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For the olivine cathode material LiFePO₄, assuming all the lithium is extracted and reinserted via the Fe²⁺/Fe³⁺ reaction, which value is closest to the theoretical capacity? Take the formula weight of LiFePO₄ as 157.8 g/mol, the Faraday constant as 96485 C/mol and 1 mAh = 3.6 C.

  1. AAbout 170 mAh/g
  2. BAbout 85 mAh/g
  3. CAbout 340 mAh/g
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Answer: A. About 170 mAh/g

One mole of Li⁺ leaves one mole of LiFePO₄ and Fe²⁺ is oxidized to Fe³⁺, so one mole of electrons is transferred. The theoretical capacity is Q = nF/(3.6M) = 1 × 96485 / (3.6 × 157.8) ≈ 170 mAh/g. About 340 mAh/g counts two electrons in the reaction, but the change from Fe²⁺ to Fe³⁺ involves one electron. About 85 mAh/g divides by 2 somewhere along the way. LiFePO₄ can in practice deliver around 160 mAh/g, close to the theoretical value, but its average voltage of about 3.4 V is relatively low, so its energy per mass is smaller than that of layered oxide cathodes.

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