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# Rate of a Chemical Reaction and Collision Theory

## Rate of a Chemical reaction :-

Some reactions such as ionic reactions occurs very fast , for example – precipitation of silver chloride occurs instantaneously by mixing of aqueous solutions of Silver nitrate and Sodium chloride .

Some reactions are very slow , for example – rusting of iron in the presence of air and moisture . Also there are reactions like inversion of Cane sugar and hydrolysis of starch , which proceed with a moderate speed or rate .

The rate of a Chemical reaction can be defined as the change in concentration of a reactant or product in unit time .

It can be expressed in in term of of –

1 . The rate of decrease in concentration of any one of the reactants .

2 . The rate of increase in concentration of any one of the products .

Consider a hypothetical reaction assuming that the volume of the system remains constant .

Reactant ( R ) → Product ( P )

One mole of the reactant produces one mole of the product .

If [ R ]₁ and [ P ]₁ are the concentrations of R and P respectively at time t₁ and [ R2 ]₂ and [ P2 ]₂ are their concentrations at time t₂ then

∆t = t₂ – t₁

∆[ R ] = [ R ]₂ – [ R ]₁

∆[ P ] = [ P ]₂ – [ P ]₁

The square brackets in the above expressions are used in express molar concentration .

Rate of disappearance of R = – decrease in concentration of R / time taken

= ∆ [ R ] / ∆t

Rate of appearance of P = + increase in concentration of P / time taken

= ∆ [ P ] / ∆t

Thus , Rate of a Chemical Reaction = – ∆ [ R ] / ∆t = + ∆ [ P ] / ∆t

### Average rate of a Chemical reaction :-

Average rate depends upon the change in concentration of reactants or products and time taken for that change to occur .

The average rate falls from 1.90 x 10⁻⁴ mol L⁻¹ s⁻¹ to 0.4 x 10⁻⁴ mol L⁻¹ s⁻¹ . Average rate cannot be used to predict the rate of a reaction at a particular instant as it would be constant for the time interval for which it is calculated .

The rate at a particular moment of time we determine the instantaneous rate . It is obtained at the smallest time interval

i . e . ∆t → 0

rᵢ = – d[ R ] / ∆t = + d[ P ] / dt

Or tanθ = rᵢ

The instantaneous rate of a Chemical reaction is the slope of the line ( the tangent to Curve ) at any time dt .

Average rate of reaction

rₐ = – ∆[ R ] / ∆t = ∆[ P ] / dt

#### Units of rate of a chemical reaction :-

Units of rate are concentration time ⁻¹

Example – If concentration is in mole L⁻¹ and time is in second then the units will be mole L⁻¹ s⁻¹

When the concentration of gases is expressed in terms of their partial pressures , then the units of the rate of equation will be atm s⁻¹

• Now consider a reaction

Hg ( l ) + Cl₂ ( g ) → HgCl₂ ( s )

Where stoichiometric coefficients of the reactants and products are same , then rate of the reaction is given as

Rate of reaction = – ∆ [ Hg ] / ∆t = – [ Cl₂ ] / ∆t

= ∆ [ HgCl₂ ] / ∆t

In the following reaction two moles of HI decomposed to produce one mole each of H₂ and I₂

2 HI ( g ) → H₂ ( g ) + I₂ ( g )

Since the rate of consumption of HI is twice the rate of formation of H₂ or I₂ to make them equal , the term ∆ [ HI ] is divided by 2 .

The rate of this reaction is given by

Rate of reaction = – 1 / 2 ∆ [ HI ] / ∆t = ∆ [ H₂ ] / ∆t = ∆ [ I₂ ] / ∆t

• Similarly for the reaction –

5 Br⁻ ( aq ) + BrO₃⁻ ( aq ) + 6 H⁺ ( aq ) →3 Br₂ ( aq ) + 3 H₂O ( l )

Rate of a Chemical reaction = – 1 / 5 ∆ [ Br⁻ ] / ∆t = ∆ [ BrO₃⁻ ] / ∆t = – 1 / 6 ∆ [ H⁺ ] / ∆t = 1 / 3 ∆ [ Br₂ ] / ∆t

= 1 / 3 ∆ [ H₂O ] / ∆t

• For a gaseous reaction at constant temperature , concentration is directly proportional to the partial pressure of a species and hence , rate can also be expressed as rate of change in partial pressure of the reactant or the product .

### Factors influencing Rate of a Chemical reaction :-

Rate of a Chemical reaction depends upon the experimental conditions such as concentration of reactants ( pressure in case of gases ) , temperature and catalyst .

#### Dependence of rate on Concentration :-

The rate of a chemical reaction at given temperature many dependent on the concentration of one or more reactants or products .The rate of a Chemical reaction decreases with the the passage of time as the concentration of reactants decrease . Conversely rate generally increase when reactant concentration increase . So , rate of reaction depends upon the concentration of reactants .

It is known as Rate Law .

Consider a General reaction

aA + bB → cC + dD

Where a , b , c and d are the stoichiometric coefficients of reactants and products .

The rate expression for this reaction is

Rate α [ A ]ˣ [ B ]ʸ

Or Rate = K [ A ]ˣ [ B ]ʸ

Where K is rate constant .

