# Order of Reaction

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### Order of Reaction:

• The overall order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised.

Let us consider a general reaction

aA  + bB  → Products

The rate law can be written as

Rate = K  [A]x [B]…………… (1)

Thus the overall order of reaction is (x + y).

• Example:

In the reaction, NO2(g)   +   CO(g)  →  NO(g)   + CO2(g)

The rate of reaction is experimentally found to proportional

to [NO2]² and independent of [CO]. Thus x = 2 and y = 0

Thus the rate law of reaction is Thus the overall order of reaction is 2.

#### Characteristics of Order of Reaction:

• Order of reaction represents the number of atoms, ions and molecules whose concentration influence the rate of reaction.
• order of the reaction is defined as the sum of the exponents to which the concentration terms in the rate law are raised. Thus it is not dependent on the stoichiometric coefficients in a balanced chemical reaction.
• Values of x and y are determined experimentally. The values of x and y in the rate law are not necessarily equal to the stoichiometric coefficients of reactants. Thus the order of reaction can be decided by performing experiment only.
• Order of reaction is defined in terms of concentration of reactants only and not of products.
• Order of reaction may be integer, fraction or zero.

#### Reactions with No Order:

• If the rate of reaction cannot be expressed in the form, Rate, then the reaction has no order and term order should not be used for such reactions.
• Example: #### Clear Concept of Stoichiometric Coefficients of Balanced Chemical Equations and Exponents in Rate Law:

Let us consider a general reaction

aA  + bB  → Products

The stoichiometric coefficients of A and B are a and b.

Let us assume that the rate of reaction depends on [A]x and [B]y

The rate law is written as

Rate = K  [A]x [B]…………… (1)

• The values of x and y for the reaction are found experimentally. The values of x and y may be integer, fraction or zero.

### Integrated Rate Law For First Order Reaction:

• The equations which are obtained by integrating the differential rate laws and which gives the direct relationship between the concentrations of the reactants and time is called integrated rate laws.
• A reaction whose rate depends on the single reactant concentration is called the first order reaction.

Let us consider a general reaction • Let [A]o be initial concentration of A (i.e at t = 0)  and be final concentration of A (i.e at t = t)

Integrating both sides of above equation This relation is known as exponential integrated law for first order reaction.

#### Expression for the Integrated Rate Constant for First Order Reaction: This is an expression for the integrated rate constant for the first order reaction.

#### Expression for the integrated rate constant in terms of initial concentration for First Order Reaction:

• Let a mol dm-3 be the initial concentration of A (i.e at t = 0) and at some instant ‘t’ the decrease in concentration is x mol dm-3.  (i.e at t = t). Thus   [A]o = a and  [A] = a – x

Substituting in equation (2) we have This is an expression for the integrated rate constant for the first order reaction in terms of initial concentration.

#### Unit of  the Integrated Rate Constant for the First Order Reaction:

The integrated rate constant for the first order reaction is given by • The quantity [A]o / [A]  is a pure ratio. Hence it has no unit. Thus the unit of  integrated rate constant is per unit time (s-1 or  min-1 , hr-1 )

#### Half-Life of First Order Reaction:

• The half-life of a reaction is defined as the time required for the reactant concentration to fall to one half of its initial value. Thus for t = t1/2,  [A] = ½ [A]o

The  integrated rate constant for the first order reaction is given by This is an expression for the half-life of the first-order reaction.

#### Graphical Representation of Half-Life:

• A graph is drawn by plotting time as a multiple of half-life on the x-axis and the concentration of reactant in terms of original concentration on the y-axis at that instant. The graph is as follows. • The graph shows that it is an exponential process. Thus this process will never complete. i.e. the graph will never touch x-axis.
• Note: Such graph is shown by the disintegration of a radioactive element. The radioactive elements obey decay law.

#### Graphical Representation of First Order Reaction in Different Ways:

The graph of Rate of reaction against time:

• The differential rate law for the first order reaction is • It is of the form y = mx + c. Thus the graph of rate reaction versus concentration at an instant  is a straight line passing through the origin (since c = 0). The slope of the straight line is k. #### The graph of Concentration of the reactants of against time:

• The exponential rate law for the first order reaction is [A]t = [A]o e-kt
• Thus it is an exponential process. Thus this process will never complete. i.e. the graph will never touch x-axis. #### The graph of Concentration of the reactants of against time: • This equation is of form y = mx + c. Thus the graph of  log10[A]t  versus time is a straight line with y-intercept log10[A]0. #### The graph of log10([A]0/ [A]t) against time: • This equation is of form y = mx + c. Where c = 0. Thus the graph of  log10([A]0/ [A]t)  versus time is  a straight line passing through the origin #### Examples of First-order Reactions: ### Zero order Reactions:

#### Integrated Law for Zero-Order Reactions:

• A reaction whose rate is independent of the concentration of reactants is called zero order reaction.
• Let us consider a general reaction • Let [A]o be initial concentration of A (i.e at t = 0)  and be final concentration of A (i.e at t = t)

Integrating both sides of above equation This relation is known as integrated law for zero order reaction.

#### Expression for the Integrated Rate Constant:

From equation (1) we have This is an expression for the integrated rate constant for the zero order reaction.

#### Unit of Integrated Rate Constant:

• The unit of  integrated rate constant is  mol dm-3 t-1 ( mol dm-3 s-1 or  mol dm-3 min-1,  mol dm-3hr-1)

#### Half-Life of Zero Order Reaction:

• The half-life of a reaction is defined as the time required for the reactant concentration to fall to one half of its initial value. Thus for t = t1/2,   [A]t  = ½[A]o

The  integrated rate constant for the first order reaction is given by This is an expression of the half-life of zero order reaction.

#### The graph of Rate of reaction against time: The differential rate law for the zero order reaction is Thus the graph of the rate of reaction versus time is a straight line parallel to the time axis.

#### The graph of Rate of reaction against Initial Concentration:

The differential rate law for the zero order reaction is • Thus the rate is independent of the concentration of reactants. Hence Thus the graph of the rate of reaction versus concentration of reactants is a straight line parallel to concentration axis. #### The graph of Concentration of the reactants of against time: • The differential rate law for the zero order reaction is

[A]t  = – kt + [A]o

• It is of the form y = mx + c. Thus the graph of concentration at instant versus time is a straight line with y-intercept. [A]o. The slope of the straight line is – k.

#### Decomposition of NH3 on a hot platinum surface: #### Decomposition of Nitrous oxide in presence of platinum as a catalyst: ### Pseudo First Order Reaction:

• The reactions that have higher order true rate law are found to behave as the first order are called pseudo-first order reactions.

#### Hydrolysis of methyl acetate:

CH3COOCH3(aq)  + H2O(l) → CH3COOH(aq)) + CH3OH(aq)

The true rate law of reaction must be

Rate = K'[CH3COOCH3][H2O]

Thus it seems that the rate of reaction is dependent on two reactants.

But the concentration [H2O]  is constant (say k’’)

Rate = K’ K”[CH3COOCH3]

Hence,  Rate = K[CH3COOCH3]

Thus the reaction actually a first order reaction. Hence it is called as pseudo first order reaction.

#### Hydrolysis of cane sugar (sucrose): Chemical Kinetics Summary
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