What is the relationship between pressure and stoichiometry ratios
The actual reaction being discussed is $$\ce{3O2 -&gt; 2O3}$$

We also know from the gas law that $$\ce{PV=nRT}$$

In the current experiment the only things changing are the pressure and the number of moles; the volume and temperature remaining constant.  In this case the gas law simplifies to $$\ce{\Delta P = \Delta n}$$

Therefor, we know the change in moles for the overall reaction (-3+2=-1) is $\ce{\Delta n}$ and by the above stoichiometry the change in the moles of oxygen will be three times this amount or $\ce{3\Delta n}$ or $\ce{3  \Delta P}$ or $\ce{3x}$.