## Chemical Kinetics

The branch of chemistry, which deals with the study of reaction rates and their mechanism, called as chemical kinetics.

### Rate of a chemical reaction:-

“ The rate of a reaction can be defined as the change in concentration of a reactant or product in unit time”
Let a reaction whose volume remain constant                  R--->P
One mole of reactant R produces one mole of product P. [R1] & [P1] and [R2] & [P2] are the concentrations of R & P at time t1 & t2 respectively.
Both above expression show average rate of reaction

#### Instantaneous rate of reaction:-

It is the rate of change of concentration (i.e. change of concentration per unit time) of any one of the reactants or products at that particular instant of time.

### 1.      Concentration:-

As concentration of reactant increase, rate of reaction also increases.

### 2.      Temperature:-

Rate of reaction increases with increase of temperature mostly reaction rate double with rise of 100 temperature.

### 3.      Catalyst :-

Catalyst generally increase the rate of reaction without undergoing in the reaction, it also help in attaining the equilibrium quickly without disturbing the equilibrium state in reversible reaction.

#### Rate expression and rate constant:-

Consider a general reaction aA + bB --> cC + dD
Where,      a, b, c, and d are stoichiometric coefficient of reactants and products.
The rate expression for this reaction is-
Rate is directly proportional to [A]x [B]y  ………………………..(iii)
Where,      component x & y may or may not be equal to the stoichiometric coefficient (a & b) of the reactants
Also,   Rate = k [A]x[B]y   ………………………………(iv)

This form of equation (v) is known as differential rate equation, where k is proportionality constant called rate constant. And the equation (iii) which relates the rate of a reaction to concentration of reactants is called Rate law or rate expression.

### Rate:-

Rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each terms raised to some power, which may or may not be same as the stoichiometric coefficient of the reacting species in a balance chemical reaction.
EX:-  Reaction --> Experimental rate expression
CHCl3 + Cl2 --> CCl4 + HCl
Rate = k[CHCl3] [Cl2]1/2
CH3COOC2H5 + H2O --> CH3COOH + C2H5OH
Rate = k[CH3COOC2H5]1 [H2O]0
2NO + O2 --> 2NO2

### Order of a reaction:-

The sum of powers of the concentration of the reactants in the rate of low expression is called as the order of that chemical reaction.
Rate = k [A]x[B]y
Order = x+y
Order of reaction may be 0, 1, 2, 3 or even in fraction, Zero order reaction is independent of concentration. To Download Chemistry Notes in PDF join our Telegram Channel (Search @ChemistryNotesInfo on Telegram App).

#### Unit of rate constant (k):-

aA + bB --> cC + dD
Rate = k [A]x[B]y
Where,                        x+y = n = order of reaction

### Molecularity of a reaction: -

The no. of reacting species (atoms, ions, 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.

## 1.      Zero order reaction: -

consider a reaction-
d[R] = -k dT
Integrating both sides,
[R] = -kt + c ……………………….(1)
Where, c is constant of integration at t = 0, the concentration of reactant R=[R]0
Where, [R]0 is initial concentration of reactant.
Substitute in equation (1),
[R]0 = -k ´ 0 + c
[R]0 =  c   ………………………………(2)
From equation (1) & (2),
[R] = -kt + [R]0
Kt = [R]0 – [R]
Also,
Rate = k[NH3]0 = k

## 2.      First order reaction: -

consider a reaction-

Integrating this equation, we get
ln[R] = -kt + c   ……………………………….(1)  [where c is constant]
At t=0, R=[R]0 where [R]0 is the initial concentration of the reactant
Put these values in equation (1), we get
ln[R]0 = -k x 0 + c
ln[R]0 =  c      ……………………..….(2)
From equation (1) & (2)
ln[R] = -kt + ln[R]0  ……….…….…(3)
kt = ln [R]0 – ln[R]
k = 1/t[ln([R]0 /[R]………………………..(4)
At time t1 from equation (3)
ln[R]1 = -kt1 + ln[R]0    ………………………...(5)
At time t2,
ln[R]2 = -kt2 + ln[R]0  ……………………………(6)
Where,
[R]1  & [R]2 are the concentration of the reactant at time t1 & t2 respectively
Subtracting equation (5) from equation (6), we get

#### Graph:

·         A plot between ln[R] and t for a first order reaction
·         A plot between log[R]0 / [R] and time for a first order reaction

## Half life of a reaction: -

#### i.            For zero order reaction: -

Rate constant is given by –

#### Temperature dependence of the rate of a reaction: -

Most of chemical reactions are accelerated by increase in temperature. It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant is nearly double.
The temperature dependence of a chemical reaction can be accurately explained by Arrhenius equation-
k = A e-Ea/RT   …………………………(1)
Where, A is Arrhenius factor or frequency factor
R is gas constant
Ea is activation energy measured in joules/mole (jmol-1)
Also, in this reaction-
H2 (g) + I2 (g)  -->  2HI (g)

According to Arrhenius, This reaction can take place only when a molecule of hydrogen and molecule of iodine collide to form an unstable intermediate. It exist for a very short time and then break up to form two molecule of hydrogen iodide.

