In chapter 2 we saw that if we had –r_{A} as a function of X, [–r_{A}= f(X)] we could size many reactors and reactor sequences and systems.
How do we obtain –r_{A} = f(X)? We do this in two steps 1. Part 1  Chapter 3 Rate Law – Find the rate as a function of concentration, –r_{A} = k fn (C_{A}, C_{B} …) 2. Part 2  Chapter 4 Stoichiometry – Find the concentration as a function of conversion C_{A} = g(X) Combine Part 1 and Part 2 to get r_{A}=f(X) 
We shall set up Stoichiometric Tables using A as our basis of calculation
in the following reaction. We will use the stoichiometric tables to express
the concentration as a function of conversion. We will combine C_{i}
= f(X) with the appropriate rate law to obtain r_{A} = f(X).
Batch System Stoichiometric Table (p.42)  top 
Species  Symbol  Initial  Change  Remaining 

A  A  
B  B  
C  C  
D  D  
Inert  I  ________ 
  ____________ 
and 
Concentration  Batch System: 
Constant Volume Batch:
Note: if the reaction occurs in the liquid phase or if a gas phase reaction occurs in a rigid (e.g., steel) batch reactor 

Then  
etc. 
if _{ }then
Constant Volume Batch 
Flow System Stoichiometric Table (p.49)  top 
Species  Symbol  Reactor Feed  Change  Reactor Effluent 

A  A  
B  B  
C  C  
D  D  
Inert  I  ________ 
  ____________ 
Where:
and 
Concentration  Flow System: 
Liquid Phase Flow System: 
Flow Liquid Phase 
If the rate of reaction were r_{A} = kC_{A}C_{B} then
we would have
This
gives us r_{A} = f(X). Consequently, we can use the methods
discussed in Chapter 2 to size a large number of reactors, either alone
or in series.
etc. Again, these equations give us information about r_{A} = f(X), which we can use to size reactors.
then 
Flow Gas Phase 
with
Rate Law in terms of Partial Pressures
Calculating the equilibrium conversion for gas phase reaction
Consider the following elementary reaction with K_{C} and = 20 dm^{3}/mol and C_{A0} = 0.2 mol/dm^{3}. Pure A fed. Calculate the equilibrium conversion, X_{e}, for both a batch reactor and a flow reactor.
Solution
At equilibrium
Stoichiometry
Batch
Species Initial Change Remaining A N_{A0} N_{A0}X N_{A} = N_{A0}(1X) B 0 +N_{A0}X/2 N_{B} = N_{A0}X/2 N_{T0} = N_{A0} N_{T} = N_{A0}  N_{A0}X/2 Constant Volume V = V_{0}
Solving
Flow
Species Fed Change Remaining A F_{A0} F_{A0}X F_{A} = F _{A0}(1X) B 0 +F_{A0}X/2 F_{B} = F _{A0}X/2 F_{T0} = F _{A0} F_{T} = F _{A0}  F _{A0}X/2 Recall
The following humorous video on limiting reactants was made by Professor Lane's 2008 Chemical Reaction Engineering class at the University of Alabama, Tuscaloosa.
You may access the video by connecting to the internet and clicking the image below
^{*} All chapter references are for the 1st Edition of the text Essentials of Chemical Reaction Engineering .