Figure 1. Schematic of a CSTR and a PFR in series

When reactors are connected in series, the effluent stream of the first reactor becomes the feed stream for the second reactor. Let's start with the definition for conversion:

We see that our two conversions, which correspond to the points marked in Figure 1 (above), are:

We can rearrange the equations to get our flow rates:

The general mole balance for a CSTR is:

We assume there are no spatial variations in the rate of reaction. At steady state:

After some rearranging:

Working in terms of conversion: F_A1 = F_A0(1-X₁)

Substituting into the equation:

See the PFR derivation, too?