# Reaction energy for a Lithium Iron Phosphate battery

• JulesP
JulesP
TL;DR Summary
Working out the specific charge and energy density for a LiFePO4 battery from the reaction equation
For my battery research, I am trying to determine the reaction (Gibbs) energy for what occurs in a LiFePO4 battery as it discharges.

For reference, I have used the approach that works for a Pb-Acid battery, as laid out below using molar masses, and am then trying to do the same for the LiFePO4 reaction.

Reaction:
Pb(s) + PbO2 (s) + 4H+ (aq) + 2SO4 2- (aq) → 2PbSO4 (s) + 2H2O (l) (𝜈e = 2)

∑I Mi = 1 x M(Pb) + 1 x M(PbO2) + 2 x M(H2SO4) = (207.2) + (239.2) + (2 x 98.1) = 642.6 g/mol

Specific Charge Density = q Pb-acid
= z F / ∑I Mi = 2 x 26.8 / 642.6 = 0.0834 Ah/g = 83.4 Ah/kg (where F is the Faraday constant)

Specific Energy Density = q x EOcell = 83.4 x 2.06 = 171.8 Wh/kg

For the Lithium Iron Phosphate, the overall reaction is:

LiFePO4 + 6xC ⇄ Li(1-x)FePO4 + Li(x)C6

∑I Mi = 1 x M(LiFePO4) + 6 x M(C) + 1 x M(Li(1-x)FePO4) + 1xM(Li(x)C6) = (158) + (36) + (??) + (??) = ??? g/mol

Clearly, due to the variable proportion ‘x’, it is hard to be precise about the molar masses of some of these components.

So my query is firstly, is the above breakdown correct and secondly, is there a better way to derive the specific charge and energy densities for the Lithium reaction, perhaps using the (Reaction energies of products) - (Reaction energies of the reactants)?

Can anyone please help me clarify the energetics of this reaction and the sources of any values used?

Thank you

Julian

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