# Mass balance of a recycle stream

I'm a chemical engineer student and I have just started to learn about mass balance without reaction.

This is my problem -

I want to find Out the mass composition and mass flowrate of stream Y (the stream into the divider).

How am I suppose to do a mass balance around process 1 (involving the divider, before process 2) ?

From the problem , I don't know any of the compositions of the recycle 1 , I only know the flow rate .

This only tells me that the flowrate into process 1 is $50000+ 1500$ . With this alone, how do I find mass composition and mass flowrate of stream Y

In generel for N species you have N mass balances. So in your case 2. Also mass is conserced ( other than moles when it comes to chemical reaction). So you definitely know that the mass flow rate of Y is 1500. Also have in mind that the divider doesn't change the composition of your species and you also know the composition of product 1 ( have in mind that all species together sum up to 1). I think from this point on it's not so hard to find out what Y is.

Let $$F$$ be the mass rate of feed 1, $$x$$ be the mass fraction of $$N_2$$ in feed 1, $$y$$ the mass fraction of $$N_2$$ in stream $$Y$$ and $$R$$ the recycle rate.

From conservation of mass over process 1:

$$F + R = F_Y + R$$

the flow rate $$F_Y$$ of stream $$Y$$ is equal to the feed rate $$F$$, i.e. $$F_Y = F = 1500$$. From an $$N_2$$ component balance we deduce:

$$Fx + Ry = (F + R)y = Fy + Ry$$

So:

$$Fx = Fy$$

And so we conclude $$x = y$$ and so the composition in $$Y$$ is the same as in the feed $$F$$. We could have concluded this directly since it is given that no reaction occurs in process 1.