Tobias Fritz wrote:

>This is called economy of scale. We can now ask what happens when we try to make many pies---then how many eggs and lemons do we need per pie? This would be the yield, right?

This is a very interesting way to express the connection between yield and economies of scale.

In chemistry, there are two kinds of [yield](, actual and theoretical. Theoretical yield assumes 100% conversion of the limiting reagent whereas actual yield is smaller to which the degree depends on equilibrium constants, losses, production of by-products, etc. So if I translate my definition of yield to orders, theoretical yield will be more like a poset where you don't have any cycles and reactions are one way tickets (\\(a+b \rightarrow c\\))and actual yield will be more like a preorder where cycles are allowed and reactions or processes can go forward and backwards (\\(a+b \leftrightharpoons c\\) which leads to the end result at equilibrium \\(a+b \rightarrow a+b+c\\)).

For example, let's say you have the reaction \\(2H_2 + 1O_2 \rightarrow 2H_{2}O\\). Theoretically, 100% conversion then you will get \\(2H_{2}O\\). But in reality 100% conversion is never observed in chemistry (It'd be interesting to make a list of real processes that do undergo 100% conversion). Nature forces equilibrium and so if you let this reaction go to equilibrium, you will end up with \\(a H_2, b O_2, c H_{2}O\\) where a, b, c are dependent on thermodynamic conditions. You will always have some reagent leftover at the end even if its a microscopic amount.

Now this is speculation but if you make this into a batch process, you will get an accumulation of reagent after each cycle which can be recycled to make more product the following round. And like you said this will reduce the amount of reagent needed to make the same amount of product in subsequent cycles.

I am probably missing out on a lot the detail behind all of this and hope to learn more as the the story progresses :)