The energy required to form this intermediate, called ‘activation complex’ (C), is known as activation energy (Ea).
Also, taking natural logarithm of both side of equation (1), we get-
The plot of ‘ln k’ vs ‘1/T’ gives a straight line according to equation (2)
Fig: A plot between ‘ln k’ vs ‘1/T’
In figure, slope = -Ea/R and Intercept = ln A
So, we can calculate Ea and A using these values.
Since A is constant for a given reaction k1 and k2 are the value of rate constant at temp. T1 and T2 respectively.
Substrate eq. (3) & (4)

### Effect of catalyst:-

A catalyst which alters the rate a reaction without itself undergoing any permanent chemical change.
The action of a catalyst can be explained by intermediate complex theory.
According to this theory, A catalyst participate in a chemical reaction by forming temporary bonds with the reactants resulting in an intermediate complex and decompose to yield products and catalyst.
R + C --> R-C --> P + C
Reactant + catalyst --> intermediate complex --> product + catalyst

## Collision theory of chemical reactions:-

According to this theory “The reactant molecules are assume to be hard spheres and reaction is postulated to occur when molecule collide with each other”
“The no. of collisions per second per unit volume of the reaction mixture is known as collision frequency (Z)”
Another factor which affects the rate of a chemical reaction is activation energy for a bimolecular elementary reaction.
A + B --> Product
Rate of reaction can be expressed as
Rate = ZAB e-Ea/RT
Where,  ZAB represents the collision frequency of the reactants, A & B and
e-Ea/RT represents the fraction of molecules with energies equal to or greater than Ea.

All collision do not lead to the formation of product. the collision in which molecule collide with sufficient kinetic energy (Threshold energy) and proper orientation, so as to facilitate breaking of bonds between reacting species and formation of new bonds to form products are called as effective collision.
Note:- Threshold energy = Activation energy + Energy possessed by reacting species.
EX:- Formation of methanol from bromoethane
CH3Br + OH- --> CH3OH + Br-

## Electrolysis:

It is the process of decomposition of an electrolyte by the passage of electricity through its aqueous solution or molten state.

### Faraday’s first law of electrolysis:

In a chemical reaction, the amount of any substance deposited or liberated is directly proportional to the quantity of electricity passed through it.
W Q
W = ZQ
W = Zit                                            ( Q= I*t )
Where, Z = Electrochemical Equivalent.
Z = atomic weight/nF                   (n = no. of electron, F = 96500 )

### Faraday’s second law of electrolysis:

When the same quantity of electricity is passed through the different electrolytes connected in series. The weights of the substance produced at the electrodes are directly proportional to their equivalent weights.
Ex: AgNO2  and CuSO4 solution connected in series,

#### Conductance of electrolytic solution:-

Electrolytes conducts electricity by decomposition.

#### Electrical resistance:-

If voltage v is applied to the ends of the conductor and current “I” floe through it, then the resistance “R” of the conductor is V/I (ohm).

#### Electrical conductance:-

The reciprocal of electrical resistance is called conductance. And is represented by G sign
Thus,    G = 1/R                              [unit of G = mho]
Specific resistance or Resistivity:- it is observed that,
There r is constant and called as resistivity.

#### Specific conductance or conductivity:-

The reciprocal of resistivity is known as conductivity. And is denoted by k (kappa).

### Equivalent conductivity:-

Equivalent conductivity of a solution at a dilution v is defined as the conductance of all the ions produced from one gram equivalent of the electrolyte dissolved in v cm3 of the solution when the distance between the electrode is one cm and the area of the electrode is so large then whole the solution is come between them.
Where, c is molar concentration.

### Kohlrausch law: -

The limiting molar conductivity of an electrolyte (i.e. molar conductivity at infinite dilution) is the sum of the limiting ionic conductivities of the cation and the anion each multiplied with the number of ions present in one formula unit of the electrolyte.

#### Kohlrausch law in terms of equivalent conductivity:-

The equivalent conductivity of an electrolyte at infinite dilution is the sum of two values one depends upon cation and other upon anion.

