[ajax0604]

This is a question from my Chemistry textbook:
A particular lithium cell has an operating voltage of 3.5 V. The overall reaction taking place when discharging is as shown by this equation: LiC₆ + CoO₂  C₆ + LiCoO₂. Calculate the increase in mass of solid LiCoO₂ if the cell delivers a 0.60 A current for 2.5 hours operating at 65% efficiency. Assume energy is lost as heat. 

I thought that if a galvanic cell operates at an efficiency less than 100%, the increase in mass at the cathode would be less than the amount predicted by Faraday's laws. Below are my calculations:
Q = It = 0.60 x 2.5 x 60 x 60 = 5400C
n(e-) = 5400 / 96500 = 0.056mol
n(LiCoO₂) = 0.056mol
m(LiCoO₂) = 0.056x 97.8 = 5.47g

m(LiCoO₂) with 65% efficiency = 0.65 x 5.47g = 3.6g


However, the solutions give a different answer. Instead of multiplying the mass of 5.47g by 0.65, they multiply it by 100/65 to give 8.4g. This is their reasoning - "only 65% of the chemical energy released by the reaction is converted into electrical energy, so the reaction will have progressed "further" than expected, to produce the stated amount of electricity, so more reactant would be used and more solid LiCoO₂ produced than if it was running at 100%".

The part regarding more reactant being consumed to produce the current of 0.60A sort of makes sense but wouldn't that "extra" chemical energy just be converted to heat energy and not lead to any extra deposition? If so, wouldn't the amount of LiCoO₂ deposited be simply equal to that predicted by Faraday's laws?

Thank you.

[Hunter2]

No, because its an galvanic cell and  not an electrolytical cell. If efficiency is less then 100% then more product has to be produced to gain the required current. The overcurrent is converted in heat in the Batterie.
The chemical equation  has to take place. Mass of product  cause the current.

If it would be electrolytical cell then you are right. Less product and energy is converted to heat. Current cause mass of product.