Are the units of mole of oxygen molecules the same with the units of mole of nitrogen molecules?
It is a good question which has already been somewhat addressed in the 1880s. This &quot;field&quot; was called quantity calculus. Calculus here is not the integration / differentiation, but rather the Latin calculus implying a method of calculation.
There is a very nice article &quot;Quantity Calculus: Unambiguous Designation of Units in Graphs and Tables&quot; by Mary Anne White in the Journal of Chemical Education. Please read this if you are seriously interested. Search on Google Scholar and it is free to download from there.
In quantity calculus Each physical quantity as the product of a numerical value and a unit:
physical quantity = numerical value × unit
This approach was introduced by British scientists and many leading physicists used it. Now there is there is nothing less or nothing more. Therefore your ambiguity arises from introducing another factor such as &quot;oxygen&quot; or &quot;nitrogen&quot;. The unit mol does not know whether it belongs to oxygen or nitrogen.
As explained in the comments, suppose we write L symbolizing the height of a tree, then I can only write, L = 10 m. For mathematical purposes, I will not introduce &quot;tree&quot; anywhere in this equation. The tree is already incorporated in L (in your mind) but not in the mathematical equation. One can also write L/m =10. Now you have a pure number on both sides.
For fun: Think about taking the derivatives or log of quantities with units. What is the unit then?