which is the correct balanced equation for a given titration process, (a) or (b)?

a) 6H+ + 2MnO4- + 3H2O2 -> 4O2 + 2Mn2+ + 6H2O
b) 6H+ + 2MnO4- + 5H2O2 -> 5O2 + 2Mn2+ + 8H2O

Process:
Make a solution in a 100mL volumetric flask using 1g of NaBO3*4H2O, 20mL of 1M H2SO4, and distilled water. Using this solution take 10mL of it and place in a beaker and add 20mL of 1M H2SO4. Now take the 30mL solution beaker and titrate with 0.0103M of KMnO4 to the endpoint. (endpoint found to be ~29mL)The H2O2 come from NaBO3*4H2O in acidic solution.

**I think the answer is (b) because this is an acidic solution, but I'm not sure. Can you please tell me the error of my ways if I am incorrect?
Also, is there a way to find this out using calculations or something? (stoichiometry perhaps or another way like?) I think knowing the theory behind this would be helpful in the future. please help me, I'd love your feedback.
** the oxygen is evolved from the H2O2, yes?

To determine the correct balanced equation for the titration process, we can consider the stoichiometry of the reaction and the oxidation state changes of the elements involved.

In this titration process, we are adding KMnO4 (potassium permanganate) to H2O2 (hydrogen peroxide) in an acidic solution. The KMnO4 acts as an oxidizing agent, and the H2O2 is being oxidized to O2 gas. The balanced equation should reflect the stoichiometry of this reaction.

Let's analyze the equation options provided:

a) 6H+ + 2MnO4- + 3H2O2 -> 4O2 + 2Mn2+ + 6H2O
b) 6H+ + 2MnO4- + 5H2O2 -> 5O2 + 2Mn2+ + 8H2O

Both equations have 6H+ and 2MnO4- on the left side, which is correct. However, when considering the oxidation of H2O2 to O2, we can observe that for every 2 moles of H2O2, we should be getting 1 mole of O2. In equation (a), it shows that for 3 moles of H2O2, we get 4 moles of O2, which is incorrect. Therefore, option (b) is the correct balanced equation:

6H+ + 2MnO4- + 5H2O2 -> 5O2 + 2Mn2+ + 8H2O

Regarding your question about how to find the correct balanced equation using calculations, stoichiometry can indeed be used. By determining the moles of KMnO4 and H2O2 used in the reaction, and comparing them to the moles of O2 produced, you can determine the stoichiometric coefficients and balance the equation accordingly.

Finally, you are correct in your understanding that the oxygen gas (O2) is evolved from the H2O2 in this reaction. The H2O2 is being oxidized, causing the release of oxygen gas.