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+

To balance the given equations, you need to ensure that the number of each type of atom is the same on both sides of the equation.

Let's begin by balancing the first equation:

C7H8 + 2KMnO4 ---> C7H6O2 + 2MnO2 + H2O + KOH

Start by balancing the carbon atoms. There are 7 carbon atoms on the left side and 7 carbon atoms on the right side, so carbon is already balanced.

Next, balance the hydrogen atoms. There are 8 hydrogen atoms on the left side and 6 hydrogen atoms on the right side. To balance hydrogen, you need to add 2 more hydrogen atoms to the right side. This can be done by inserting an H2O molecule on the right side of the equation:

C7H8 + 2KMnO4 ---> C7H6O2 + 2MnO2 + H2O + KOH

Now let's balance the oxygen atoms. On the left side, there are 4 oxygen atoms from the KMnO4 molecules. The benzoic acid (C7H6O2) contains 4 oxygen atoms, so that is balanced. However, on the right side, you only have 2 oxygen atoms from the H2O molecule. To balance oxygen, you need to add 2 more oxygen atoms. This can be done by adding another H2O molecule:

C7H8 + 2KMnO4 ---> C7H6O2 + 2MnO2 + 2H2O + KOH

Now, let's balance the potassium (K) atoms. On the left side, there are 2 potassium atoms from the 2 KMnO4 molecules. To balance this, you need to add 2 KOH molecules to the right side:

C7H8 + 2KMnO4 ---> C7H6O2 + 2MnO2 + 2H2O + 2KOH

Finally, the equation is balanced.

Moving on to the second equation:

KMnO4 + NaHSO3 ---> MnO2 + H2O

This equation is already balanced. You have 1 potassium (K) atom on the left side and 1 potassium (K) atom on the right side. However, if you want to include the by-products, you can balance them as follows:

4KMnO4 + 6NaHSO3 ---> 4MnO2 + H2SO4 + 2H2O + 2K2SO4 + 3Na2SO4

This equation includes the formation of sulfuric acid (H2SO4), potassium sulfate (K2SO4), and sodium sulfate (Na2SO4) as by-products.

So, your balanced equations are:

1) C7H8 + 2KMnO4 ---> C7H6O2 + 2MnO2 + 2H2O + 2KOH

2) 4KMnO4 + 6NaHSO3 ---> 4MnO2 + H2SO4 + 2H2O + 2K2SO4 + 3Na2SO4