Li_{1 + y} CoO₂ is an anode for lithium batteries. Cobalt is present as a mixture of Co(III) and Co(II). Most preparations also contain inert lithium salts and moisture. To find the stoichiometry, Co was measured by atomic absorption and its average oxidation state was measured by a potentiometric tritration. For the titration, 25.00 mg of solid were dissolved under N₂ in 5.000 mL containing 0.100 0 M Fe²⁺ in 6 M H₂S_O4 plus 6 M H₃PO₄ to give a clear pink solution:

Co₃+ + Fe²⁺ → CO²⁺ + Fe³⁺

Unreacted Fe²⁺ required 3.228 mL of 0.015 93 M K₂Cr₂O₇ for complete titration.

(a) How many mmol of Co³+ are contained in 25.00 mg of the material?

(b) Atomic absorption found 56.4 wt% Co in the solid. What is the average oxidation state of Co?

(c) Find y in the formula Li_{1 + y} CoO2.

(d) What is the theoretical quotient wt% Li/wt% Co in the solid? The observed quotient, after washing away inert lithium salts, was 0.138 8 ± 0.000 6. Is the observed quotient consistent with the average cobalt oxidation state?