The promised balanced reaction is as follows:

1. 3CH2CH2 + 2KMnO4 + H2O = 2MnO2 + 3CH3CHO + 2KOH
2. 3CH3CHO + 2KMnO4 + H2O = 3CH3COOH + 2MnO2 + 2KOH
3. 3CH3COOH + 8KMnO4 = 6CO2 + 8MnO2 + 8KOH + 2H2O

Combining equations 1-3, we get:

4. 3CH2CH2 + 12KMnO4 = 12MnO2 + 12KOH + 6CO2

Even if the reaction does not go all the way through to the carbon dioxide-producing step, many of the intermediate products formed either become irreversibly bound to the media or act as reactants themselves. Such is the case of the potassium hydroxide (KOH) formed in equation 1 and 2. The KOH will react with the acetic acid formed in equation 2 to produce the potassium acetate salt (KCOOCH3) through a simple acid-base neutralization reaction. This is shown below.

5. CH3COOH + KOH = KCOCH3 + H2O

Combining equations 1, 2, and 5 we get:

6. 3CH2CH2 + 4KMnO4 = 3KCOOCH3 + 4MnO2 + KOH + H2O