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# Order of Reaction

The order of the reaction is a relationship between the rate of a chemical reaction and the concentration of the species.

## Definition:

The order of reaction is defined as the power dependence of the rate on the concentration of each reactant.

Once the rate law of a reaction is determined the same law can be used to understand the composition of the reaction mixture completely. In other words, the reaction order is the exponent to which the concentration of the specific species is raised, and it shows to what level the concentration of the species affects the rate of reaction. It also indicates up to which extent the species has a considerable effect. For example, the rate of a first-order reaction is determined only by the concentration of one species in the reaction.

### Characteristics of the reaction order:

• Reaction order indicates the number of species whose concentration affects directly the rate of reaction.
• The reaction order is always defined with the assistance of the reactant concentrations (but not with product concentrations).
• Reaction order can be obtained by summing up all the exponents of the concentration terms in the rate expression.
• In the balanced reaction, the order of reaction does not depend on the stoichiometric coefficients corresponds to each species.
• The order of reaction vale can be in an integral form or a fraction or even having a zero value

Where:

[A] represents the concentration of specie A

[B] represents the concentration of specie B

x indicates the order concerning specie A

y indicates the order concerning specie B

k is known as the rate constant

Note:

The exponents x and y are known as partial orders of the reaction. Hence, the sum of all partial orders of the reaction gives the overall order of a reaction.

Units of the rate constant:

The units of a rate constant vary and are dependent on the overall order.

The units of the rate are M/s or Ms-1.

To determine the units of a rate constant for a specific rate law, divide the units of rate by the units of molarity in the concentration term of the law rate.

Methods of determining Reaction Order:

There are many ways for determining the order of a reaction. Let’s have a glance at these methods.

1. The differential Method:

This is one of the easiest methods to obtain the order of a reaction.

• The rate equation of the reaction is written as r= k [A]x [B]y
• by adding the exponents x+y+…… gives us the final value of the reaction order.
• Integral method:

This method is used by taking the order of reaction from the initial rate method.

The concentrations of the reactants that are measured are compared with the integral form of the rate equation.

For example, the integrated rate equation of a first-order reaction is:

ln [A] = -kt + ln [A]0

where [A] represents the concentration at time t, [A]0 represents the initial concentration at zero time, k is known as the rate constant and is equal to the slope with a negative sign. The first order law is verified if Ln[A] is a linear function of time.

• Initial rates method:

The natural logarithm of the power-law rate equation is given by:

Ln r =ln k+ x ln [A] + y ln [B] + …….

This equation can be used to approximate the order of reaction of each reactant. For example, in a series of experiments the initial rate can be measured at different initial concentrations of the reactant A with every other concentration [B], [C], …… that is kept constant so that the relationship becomes as follows:

ln r = x ln [A] + constant

The graph slope of ln r as a function of ln[A] corresponds to the order x concerning reactant A.

This method is however not always reliable because of the following reasons:

the initial rate measurement needs an accurate determination of even a small change in concentration in short times and is sensitive to errors.

Complete determination of the rate equation is not possible if the rate depends on the substances that are not present at the start of the reaction i.e. intermediates/products.

• Flooding method:

In this method, the partial order regarding a given reactant can be calculated. The concentration of a single reactant can be calculated with all other reactants present in large excess; therefore, their concentration will remain constant.

For a reaction a.A + b.B → c.C with the help of rate law: r = k . [A] x. [B]y, the partial order x concerning A is evaluated by using a large excess of B., in this case,

r =k` . [A]x with k’ = k. [B]y ,

Here x can be measured by an integral method while they will be measured with respect to B under the same conditions by a series of same experiments with an initial concentration of a larger range so that the variation in k’ can be calculated.

Different values of Reaction Order:

The value of the order of reaction comes out in different forms like an integer, zero or a fraction. The graph given below explains the reaction rates for different orders.

The chemical reactions are divided based upon the dependence of the rate of concentration given below:

1. Zero Order Reactions:

A zero-order reaction is considered among one of those whose rate is independent of the concentration.

If there is a change in the concentration of the reactants, it does not affect the speed of the reaction.

Its differential rate law in rate=k. we call these reactions as zeroth-order because it can also be written in such a form that the exponent of the reactant in the rate law is zero.

A graph given below between the concentration of reactant and time is a straight line having a slope of –k because the rate is not dependent on reactant concentration. The value of k is negative because with time the concentration of the reactant decreases. On the other hand, a graph between the concentration and time is a straight line having a slope of k, with a positive value.

An integrated rate law for a zero-order reaction also gives a straight line and is generally written as:

[A] = [A]0kt

Where [A]0 is an initial concentration of reactant A. in zero-order reaction, the rate constant has the same units as moles per liter per second.

Many enzymes catalyzed reactions are of zero-order, which says that the reactant concentration is much more than the enzyme concentration which controls the rate so that the enzyme is saturated.

For example, the biological oxidation of ethanol to acetaldehyde by the enzyme is zero order in ethanol.

Similarly, if the catalytic surface is saturated, the heterogeneous catalysis can be zero. For example, on a hot tungsten surface, the decomposition of phosphine (PH3) at high pressure is zero order in phosphine that decomposes at a constant rate.

In homogeneous catalysis, zero-order behaviour can be attained from reversible inhibition. For example, the ring-opening metathesis polymerization used third-generation Grubbs catalyst that exhibits zero-order nature in catalyst because of reversible inhibition that can occur between the pyridine and the ruthenium centre.

• First order:

A first-order reaction is the one in which the rate is directly proportional to the concentration of a single reactant. Consider a liquid reaction

A+B → C + D

The rate equation for this reaction is

-ra = kCa

As we know the liquid phase reaction is

For the above first-order reaction, we have

This equation is known as the differential rate equation of the first-order equation. The half-life is independent of the initial concentration and is given by

Examples:

• Second-order reaction:

The reaction is said to be a second-order reaction when the order of a reaction is 2.

The second-order rate reactions can be achieved by squaring the concentration of one reactant or from getting the concentration of two separate reactants.

The rate equation corresponds to

r = k[A]2 or r = [A][B]

example:

NO2 + CO NO + CO2

• Pseudo-First Order Reactions:

In a pseudo-first-order reaction, the concentration of one reactant remains constant and hence it includes the rate constant in the rate expression.

The reactant concentration might be constant as it is present in large amounts when it is compared to the concentration of other reactants or maybe because it is a catalyst.

Consider an elementary reaction

A+ B  → C

Rate expression is given by

ra = k’ Ca Cb

If anyone of the reactants i.e. B has a high concentration and there is a small change in the concentration during an entire reaction its value can be supposed to be a constant and we will get a first-order reaction with respect to A. this type of reaction is called a pseudo-first-order reaction:

-ra = (k`Cb) Ca = kCa

Where k is a constant.

The second-order reaction requires the determination of the concentration of both the present reactants together. The pseudo-first-order reaction method helps in the study of chemical kinetics.

Example:

CH3COOCH3 + H2O  → CH3COOH + CH3OH

This reaction follows pseudo-first-order kinetics because water is present in a considerable amount.

References: