Chromium has been investigated as a coating for steel cans. The thickness of the chromium film is determined by dissolving a sample of a can in acid and oxidizing the resulting Cr³⁺ to Cr₂O₇ ^2- with the peroxydisulfate ion:

S₂O₈ ^2-(aq) + Cr³⁺(aq) + H₂O(l) → Cr₂O₇ ^2-(aq) + SO₄ ^2-(aq) + H⁺(aq)_(Unbalanced)

After removal of unreacted S₂O₈^2-, an excess of ferrous ammonium sulfate [Fe(NH₄)₂(SO₄) ₂ ? 6H₂O] is added, reacting with Cr₂O₇ ^2- produced from the first reaction. The unreacted Fe²⁺ from the excess ferrous ammonium sulfate is titrated with a separate K₂Cr₂O₇ solution. The reaction is: 

H⁺(aq) + Fe²⁺(aq) + Cr₂O₇ ^2-(aq) → Fe³⁺(aq) + Cr³⁺(aq) + H₂O(l) (Unbalanced)

a. Write balanced chemical equations for the two reactions.

b. In one analysis, a 40.0- cm2 sample of a chromium-plated can was treated according to this procedure. After dissolution and removal of excess S₂O₈ ^2-, 3.000 g of Fe(NH₄) ₂(SO₄) ₂ ? 6H₂O was added. It took 8.58 mL of 0.0520 M K₂Cr₂O₇ solution to completely react with the excess Fe²⁺. Calculate the thickness of the chromium film on the can. (The density of chromium is 7.+9 g/ cm3.)