The answer is given but I'd like to understand how one would get to the answer.

Find the limiting reactant.

Explanation:

Using the ratio in the chemical formula, find the limiting reactant.

The second equation results in less mol of MnO₃, therefore it is the limiting reactant and changing the moles of O₂ to moles of MnO₃ which will give the theoretical yield which is 1.55 mol MnO₃.

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hope i !