### Electrode Potential :-

The electrical potential difference set up between metals and its ions in the solution is called electrode potential.
Cell potential or EMF of a cell:- The difference between the electrode potential of the two half cell is known as cell potential or cell voltage it is called Electromotive Force or EMF of the cell if no current is drawn from the cell.

### Electrochemical series:-

The various electrodes have been arranged in order of their increasing value of standard reduction potentials. This arrangement is called electrochemical series.

### Nernst equation for electrode potential:-

Mn+ + ne- -->  M
Then Nernst equation is,
Where, E = electrode potential under given concentration of Mn+ ions and temperature T.
E0 = standard electrode potential.
R = gas constant.
T = Temperature in K
n = No. of electrons involves in the electrode reaction.
Also put,         R = 8.314 Jk-1mol-1
F = 96500 coulombs

## Primary Cells

### Dry cell:-

It consist of a cylindrical zinc container which acts as a anode. A graphite rod is placed between the center, acts as a cathode. The space between the cathode and the anode is so packed with the paste of NH4Cl and ZnCl2 and graphite is surrounded by MnO2 and carbon.
Reactions,
At Anode: - Zn (s)  -->  Zn2+ (aq) + 2e-
At cathode: - 2MnO2 (s) + 2NH4+ (aq) + 2e- --> Mn2O3 (s) + 2NH3 (g) +H2O
These cells have voltage in range of 1.25 V to 1.50 V have no long life.

### Mercury cell (Ruber Mallory cell) :-

It consists of zinc container as anode, a carbon rod as cathode and a paste of mercuric oxide mixed with KOH as the electrolyte a lining of porous paper separate the electrolyte from zinc container.
Cell reaction:-
At Anode     : - Zn + 2OH- --> ZnO + H2O + 2e-
At Cathode : - HgO + H2O+2e- --> Hg + 2OH-

## Secondary cell

cell consist of lead anode and a grid of lead packed with lead dioxide acts as lead cathode. These electrodes are arranged alternatively separated by fiber glass sheet and suspended in sulfuric acid (dilute) which acts as electrolyte.

#### Electrode reaction occurs during discharge battery:-

At Anode    :- Pb + SO42- --> PbSO4 + 2e-
At Cathode :- PbO2 + SO42- + 4H+ + 2e- --> PbSO4 +2H2O
In above reactions H2SO4 is used hence density of H2SO4 is decreases so battery will discharge.

#### During charging:-

The electrode reaction is reserved.
PbSO4 + 2e- --> Pb + SO42-
PbSO4 +2H2O --> PbO2 + SO42- + 4H+ + 2e-

It consists of cadmium electrode (as Anode) and metal grid of nickel (iv) oxide as cathode immersed in KOH solution.

#### Reaction occurs during discharge of cell:-

At Anode :- Cd + 2OH- --> Cd(OH)2 + 2e-
At Cathode :- NiO2 + 2H2O +2e- --> Ni(OH)2 + 2OH-
Hence,
The reaction can be reversed during charging. The potential of each Ni-Cd cell is approximately 1.4 V

### Fuel cell: -

It consists of porous carbon electrodes containing suitable catalyst incorporated in them. Concentrated KOH or NaOH solution is placed between the electrodes to act as the electrolyte. The hydrogen or oxygen gases are bubbled through the porous electrode into the KOH/NaOH solution.
Reactions:-
At Anode: -  2H2 + 4OH- --> 4H2O + 4e-
At Cathode: - O2 + 2H2O + 4e- --> 4OH-

## CORROSION

### Corrosion:-

The process of slowly eating away of metal due to attack of atmospheric gases on the surface of metal resulting into the formation of compounds such as oxides, sulphides, carbonates, sulphates etc. is called as corrosion.
In corrosion the metal is oxidized by loss of electrons to oxygen and formation of oxides. The corrosion of iron occurs in the presence of air & water.
In iron sheet or object or a particular pot behaves like a where oxidation takes place.
Anode: - 2Fe (s) --> 2Fe2+ + 4e-
And these electron moves to another spot where reduction takes place in the presence of H+ ion (H2CO3)
At Cathode: - O2(g) + 4H+ (aq) + 4e- --> 2H2O (l)
The overall reaction being   2Fe + O2 + 4H+ --> 2Fe2+ + 2H2O
E0(cell) = 1.67 v
Fe2+ (ferrous ion) oxidised by O2to form ferric ion (Fe3+) which comes out as Rust Fe2O3.xH2O.

## NOTE:

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