the process. So, the only thing that changes is the concentration (or more precisely activity) of the sulfuric acid (this can be more tricky, but for now let's leave it as it is). And that's correct - when battery is discharged, concentration of the acid is low and potential is low. When battery is charged concentrations of acid is high and potential is high - everything perfectly fits Nernst equation as written.

Chemical explanation... As I already told you - conductivity of the solution increases with the increase of ions concentrations. Think how it is related to the charged/uncharged battery.

 

[isaaclimdc]

Okay, I understand what you said about the Nernst Equation, but I think that does not link to the variables I'm testing. Well, I have two options: one is to look at the distance between the electrodes against the potential, and the other is to investigate the effects of sulfation on the cell.

Any ideas how the second one can be done given that I have experimentally determined the amount of lead sulphate present after discharge?

 

[isaaclimdc]

Please help me!

 

[Borek]

First option is relativelyy simple - resistance is l*ro/A (length, specific resistance, area). Specific resistance can be calculated if you know what ions in what concentrations are present in the solution. You will be probably able to Google something, I honestly don't know any website dealing with the subject, as all I need is in books behind my back. Unfortunately for you, most are in Polish. Start with terms like conductometry and solution resistance.

 

[isaaclimdc]

Is this the resistance and special resistance of the lead electrodes or the sulphuric acid? Also, how can I relate this to the distance between the electrodes?

Sorry if I'm not comprehending...

 

[Borek]

Both - resistance of electrode and resistance of solution are described the same way, just the specific resistance differs between lead and sulfuric acid solution. And resistance of battery is just a sum of resistances of electrodes and solution, as they are connected in serie.