How many atoms are represented in this equation?
The referenced atoms on both sides of the arrow are the exact same atoms? I like your thinking!

But, chemical equations do not refer to individual atoms.

The formula $\ce{Pb(NO3)2}$ can be read as "A molecule of this substance consists of six atoms of O, two atoms of N, ...". That is correct.

But the equation $\ce{Pb(NO3)2 + 2KI -&gt; PbI2 + 2KNO3}$, strictly speaking, does not talk about single molecules. The numbers (including the 1's that are nor written) are called "stoichiometric coefficients". The equation means: "Any number of $\ce{Pb(NO3)2}$ molecules react with the double amount of $\ce{KI}$ molecules to yield ...".

Wikipedia supports my view:


  In lay terms, the stoichiometric coefficient (or stoichiometric number in the IUPAC nomenclature) of any given component is the number of molecules that participate in the reaction as written.
  
  ...
  
  In more technically precise terms, ...


... the stoichiometric coefficient is the number of molecules divided by the progress variable or extent of reaction.


  ...
  
  The (dimensionless) "units" may be taken to be molecules or moles. Moles are most commonly used, but it is more suggestive to picture incremental chemical reactions in terms of molecules.