Two possible reactions of MnO₄ with H₂O₂ to produce O₂ and Mn₂ are

(a) Complete the half-reactions for both schemes by adding e^-, H₂O, and H^- and write a balanced net equation for each scheme.

(b) Sodium peroxyborate tetrahydrate, NaBO₃•4H₂O (FM 153.86), produces H₂O₂ when dissolved in acid: BO₃ +  2H₂O  → H₂O₂  H₂BO^-₃ . To decide whether Scheme 1 or Scheme 2 occurs, students at the U.S. Naval Academy 30 weighed 1.023 g NaBO₃•4H₂O into a 100-mL volumetric flask, added 20 mL of 1 M H₂SO₄, and diluted to the mark with H₂O. Then they titrated 10.00 mL of this solution with 0.010 46 M KMnO₄ until the first pale pink color persisted. How many mL of KMnO₄ are required in Scheme 1 and in Scheme 2? 

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Scheme Scheme 2: Mn02 Mn2