Or

– d[ R ] / dt = K [ A ]ˣ [ B ]ʸ

Thus , rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some Power , which may or may not be same as the stoichiometric coefficient of the reacting species in a balanced Chemical equation .

Example – 2NO ( g ) + O₂ ( g ) → 2NO₂ ( g )

The rate equation for this reaction will be

Rate = K [ NO ]² [ O₂ ]

The differential form of this rate expression is given as

• – d[ R ] / dt = K [ NO ]² [ O₂ ]

#### Temperature dependence of the Rate of a Chemical reaction :-

Most of the Chemical reactions are accelerated by increase in temperature .

Example – In decomposition of N₂O₅ ,the time taken for half of the original amount of material to decompose is 12 minutes at 50⁰C , 5 hours at 25⁰C and 10 days at 0⁰C .

It has been found that for a Chemical reaction with rise in temperature by 10⁰C , the rate constant is nearly double .

• The temperature dependence of the rate of a Chemical reaction can be accurately explained by Arrhenius equation

Where A is the Arrhenius factor for frequency factor . It is a constant specific to a particular reaction . R is gas constant and Eₐ is activation energy measured in joules per mole .

It can be understood clearly using the following simple reaction –

H₂ ( g ) + l₂ ( g ) → 2HI ( g )

According to Arrhenius , this reaction can take place only when a molecule of hydrogen and a molecule of iodine collide to form and unstable intermediate .

It exists for a very short time and then breaks up to form two molecules of hydrogen iodide .

The energy required to on this intermediate called activated complex ( C ) is known as activation energy Ea .

The above figure is obtained by plotting potential energy Vs reaction Coordinate .

Reaction coordinate represents the profile of energy change when reactants change into products .

• some energy is released when the complex decomposes to form products . So , the final heat of the reaction depends upon the nature of reactants and products .
• All the molecules in the reacting species do not have the same kinetic energy . According to Boltzmann and James clerk Maxwell , the distribution of kinetic energy may be described by plotting the fraction of molecules with a given kinetic energy ( E ) vs kinetic energy .

#### Effect of Catalyst :-

A catalyst is a substance which increases the rate of a Chemical reaction without itself undergoing any permanent chemical change .

Example – KClO₃ + MnO₂ → 2KCl + 3O₂

Where MnO₂ is a catalyst . The word catalyst should not be used when the added substance reduces the rate of a Chemical reaction .

• A small amount of the catalyst can catalyse a large amount of reactants . A Catalyst does not alter Gibs energy , ∆ G of a reaction . It Catalyses spontaneous reaction only .
• It is believed that the catalyst provides an alternate pathway for reaction mechanism by reducing the activation energy between reactants and products and hence lowering the potential energy barrier .
• It is clear from Arrhenius equation that lower the value of activation energy faster will be the rate of reaction .

### Molecularity of a reaction :-

The number of reacting species ( atoms , ions or molecules ) taking part in an elementary reaction , which must collide simultaneously in order to bring about a chemical reaction is called molecularity of a reaction .

Examples –

1 . N₂O₅ → N₂O₄ + 1 / 2 O₂

Order = 1

Molecularity = 1

2 . 2HI → H₂ + I₂

Order = 2

Molecularity = 2

3 . 2NO + O₂ → 2NO₂

Order = 3

Molecularity = 3

• Unimolecular reaction involves one reacting species , biomolecular reaction involves simultaneously collision between two species .

Trimolecular or tetramolecular reaction involves simultaneous collision between three reacting species .

## Order of Reaction :-

The sum of powers of the concentration of the reactants in the rate law expression is called the order of that chemical reaction .

Example – Rate of reaction = K [ A ]ˣ [ B ]ʸ

Here x and y represent the order with respect to the reactants A and B respectively . Sum of these components i . e . x + y give the overall order of a reaction .

Order of a Chemical reaction can be 0, 1, 2, 3 and even a fraction . A Zero order reaction means that the rate of a Chemical reaction is in dependence of the concentration of reactants .

## Collision theory of Chemical Reactions :-

Collision theory states that for a Chemical reaction to occur , the reacting particles must collide with one another . It is based on kinetic theory of gases .

• The rate of reaction depends on the frequency of collisions . The theory also tells us that reacting particles often collide without reacting .

For Collision to the successful , reacting particles must collide with sufficient energy and with the proper orientation . The collision is called effective collision .

• The number of collisions per second per unit volume of the reaction mixture is known as collision frequency ( Z ) .

Example – A + B → Product .

Rate = Z e⁻ Eₐ / RT

Where Z represents the collision frequency of reactants , A and B and e ⁻ Eₐ / RT represents the fraction of molecules with energies equal to or greater than activation energy ( Eₐ )

For example , formation of methanol from Bromoethane depends upon the orientation of reactant molecules .

The proper orientation of reactant molecules lead to bond formation where as improper their orientation makes them simply bounce back and no products are formed .

• In collision theory activation energy and proper orientation of the molecules together determine the criteria for an effective collision and hence the rate of a chemical reaction .
• Collision theory also has certain drawbacks as it considers atoms / molecules to be hard spheres and ignores their structural aspect .