Cell notation for the lead-acid battery

Reactions for the lead acid battery are: 


$$
\begin{array}{}
\text{Oxidation}&\ce {Pb(s) + HSO4^-(l) &-> PbSO4(s) + H+(l) + 2e-}\\
\text{Reduction}&\ce{PbO2 + HSO4^-(l) + 3H+(l) + 2e- &-> PbSO4(s) + 2H2O}\\
\text{Total reaction}&\ce{Pb(s) + PbO2(s) +2HSO4^- +2H+ &-> PbSO4 + 2H2O}\\
\end{array}
$$ 


What will be the cell notation for this battery? My attempt:$$\ce{Pb(s), Pb^2+(s)| HSO4^-(l)| PbO2(s), Pb^2+(s),Pb(s)}$$


The things that I have in mind,


1. In both sides the electrode material is $\ce{Pb(s)}$
2. Separate every element that is in the same phase with a comma
3. Separate every element with different phases with a single bar
4. Separate the two half reactions with a single bar (as I find no salt bridge here)


I am having a tough time learning cell notation. Anyways this was a challenging one for me and I tried my best shot. I am really not sure whether everything is right or not. So please identify my mistakes and show me the right way to do it. 




There are a couple of things wrong here. First off, your final reaction is **unbalanced**. Once you've fixed the balancing, read the other mistakes:


1. The ions do not exist in the **liquid** state! They are solvated/hydrated by the solvent. Since the solvent is water here, we'll say that the ions are in the **aqueous** **(aq)** phase instead.
2. While there is certainly no salt bridge here, there is still an **electrolyte** - an aqueous solution of sulphuric acid. Hence, you must mention it in your cell notation, between the anode and the cathode.
3. The $\ce{PbSO4}$ formed at the anode is in **solid state**. Hence, writing it as $\ce{Pb^2+(s)}$ is incorrect, as it is *not* dissociated into the ions $\ce{Pb^2+}$ and $\ce{SO4^2-}$.


With all these corrections, your final, correct cell representation should be:



> 
>  $$\small{\ce{Pb(s), HSO4^-(aq) | PbSO4(s), H+ | H2SO4 ($\pu{x~M}$) | PbO2(s), HSO4-(aq), H+(aq) | PbSO4(s)}}$$
> 
> 
> 




---


Some websites (like [KhanAcademy](https://youtu.be/PQ48N5jaG2w)) and texts (NCERT 12), cite the lead-acid battery reaction as this instead:


$$
\begin{array}{}
\text{Oxidation}&\ce {Pb(s) + SO4^2-(aq) &-> PbSO4(s) + 2e-}\\
\text{Reduction}&\ce{PbO2 + SO4^2-(aq) + 4H+(aq) + 2e- &-> PbSO4(s) + 2H2O(l)}\\
\text{Total reaction}&\ce{Pb(s) + PbO2(s) +2SO4^2(aq)- + 4H+(aq) &-> 2PbSO4(s) + 2H2O(l)}\\
\end{array}
$$ 


assuming the bisulphite ion to be further ionized. The cell notation in this case would then be:



> 
>  $$\small{\ce{Pb(s), SO4^2-(aq) | PbSO4(s) | H2SO4 ($\pu{x~M}$) | PbO2(s), SO4^2-(aq), H+(aq) | PbSO4(s)}}$$
> 
> 
> 


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