CHEE 221: Chemical Processes and Systems

Module 3. Material Balances with Reaction 

Part a: Stoichiometry and Methodologies

(Felder & Rousseau Ch 4.6‐4.8not 4.6c )

CHEE 221 2

Material Balances on Reactive Processes

What does a reaction do to the general balance equation?

Accumulation = In – Out + Generation – Consumption

0 = In – Out + Generation – Consumption

For a reactive process at steady‐state, the general balance equation becomes:  

The stoichiometric equation of the reaction imposes constraints on the relative amounts of reactants and products in the input and output streams.

Accounts for material produced or consumed within the system

CHEE 221 3

Material Balances on Reactive Processes

What quantities are conserved?

Type of Balance Without Rxn With Rxn

Total mass Total moles Mass of a chemical compound Moles of a chemical compound Mass of an atomic species Moles of an atomic species

CHEE 221 4

Stoichiometry Basics

Stoichiometry – theory of the proportions in which chemical species combinewith one another in a reaction

Stoichiometric Equation – an equation that relates the relative number ofmolecules or moles of reactants and products (but not mass!) that participatein a chemical reaction. To be valid, the equation must be balanced.For example, are the following stoichiometric equations balanced?

C2H5OH + O2 CO2 + H2O

(NH4)2Cr2O7  Cr2O3 + N2 + H2O

2 SO2 + O2 2 SO3

Stoichiometry imposes additional constraints to balances Defines relationship between generation of products and consumption of 

reactants Always in terms of molar units (not mass)

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Stoichiometry Basics… cont’d

Stoichiometric Coefficients (i) – values preceding each molecular species (i)in a balanced stoichiometric equation. Values are defined to be positive forproducts and negative for reactants. For the reaction,

Stoichiometric Ratio – ratio of stoichiometric coefficients in a balancedstoichiometric equation. For the above reaction for example,

Two reactants, A and B, are in stoichiometric proportion if the ratio (molesof A present)/(moles of B present) equals their stoichiometric ratiodetermined from the balanced stoichiometric equation.

2 1 2 322 SOOSO ;;

2 SO2 + O2 2 SO3 

consumedO mol 1generated SO mol 2

2

3

F&R Ch 4.6a

CHEE 221 6

Limiting and Excess Reactants

If the reactants are not present in stoichiometric proportions, the reactantthat would be completely consumed if a reaction went to completion isknown as the limiting reactant (LR). The other reactant(s) are termedexcess reactant(s).

The fractional excess of the reactant is the ratio of the excess to the stoichiometric requirement:

where (nA)feed is the number of moles of an excess reactant, A, present in the feed to a reactor and (nA)stoich is the stoichiometric requirement of A, or the amount needed to react completely with the limiting reactant, even if the reaction does not go to completion.Percentage excess is 100 times the fractional excess.

stoichA

stoichAfeedA

stoichA

stoichAfeedA )( - )( or )( - )( Aof excess fractional)()( n

nnn

nn

F&R Ch 4.6b

CHEE 221 7

Fractional Conversion

Chemical reactions do not occur instantaneously, but often proceed quite slowly.Therefore, it is often not practical to design a reactor for complete conversion of thelimiting reactant. Instead, the reactant is separated from the reactor outlet streamand recycled back to the reactor inlet. The fractional conversion of a reactant is theratio of the amount reacted to the amount fed:

If no reactant is specified, then fractional conversion refers to the limiting reactant(LR). This is usually the case.

Fractional conversion is unitless. The percentage conversion is 100 × fA.     The fraction unreacted (i.e., in exit stream) is 1 – fA.  

“Fractional Conversion” can be considered as a process constraint (extra equation), asit describes how the process is operating (i.e. how much rxn did take place?).

fedA

reactedAA n

nf

fedA

reactedAA n

nf

or

CHEE 221 8

Identifying the Limiting Reactant

1. Balance the stoichiometric equation2. Compare the ratios 

,

,

stoichy

x

feedy

x

stoichy

x

feedy

x

nn

nn

nn

nn

stoichy

x

feedy

x

nn

nn

versus

If,

If, reactant x is the limiting reactant

reactant x is not the limiting reactant

CHEE 221 9

Example 1: Butane Combustion

The complete combustion of butane can be described as:C4H10 +  O2             CO2 + H2O

For a continuous flow process at steady state with a feed of 100 moles ofbutane per second, and 1000 moles of oxygen per second, determine theoverall flowrate (mol/s) and molar composition of the outlet stream, if thefractional conversion of the limiting reactant in the burner is 70%

Always make sure that the stoichiometric equation is balanced!

CHEE 221 10

Extent of Reaction‐How to Handle Different Stoichiometric Ratios

The extent of reaction is a quantity that characterizes the reaction andcan significantly simplify calculations.

For a continuous process at steady‐state:   

where and are the molar flow rates of species i in the feed and outletstreams, respectively (out = in +/‐ conversion).

For a batch process:  

where       and     are the initial and final molar amounts of species i, respectively.   The extent of reaction                        has the same units as n (or   ).  Every reaction has a single, unique value of .

iii nn 0

iii nn 0

)( or n

0in in

0in in

)( or

F&R Ch 4.6b

How do these equations arisefrom the general M.B.?

CHEE 221 11

Reactor Types

Wk 5 pre‐tutorial exercise: CSTRs (continuous stirred tank reactors) andPFRs (plug flow reactors) are two of the more common continuous reactorconfigurations.

Explain the basic differences (simple diagrams may help), and state theapplication advantages of each.

