Rate equations for heterogeneous reactions combining linear and nonlinear expressions

1. SUBJECT : CHEMICAL REACTION ENGINEERING-II
SEM :- 7
GOVERNMENT ENGINEERING
COLLEGE, BHARUCH
•VAGADIA HARDIK (140140105018)
•PATEL RASHMIN (140140105045)
•PATEL RONAK (140140105046)
•RAJ PRIYANK (140140105050)
•MODI SAGAR (140140105057)
TOPIC : RATE EQUATIONS FOR HETEROGENEOUS
REACTIONS COMBINING LINEAR AND
NON- LINEAR RATE EXPRESSIONS

2. • Introduction to Heterogeneous Reactions
• Rate equations for Heterogeneous Reactions
• Overall rate for Linear Process
• Overall rate for Non-Linear Process
INDEX

3. Introduction to Heterogeneous
Reactions
• Heterogeneous reactions are those in which more than one
phase is involved to proceed
• A heterogeneous reaction involves substances which exist in
different phases and reaction usually takes place at an
interphase between the phases or in one of the phases.
• Heterogeneous reactions may be catalytic or non-Catalytic.
• In catalytic heterogeneous reactions, the catalyst is a solid.

4. Some examples of catalytic Heterogeneous
reactions :
• Gas-solid reactions: synthesis of ammonia, catalytic cracking of
crude oil, Oxidation of SO2 to SO3 using V2O5 catalyst in H2SO4
manufacture.
• Gas-solid-liquid reactions: Catalytic oxidation of liquid
hydrocarbons using air or O2
• to acetic acid, catalytic hydrogenation of acetone to propanol.

5. Some examples of non-catalytic Heterogeneous reactions:
• Gas-solid reactions: roasting of sulphide ores, combustion of coal.
• Gas-liquid reactions: chlorination of liquid aromatic hydrocarbons
using chlorine gas, purification of gas mixtures, manufacture of
ammonium nitrate by absorption of ammonia in aqueous nitric
acid.
• Liquid-liquid reactions: nitration of organic compounds with
aqueous nitric acid, formation of soaps by the action of aqueous
alkalies on fats or fatty acids.
• Liquid-solid reactions: production of acetylene by the action of
water on calcium carbide.

6. • Heterogeneous reactions have one thing in common: Before a
chemical reaction can occur, the reactants from the bulk of one
phase must be transported to the interface between the phases
or into the bulk of other phase.
• Following factors are considered for heterogeneous systems:
1. The modification of the rate equation resulting from the mass
transfer between phases.
2. The contacting patterns for the reacting phases.

7. Rate equations for heterogeneous
reactions:
• A heterogeneous reaction takes place in number of steps- one
or several chemical steps are always accompanied by steps
that are physical in nature.
• These physical steps are associated with the transport of
matter from one phase to other.
• The concentration of matter in the bulk of one phase and at
the interface is different and the concentration difference is
the driving force for these physical transport process.

8. • Heterogeneous reactions are treated as consisting of a series of
steps and parallel steps.
• In heterogeneous system, the overall rate equation in general
will consist mass transfer terms in addition to the usual kinetic
term.
• If a heterogeneous reaction consists of parallel steps, then the
overall rate is equal to the sum of all individual rates:

9. • If on the other hand, a heterogeneous reaction consist of
several consecutive steps i. e., overall change results from a
number of series steps, then at steady-state conditions, the
rates of the individual steps in series are all the same and equal
to the overall rate of reaction:

10. • when rates of the various steps are to be compared or
combined, then they must be expressed identically.
• Thus, when mass transfer takes, the rate is defined in terms of
molar flux (moles per unit time per unit surface), the rate of
chemical reaction should also be based on unit surface area
instead on unit volume.

12. • Consider steps in series. In general, if all the steps are linear in
concentration, then it is easy to combine them. But if any step is
non-linear it will be complicated. Therefore we may try to bypass
this non-linear step.
• Moreover, as we usually do not know the concentration at
intermediate positions, we have to eliminate these concentrations
and express the overall rate in terms of overall concentration
difference.

13. OVERALL RATE FOR LINEAR PROCESS
• Dilute A diffuses through a stagnant film onto a plane surface
consisting of B, reacts there to produce R which diffuses back
into the mainstream.
• The rate expression for the L/S reaction,
A(liquid) + B(solid) R(liquid)
• Which takes place on flat surface as shown in fig. below


14. • By diffusion, the flux of A to the surface is
• Reaction is first order with respect to A, so based on
unit surface
• At steady state the flow rate to the surface is equal
to the reaction rate at the surface (step in series). So
• Now from first two equation

15. • For which
• Replacing third equation either in first or in second and then
eliminates which cannot be measured, giving
• This result shows that and additive resistance. It so
happens that addition of resistance to obtain on overall
resistance is permissible only when the rate is linear function
of driving force and when the processes occur in series.
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16. OVERALL RATE FOR NON-LINEAR PROCESS