# CSTR properties - What happens to conversion of products if I change the reactor size?

For example, initially this reactor is having a 2nd order reaction of $$-ra=kaCa^2$$ and it has a fractional conversion of 50% in a CSTR.

I replace it with something 1/6 as large. What happens to the conversion assuming everything else stays the same

Through theory, I know the conversion will decrease as its a smaller CSTR, but is there a way to calculate it using the formula - $$fa = Fao - Fa1 / Fao$$?

• Are the volumetric flow rates in and out to the reactor the same? – Jeffrey J Weimer Dec 12 '18 at 4:52
• @JeffreyJWeimer yes – mutu mumu Dec 12 '18 at 5:03
• What do you mean by "fa"? fa has one meaning I am clear on... – Solar Mike Dec 12 '18 at 7:05
• @SolarMike fa is the fractional conversion, Fao is the Initial Molar flowrate of reactant A – mutu mumu Dec 12 '18 at 7:07

The mole balance on component A through the reactor balances flow rates out and in with rate of change.

$$\dot{n}_{Ao} - \dot{n}_{Ai} = \frac{dn_A}{dt}$$

The left side can be written in terms of overall conversion for a consumption reaction.

$$f_A \equiv \frac{\dot{n}_{Ai} - \dot{n}_{Ao}}{\dot{n}_{Ai}}$$

The right side can be rewritten as a rate expression on concentration $$dn_A / dt = V dC_A/dt$$. Use an empirical rate law expression for the rate. Assume the reaction consumes component A. In a CSTR, the outlet concentration is the reactor concentration. Combined we obtain

$$f_A\ \dot{n}_{Ai} = V\ k\ C_{Ao}^n$$

When you want to decrease the volume of the reactor $$V$$, you must change these factors with these consequences:

• Decrease the volumetric flow rate of A in to keep the overall conversion $$f_A$$ constant.

• Decrease the overall conversion $$f_A$$ to keep the same volumetric flow rate of A in.

• Increase the concentration of A in the outlet for the same overall conversion and volumetric flow rate of A in.