permanganate ion oxidizes hydrogen peroxide to oxygen gas and Mn2+ in acidic solution

balance this equation: MnO4- + H2O2 yield Mn2+ + O2

this is what i got
16H+ + 2MnO4- + 5H2O2 yield 2Mn2+ + 8H2O + 5O2 + 10H+

all the atoms and charges are balanced but why did my professor say its wrong

change the 16H+ to 6H+, and zero out the 10H+ on the right, then check it again.

Your professor said it's wrong because the equation you wrote does not satisfy the law of conservation of mass. While the atoms and charges are balanced, there are an incorrect number of water molecules and hydrogen ions on each side of the equation.

To correctly balance the equation, you need to ensure that the number of atoms of each element is the same on both sides and that the charges are balanced as well. Here is the balanced equation:

2MnO4- + 3H2O2 + 2H+ -> 2Mn2+ + 4H2O + 3O2

To explain how to balance the equation step by step:

1. Start by balancing the atoms of oxygen by placing a coefficient of 3 in front of H2O2 to give you 3 O atoms.
2. Next, balance the atoms of hydrogen by placing a coefficient of 2 in front of H2O2, giving you 6 H atoms.
3. Now, balance the atoms of manganese by placing a coefficient of 2 in front of MnO4-, which gives you 2 Mn atoms.
4. At this point, the oxygen and hydrogen atoms are balanced on both sides, but the charges are not. To balance the charges, add 2 hydrogen ions (H+) to the reactant side.
5. Finally, balance the number of water molecules by placing a coefficient of 4 in front of H2O on the product side.

The balanced equation now satisfies the conservation of mass and charge, so it correctly represents the reaction.