F&R Encyclopedia of Chemical Engineering Equipment(textbook website)

CHEE 221 12

Example 2

The biological removal of nitrogen (in the form of nitrate) from wastewater isaccomplished by anaerobic bacteria in which methanol is added as a carbon(energy) source for the cells according to the reaction shown below:

6 NO3 + 5 CH3OH 5 CO2 + 3N2 + 7 H2O + 6 OH

If 100 g methanol is added to a water source containing 50 g of nitrate,determine which is the limiting reactant and the % excess of the non‐limitingreactant. For a fractional conversion of 30% of the limiting reactant,determine the composition of the molecular species at the end of thereaction.

CHEE 221 13

Example 3: F&R Ex 4.6‐1 (Acrylonitrile Production)

Acrylonitrile is produced in the reaction of propylene, ammonia, and oxygen:

The feed contains 10.0 mole% propylene, 12.0 mole% ammonia, and 78.0mole% air. A fractional conversion of 30.0% of the limiting reactant isachieved. Taking 100 mol of feed as a basis, determine which reactant islimiting, the percentage by which each of the other reactants is in excess, andthe molar amounts of all product gas constituents.

Try this on your own , then see the textbook for the solution!  

OH 3NHCO 23NHHC 2332363

CHEE 221 14

Multiple Reactions

Generally, the synthesis of chemical products do not involve a single reactionbut rather multiple reactions. The goal is to maximize the production of thedesirable product and minimize the production of unwanted byproducts. Forexample, ethylene is produced by the dehydrogenation of ethane:

C2H6 C2H4 + H2

C2H6 + H2 2CH4

C2H4 + C2H6 C3H6 + CH4

This leads to the following definitions:  

mols of desired product formedYieldmaximum mols of product formed (if there were

no side rxns and limiting reactant reacted completely)

undesirable side reactions

formed product undesired of molsformed product desired of molsySelectivit

F&R Ch 4.6d

CHEE 221 15

Multiple Reactions – Extent of Reaction

The extent of reaction method can also be applied to multiple reactions, witheach reaction having its own extent.

For a single reaction:

If a set of reactions takes place in a batch or continuous steady‐state reactor,we can write:

where, ij is the stoichiometric coefficient of substance i in reaction jj  is the extent of reaction for reaction j.

( ) ( )i out i fed

i

n n

( ) ( )i out i fed in n

1( ) ( )

rxnN

i out i fed ij jj

n n

CHEE 221 16

Balances on Reactive Species

Systems that involve chemical reactions can be analyzed using one of three possible methods:

(a) Molecular species balances – the approach always used fornonreactive systems, but approach is more cumbersome for reactiveprocesses. Balances must include generation and consumptionterms for each species.

(b) Atomic species (C, H, O, etc.) balances – straightforward method.Balances are of the form input=output since atomic species cannotbe created or destroyed.

(c) Extents of reaction (Molecular balances)

Each approach provides the same results, but one method maybe more convenient than the other for a given calculation, soyou should be comfortable with both methods.

F&R Ch 4.7

CHEE 221 17

Example 4: Ethylene Oxide

The ethylene oxide reactant used in the production of ethylene glycol is madeby the partial oxidation of ethylene with excess oxygen over a silver catalyst.The primary reaction is:

C2H4 + O2 C2H4O

Unfortunately some of the ethylene also undergoes complete oxidation to CO2and water according to:

C2H4 + O2 CO2 + H2O

For a feed flow of 1000 moles/h containing 10% (mole basis) ethylene, and anethylene conversion of 25%, a yield of 8% ethylene oxide is obtained.Determine the flowrates of the species leaving the reactor.

Solve using both “extents of reaction” and “atom balance” methodology

CHEE 221 18

DFA for Reactive Processes

Molecular Species Balances and Extent of Reaction:  ndf = nunknowns + n independent chemical reactions  – nindependent molecular species balances      

– n other equations relating variables

Atomic Species Balances:ndf = nunknowns – nindependent atomic species balances 

– nmolecular balances on independent nonreactive species  – nother equations relating variables

Note: F&R develops a separate DFA equation for molecular species balancesand extent of reaction technique, but they are the same.

F&R gives several good examples of these methods in sections 4.7 a‐e; READ THESE SECTIONS CAREFULLY.

CHEE 221 19

Notes on Independent Chemical Reactions

Chemical reactions are independent if the stoichiometric equation of any oneof them cannot be obtained by adding and subtracting multiples of thestoichiometric equations of others.

Consider the following equations:

These three reactions are not all independent, since (3) = (1) + 2 x (2)

A 2B (1)

B C (2)

A 2C (3)

CHEE 221 20

Remember about Independent Species Balances!

Generally, there are n balances for n independent species.  

BUT…

If 2 species are in the same ratio to each other wherever they appear in theprocess, balances on these species will not be independent equations.

Example: Air is 3.76 mol N2/mol O2, but only if neither one reacts (e.g. whenevaporating a volatile compound in Air). If one of them does participate in areaction (e.g. O2 in a combustion reaction), then these compounds will not bein the same proportion in different streams.

CHEE 221 21

MB and Reactive Processes: Solution Methodology

What quantities are conserved?

Type of Balance Without Rxn With Rxn

Total mass Total moles Mass of a chemical compound Moles of a chemical compound Mass of an atomic species Moles of an atomic species

CHEE 221 22

Example 5: F&R Ex 4.6‐3

The reactionsC2H6 C2H4 + H2

C2H6 + H2 CH4

take place in a continuous reactor at steady‐state. The feed contains 85.0mole% ethane (C2H6) and the balance inerts (I). The fractional conversion ofethane is 0.501, and the fractional yield of ethylene is 0.471. Calculate themolar composition of the product gas and the selectivity of ethylene tomethane production.

Try this on your own, then see the textbook for the solution!