2013 EnerSys Genesis NP18-12B KOP Battery/FIRST Choice Weak?

[simpsonboy77]

Originally Posted by Ether

Does anyone know: What causes the sharp bend in the curve at 11 volts? What is going on inside the battery at that point?

I pulled off my chem book from the shelf so I don't give out false information. I am also going to assume a semi-ideal battery, basically I'm going to assume the concentration gradient of everything in the electrolyte will be constant. This is the reason you can overcharge a cell and also over discharge a cell.

If the reaction is moving from left to right side then it is discharging

Positive electrode: PbO2 + H2SO4 + 2H+ + 2e- <> PbSO4  2H2O

Negative electrode: Pb + H2SO4 <> PbSO4 + 2H+ + 2e-   

Overall cell reaction: PbO2 + Pb + 2H2SO4 <> 2PbSO4 + 2H2O

H+ is notation for the hydronium ion, its just hard to type it in here. H30+(aq) e- is for an electron or the hydroxide ion OH-(aq)

If the cell is fully charged then the plates are lead and the electrolyte is sulfuric acid. As the cell becomes more discharged the concentration of H2SO4 will decrease, and the concentration of lead sulfate will increase.

We can apply the Nernst equation.
V(cell) = V(standard cell potential) - RT/(2F)*ln(Q)
V(cell) is the current cell voltage
V(standard cell potential) is how much voltage the cell gives nominally, ic 2 for SLA, 1.6 for Li-ion etc.
R is the gas constant
T is temperature
2 is the number of electrons transferred between anode and cathode per reaction.
F is faraday's constant
Q is very important

Q is the reaction quotient, basically its the concentration of sulfuric acid divided by the concentration of lead sulfate. This is simplified from the actual definition because we can ignore other terms as they are not aqueous.

ln(Q) = ln(concentration of sulfuric acid) - ln(concentration of lead sulfate)

What makes batteries really nice is that the sum of the number of lead sulfate and sulfuric acid molecules must be constant. This is assuming the battery isn't venting a whole lot, leaking, or lead sulfate drops to the bottom or significant sulfation on the plates. For the short term these are fine assumptions, and honestly I don't know if I could take all of these into account properly.

Lets say the battery starts with N moles molecules of sulfuric acid and lead sulfate.
N//volume of electrolyte is concentration of sulfuric acid + lead sulfate

ln(Q) = ln(concentration of sulfuric acid) - ln(N/volume of electrolyte - concentration of sulfuric acid)

ln(Q) = ln(concentration of sulfuric acid/(N/volume of electrolyte - concentration of sulfuric acid))
This is going to relate DIRECTLY to how much charge the battery moves.
charge = current times Time. By discharging it reduces the concentration of sulfuric acid in a linear rate, yet the cell voltage is going to be reduced in a logarithmic fashion.

V(cell) = V(standard cell potential) - RT/(2F)*ln(Q)