# More than one way of balancing a chemical equation

My textbook had this question on balancing chemical reactions

Ozone reacts with nitric oxide to give nitrogen dioxide and oxygen gas

Here's how I balanced it: $$\ce{O3 + NO -> NO2 + O2}$$

However I realised that the equation is also balanced if I write it as: $$\ce{2O3 + 4NO -> 4NO2 + O2}$$

and when it is written as: $$\ce{3O3 + NO -> NO2 + 4O2}$$

This seems wrong as I am sure that there cannot be more than one way of balancing a reaction but I do not have a satisfactory explanation. What is going wrong here?

## 1 Answer

This happens when you have a sum of two (or more) independent reactions. You can balance each one, and then add them together in an arbitrary proportion. People usually run into this when trying to come up with an equation for combustion of gunpowder, where the oxidation of carbon and oxidation of sulfur are pretty much independent.

Now, in your case the reactions are: $$\ce{2O3 -> 3O2}\tag A$$ and $$\ce{2NO + O2 -> 2NO2}\tag B$$ Your first reaction is a combination of ${1\over2}A+{1\over2}B$, the second is $A+2B$, and the third is ${3\over2}A+{1\over2}B$. There are infinitely many possible combinations.

Ozone, being an extremely powerful oxidant, is known to participate in certain reactions where it spends one atom of oxygen and the rest falls off as the less reactive $\ce {O2}$, but this is not the case here. $\ce {O2}$ reacts with $\ce {NO}$ instantly, as well as $\ce {O3}$.

• I am still confused. You said that I could add the equations in any 'arbitrary' proportion. That would deem the second and third questions correct, wouldn't it? – Nishant Kumar Gupta Dec 14 '16 at 17:52
• Sorry, I didn't get it. What questions? You've balanced the reaction in three different ways. Yes, each of them is correct. – Ivan Neretin Dec 14 '16 at 18:13
• Sorry. I meant the second and third eqautions – Nishant Kumar Gupta Dec 15 '16 at 3:43
• Like I said, they are as good as the first one. – Ivan Neretin Dec 15 '16 at 4:52