# What defines a discharged battery?

In the case of an AA Alkaline battery, what actually happens inside the battery once it is fully discharged? What components of the battery change as we use it?

• I think perhaps discharged is a highly relative term in reference to the surrounding chemical environment. – glucose Apr 19 at 15:12

what actually happens inside the battery once it is fully discharged?

Alkaline batteries use the exchange of electrons from zinc to manganese dioxide to produce electricity

$$\begin{array}{rcl}\\ \ce{Zn (s) +2 OH- (aq)}& \ce{->}& \ce{ZnO (s) + H2O (l) + 2 e-}\qquad \text{(anode)}\\ \text{(high potential anode)}\quad \ce{2e-}&\ce{->[load][\ ]}&\ce{2e-}\quad\text{(low potential cathode)}\\ \ce{2MnO2 (s)+ 2e- + H2O (l)} &\ce{->}&\ce{Mn2O3 (s) + OH- (aq)}\qquad \quad\text{(cathode)}\\ \end{array}$$

typically a battery voltage would decline according to:

$$\mathscr{E} = \mathscr{E}^{\circ} - \frac{RT}{nF}\ln Q$$

but in alkaline batteries all of the products and reactants are solids, which without going into heavy detail of the thermochemistry means that $$Q = 1$$ thus $$\frac{RT}{nF}\ln Q = 0$$ which means cell potential remains fairly constant ($$\mathscr{E} = \mathscr{E}^{\circ}$$). But this is only in theory as we can see alkaline batteries do lose voltage:

This is partly because the internal resistance of the cell will increase with time meaning that for a given external load the total load will increase with time reducing current and apparent voltage. But even with no load voltage drops, the the zinc oxide will dissolve in alkaline medium meaning the reactions depart from ideal equations:

$$\ce{ZnO (s) ->[+ H2O (l)] Zn(OH)2 ->[+2OH- (aq)] [Zn(OH)4]^2-}$$

this is not to say that $$\mathscr{E} = \mathscr{E}^{\circ} - \frac{RT}{nF}\ln Q$$ is an unreliable equation, but it does not account well for the complexity of the system and does not apply well to alkaline batteries. Additionally it cannot explain the vertical slope of the discharge curve. What can explain the vertical slope is that once all of either zinc or manganese dioxide is consumed, there is no more matterial to react and the battery is considered fully discharged.

A discharged battery means that cell reaction has achieved equilibrium. When this system is at equilibrium no (useful) work can be done by the battery. It cannot drive or pump electrons in the circuit. In other words, people say that its Gibbs free energy is zero.

• I think you can improve this answer by incorporating the Nernst equation. – Zhe Apr 19 at 14:05
• Good idea Zhe. I find MathJax difficult. Feel free to edit. – M. Farooq Apr 19 at 14:07
• I don't quite feel comfortable editing to say something different, but I will add an addendum as a separate answer. – Zhe Apr 19 at 15:00
• @M.Farooq You cannot rely on other's edits and avoid proper markup forever. You'll just have to bite a bullet and get to know formatting of scientific documents. This may also help you to get started with $\mathrm{\LaTeX}$ when you start publishing your work. Please visit this page, this page and this one on how to format your future posts better with MathJax and Markdown. – andselisk Apr 19 at 15:09
• It depends on the field. What is your field of specialization? MS Word has a decent professional equation editor. Most of good science was also done when we had typewriters :-). LaTex is not the end of the world. I also review articles for ACS, Elsevier, Springer etc. Most articles are written in Word, and then converted into pdf. Anyway, this is just a distraction for the OP. – M. Farooq Apr 19 at 15:45

To extend @M.Farooq's answer, let's look at this a slightly different way.

From the Nernst equation:

$$\mathscr{E} = \mathscr{E}^{\circ} - \frac{RT}{nF}\ln Q$$

As the reaction progresses, the value of $$Q$$, the reaction quotient, increases because product concentrations are higher and reactant concentrations are lower. As a result, the cell potential $$\mathscr{E}$$ decreases.

When $$\mathscr{E}$$ reaches zero, then battery is fully discharged. There is no potential to push electrons through any circuit.

• AFAIK there are only two accepted notations for the standard state: uppercase plimsoll "$^⦵$" and a circle "°". "∅" looks like an "empty set symbol" and doesn't make any sense here in this context. – andselisk Apr 19 at 15:08
• I reverted to using \varnothing because there is no simple LaTeX symbol and I had various instances where the plimsoll unicode was not supported. I'll use circ instead, though to be fair, the empty set symbol (and that's what I'm using) is just a rotated plimsoll. @andselisk – Zhe Apr 19 at 15:28
• May I ask you where the "⦵" Unicode symbol isn't supported? I've been using it thorough with MathJax and XeLaTeX for the past couple of years and it always worked for me just fine. – andselisk Apr 19 at 15:31
• It appears as a small rectangle on this Android tablet. – badjohn Apr 19 at 16:07
• @badjohn Interesting, your Android must be lacking fonts with the plimsoll symbol. Personally, I've never experienced this issue on any of the Android devices (I used AOSP since version 4 and later LineageOS), but it's good to know some vendors might cut off support for special characters. – andselisk Apr 19 at 16:32