Question

I have a Lab assignment that requires the synthesis of carboxylic acid and our final product is Benzoic Acid. The following equation was provided:
C7H8 + KMnO4 ---> MnO2
1) KMnO4, OH-, heat
2) H3O+
We were asked to balance the equation including the by-products. I was able to come up with but I got stuck and am unable to balance the K:
C7H8 + 2KMnO4 ---> C7H6O2 + 2MnO2 + H2O + KOH
The second equation given was:
KMnO4 + NaHSO3 ---> MnO2
with OH- and H2O above and below the arrow. I was able to obtain the following and wanted to know if it was correct:
4KMnO4 + 6NaHSO3 ---> 4MnO2 + H2SO4 + 2H2O + 2K2SO4 + 3NA2SO4
C7H8 + 2KMnO4 ---> C7H6O2 + 2MnO2 + 2KOH will balance that one.

I would balance the second one this way.
2KMnO4 + NaOH + 3NaHSO3 ==> 2MnO2 + 2Na2SO4 + K2SO4 + 2H2O
Your equation balances in every respect but it doesn't use the OH^-. If the OH is omitted, as you did, then KMnO4 doesn't go to MnO2 but to Mn^2+

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