# Chemical kinetics rate law- second order and nth order reaction- Chem Article

Welcome to Chem Article. Today we will discuss Chemical kinetics. We have already started a series of Chemical kinetics.

## Chemical kinetics class introduction

Chemical kinetics-1 we are discussing Introduction of chemical kinetics, Rate equation, Rate expression of First order Reaction and zero order Reaction.

### Previous question with answer

How to determine the Rate of First order reaction?

What's the half life time of a reaction?

How to determine the Rate equation of a reaction?

How to determine half life time for first order or zero order reaction?

Why not complete the first order reaction?

We are seen in chemical kinetics-1 class all question answers. Now today we will discuss Chemical kinetics-2 , second order reaction, third order reaction rate equation, and nth order reaction rate equation.

### Rate expression for second order reaction

First of all we are considering a second order reaction A + B to P Product formation. Where A and B are reactant they are concentration a and b respectively. At a time equal to zero there concentration of reactant a and b respectively. When time equals t Then there concentration is is (a-x) and (b-x). Where X is Concentration of product.

Then we can write the rate expression for the second order reaction..

r = -d[A]/dt = -d[B]/dt = dx/dt =k2[A][B]

Therefore , we can write r =dx/dt =k2(a-x)(b-x) where k2 is the rate constant of the second order reaction.

Now, dx/(a-x)(b-x) =k2t…..(i) where we can assume that a>b. Then we can integrate the equation no.(i) get..

K2t =1/(b-a).ln{a(b-x)/b(a-x)} then we can easily write k2,=1/(a-b)ln{b(a-x)/a(b-x)}

This is the rate equation for second order reaction. Incase two different concentrations of two different reactants like A and B.

Rate equation for second order reaction| chemical kinetics-2 chemarticle.com |

For two reactants to have the same concentration then how to determine the rate equation for second order reaction.

First of all we assume two reactants at the same concentration.

2A→P The rate expression for this reaction is r = -d[A]/dt = k2[A]2

Then we can write -d[A]/[A]2=k2t…..(ii) where k2 is the rate constant of the reaction. Now similarly integer the equation no..(1) then resulting value we get -1/[A] +1/[A]0= -k2t. Where [A]0 is Initial concentration of A and [A] Is the concentration of reactant a at time t. This is the rate equation for second order reactions at two similar concentrate reactants.

### How to calculate half lifetime of Second order reaction?

First of all we are already in first order reaction and how to calculate the half life time for a reaction. Similarly we can calculate the half life time of a second order reaction. We are considered the time t is equal to zero then concentration of A is [A]0. Now at time t the concentration of the reactant [A] is [A]. For half life time the concentration of reactant will be half of the initial concentration of reactant. That means we can say at t=t1/2 The concentration of reactant [A] =[A]0/2.

Now considering these factors are put in the rate expression of the second order reaction equation.

We get a rate equation..

K2 =1/t1/2{1/([A]0/2) +1/[A]0)}

Now simplify this rate equation Then we get the half life time for second order reaction.

t1/2 =1/k2[A]0 This is the half life time read equation for second order reaction. Where k2 is rate constant Of second order reaction. And [A]0 is concentration of reactant.

### Rate expression for third order reaction

For third order reaction We are considered a reaction.

3A→P

Similarly we have to write the rate expression for the third order reaction. Where concentration of reactant is [A].

Rate of the reaction r = -d[A]/dt = k3[A]3

Where k3 is the rate constant of this reaction. Now at time t = 0 for initial concentration Of reactant is [A]0 . And at time t = t when concentration of reactant is [A].

Now integrating the rate Expression we get the value of Rate constant is

K3 =1/2t{1/[A]2 +1/[A]2} This is the rate equation for third order reaction. You can simplify easily the rate constant of this reaction given by concentration of reactant and how many times are required t.

### nth order reaction

Finally we have to conclude the rate equation of the reaction Easily calculated in first order second order and third order reaction. We can then analyse the rate equation for the month order reaction ( where n is Greater equals to 2). This generalisation equation does not predict or does not determined the first order reaction rate. This generalisation equation is applicable for second order Third Order... up to nth order. Now what is the generation formula for in order reaction in chemical kinetics.

The nth order reaction rate equation is

Kn =1/(n-1)t {1/[A]n-1 - 1/[A]0n-1}....(3)

This is the radio creation of nth order reaction. Where kn is the rate constant of the nth order reaction. [A]0 is initial concentration of reactant and [A] is Concentration of reactant at time t. This General formula of chemical kinetics order determination equation only applicable for n>2 and n=2. This equation does not apply in first order reactions. That means we can write the n value n= 0, 2, 3, 4, 5, 6…..n.

General formula of chemical kinetics rate equation | Units of rate constant |

This is the general formula of nth order reaction.

We can easily find out the order of reaction where known the rate constant value and concentration of reactant React At time t.

### Unit of rate constant

We can put in a unit of radiation concentration of reactant at time t. We can easily find out the unit of rate constant. The unit of rate constant is (mol)1-n(Liter)n-1(sec)-1. Where n equals to the order of this reaction.

When n = 0 , The unit of rate constant is (mol)1(Liter)-1sec-1. This is the unit of rate constant for zero order reaction.

When n=2, then the unit of rate Constant is (mol)-1(Liter)1(sec)-1. This is the unit of rate constant for second order reaction. You can easily find out the unit of rate constant from the general rate equation.

### Conclusion

We hope that this chemical kinetics note is understandable for the audience. We are trying to discuss the chemical kinetics formula, Rate equation, Second order reaction, nth Alder reaction, The unit of rate constant, What is half time life? All things. We are consequently briefly discussing the Chemical kinetics series in chemarticle.com. This is the chemical kinetics-2 Second order, Height order, nth order Reaction. Thank you for reading. Thank you, reader. If you have any query e you can ask on Gmail- chemarticle.open@gmail.com.

### Frequently asked question

#### What is the rate law equation?

Ans: The rate law equation is one of the equations they use to easily calculate the rate of the chemical reaction. In reaction kinetics What is the Accurate rate of the equation we can easily Calculate using rate law equation. The Rate Law equation is varies in different types of order reaction. Success We can see in the second order rate equation.

#### How is the rate of reaction calculated?

Ans: First of all determine the reaction which order belongs. In order to determine this reaction Then easily calculate the rate of reaction. And another thing that must be known is the concentration of the reactant. Then define the rate equation of the reaction and put in the value on this required.