Chapter 4: Stoichiometry

Rationale For Chapter 4

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)

Stoichiometry

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

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Species	Symbol	Initial	Change	Remaining
A	A
B	B
C	C
D	D
Inert	I	________	-------	____________

Where:

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

and we have -r_A=f(x)

Writing -r_A solely as a function of X

Flow System Stoichiometric Table

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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

etc.

If the rate of reaction were -r_A = kC_AC_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.

Gas Phase Flow System:

etc.

Again, these equations give us information about -r_A = f(X), which we can use to size reactors.

For example if the gas phase reaction has the rate law

then

Flow Gas Phase

with

Rate Law in terms of Partial Pressures

Stoichiometry Table for Conversion

Oxidation of Naphthalene to Phtahalic Anhydride

Critical Thinking Questions for the Oxidation of Naphthalene

Production of Nitric Acid

Expressing a Catalytic Rate Law in Terms of Conversion

Calculating the equilibrium conversion for gas phase reaction

Consider the following elementary reaction with K_C and = 20 dm³/mol and C_A0 = 0.2 mol/dm³. 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_A0X N_A = N_A0(1-X)

B 0 +N_A0X/2 N_B = N_A0X/2

N_T0 = N_A0 N_T = N_A0 - N_A0X/2

Constant Volume V = V₀

Solving

Flow

Species Fed Change Remaining

A F_A0 -F_A0X F_A = F _A0(1-X)

B 0 +F_A0X/2 F_B = F _A0X/2

F_T0 = F _A0 F_T = F _A0 - F _A0X/2

Recall