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Rate of Rxn

The reaction rate is the rate at which a species loses its chemical identity per unit volume. The rate of a reaction canbe expressed as the rate of disappearance of a reactant or as the rate of appearance of a product. Consider species A:

A B

rA= the rate of formation of species A per unit volume-rA= the rate of a disappearance of species A per unit volumerB= the rate of formation of species B per unit volume

Example:

A B

If B is being created at a rate of 0.2 moles per decimeter cubed per second, ie, the rate of formation of B is,

rB= 0.2 mole/dm3/s

Then A is disappearing at the same rate:

-rA= 0.2 mole/dm3/s

the rate of formation of A is

rA= -0.2 mole/dm3/s

For a catalytic reaction, we refer to -rA', which is the rate of disappearance of species A on a per mass of catalyst basis.

NOTE: dCA/dt is not the rate of reaction but it is simply mole balance that is ONLY valid for a constant volume batchsystem.

The Convention for Rates of Reaction

Consider the reaction

in which the rate of disappearance of A is 5 moles of A per dm3per second at the start of the reaction.

At the start of the reaction

(a) What is -rA?(b) What is the rate of formation of B?(c) What is the rate of formation of C?(d) What is the rate of disappearance of C?(e) What is the rate of formation of A, rA?

(f) What is -rB?

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Answers

(a) -rAis the rate of disappearance of A is

(b) For every one mole of A that disappears, two moles of B disappear. Reactant B is a is disappearing twice as fast

as reactant. i.e., A.-rB= 2 x -rA= 10 moles/dm3/s

Multiplying by minus one (-1) we get the rate of formation of B

B is being used up therefore its rate of formation is a negative number.

(c) C is a product that is being formed three times as fast as A is disappearing

Because C is a product is being formed, its rate of formation is positive.

(d) The rate of disappearance of C is -rC. Therefore we multiply the rate of formation of C, rC, by minus one (-1) toget

Because C is a product, its rate of disappearance, -rC, is a negative number.

(e) A is a reactant that is being used up therefore its rate of formation is negative

(f) -rBis the rate of disappearance of B

Summary

Rate of disappearance of A = -rA= 5 mole/dm3/sRate of disappearance of B = -rB= 10 mole/dm3/sRate of disappearance of C = -rC= -15 mole/dm3/sRate of formation of A = rA= -5 mole/dm3/sRate of formation of B = rB= -10 mole/dm3/sRate of formation of C = rC= 15 mole/dm3/s

For reactantsthe rate of disappearanceis a positive (+) number.Forproductsthe (-) rate of disappearanceis a negative number because they are being formed and not disappearing.

For reactantsthe rate offormationis a negative (-) number because they are disappearing and not being formed.Forproductsthe rate offormationis a positive (+) number.

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Relative Rates of Reaction

The Reaction:

is carried out in a reactor. If at a particular point, the rate of disappearance of A is 10 mol/dm3

/s, what are the rates of B and C?

Solution

The rate of disappearance of A, -ra, is

or the rate of formation of species A is

The relative rates are

Species B

The rate of formation of species B is

The rate of disappearance of B, -rb ,is

Species C

The rate of formation of C, -rc, is

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Power Law Model

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Rate Constant, k

k is the specific reaction rate (constant) and is given by the Arrhenius Equation:

Where:

Where:E = activation energy (cal/mol)

R = gas constant (cal/mol*K)T = temperature (K)

A = frequency factor (units ofA, and k, depend on overall

reaction order)

The larger the activation energy, the more temperature sensitive k and thus the reaction rate.

You can tell the overall reaction order by the units of k

CA -rA Reaction Order Rate Law k

(mol/dm ) (mol/dm *s) zero -rA= k (mol/dm *s)

(mol/dm ) (mol/dm *s) 1st -rA= kCA s-

(mol/dm ) (mol/dm *s) 2nd -rA= kCA (dm /mol*s)

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Elementary Rate Laws

A reactionfollowsan elementary rate lawif and only if the (iff)stoichiometric coefficients are the same as the individual

reaction order of each species. For the reaction in the previous example( ),

the rate law would be:

if 2NO+O2 2NO2 then -rNO = kNO (CNO)2

CO2 if elementary!

Self Test

Rate Laws

What is the reaction rate law for the reaction:

if the reaction is elementary?What is rB?What is rC?Calculate the rates of A, B, and C in a CSTR where the concentrations are CA= 1.5 mol/dm3, CB= 9mol/dm3and kA= 2 (dm3/mol)(1/2)(1/s).

Solution

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Let's calculate the rate if,

Then

Non-Elementary Rate Laws

Example: If the rate law for the non-elementary reaction

is found to be

then the reaction is said to be 2nd order in A, 1st order in B, and 3rd order overall.

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Reversible Reactions

The net rate of formation of any species is equal to its rate of formation in the forward reaction plus itsrate of formation in the reverse reaction:

ratenet

= rateforward

+ ratereverse

At equilibrium, ratenet 0 and the rate law must reduce to an equation that is thermodynamicallyconsistent with the equilibrium constant for the reaction.

Example: Consider the exothermic, heterogeneous reaction

At low temperature, the rate law for the disappearance of A is

At high temperature, the exothermic reaction is significantly reversible:

What is the corresponding rate law? Let's see.

If the rate of formation of A for the forward reaction (A + B C) is

then we need to assume a form of the rate law for the reverse reaction that satisfies the equilibrium

condition. If we assume the rate law for the reverse reaction (C A + B) is

then:

and:

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Deriving -rA:

The forward rate is:

And the reverse rate law is:

The net rate for species A is the sum of the forward and reverse rate laws:

Substituting for rforand rrev:

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Self Test

Rate Law for Reversible Reactions

Write the rate law for the elementary reaction

HerekfAandkrAare the forward and reverse specific reaction rates both defined with respect to A.

Hint

What is the net rate of reaction?

(1)

(2)

Solution

Write the rate law for the elementary reaction

Here kfAand krAare the forward and reverse specific reaction rates both defined with respect to

A.

(1)

(2)

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At equilibrium;

Examples of Rate Laws

First Order Reactions

(1)

(2)

(3)

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(4)

While overall this reaction is first order, it is 1/3 order in ethylene and 2/3 order in oxygen.

(5)

(6)

(7)

Where and

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Second Order Reactions

(1)

This reaction is first order in ONCB, first order in ammonia and overall second order.

(2)

This reaction is first order in CNBr, first order in CH3NH2and overall second order.

(3)

with KC= 1.08 and

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Nonelementary Reactions

(1)

Cumene Benzene Proplene

(C) (B) (P)

(2)