# 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?

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 $\ce {O3}$.