Rate of a Chemical Reaction

In any chemical reaction, some bonds going to cleave in reacting molecules and some new bond formed in product molecules.
Th rate of reaction depends on the number and nature of bonds of different substances which are different in different substances; hence the rate of chemical reactions differs a lot from one another. Thus the reactions involving ions, like precipitation reactions, are almost instantaneous as there is no bond has to be broken during ionic reactions. The reactions which involve large covalent
molecules like inversion of sugar are proceeding slowly. Because in such reactions large number of bond have been broken in reactants molecules and formed in product molecules. There is no relation between thermodynamic stability of reactant as well as product and in the rate of reaction. Rate of reaction depends only on the structural and energetic factors substances involve in reaction.

Guldberg and Waage (1864–1879) purposed the law of mass action according to which the rate of
reaction depends upon the molar concentration of the reactants involve in any chemical reaction.
Since the concentration of reactant decreases continuously, hence the rate of reaction
also decreases, at the same time the concentration of product increases.  For example; for a reaction of reactant A to form product B;
          A---------->B
The rate of reaction at any given time will depend upon the concentration of reactant A at that
time. As the reaction proceeds, the concentration of A decreases and the rate of reaction at any given instant is written as;
                                  R=-dC_A/dt =kC_A
Where Negative sign indicates the decrease in concentration of reactant A.
–dC_A = infinitesimally small decreases in the concentration of reactant A
 dt=Small time interval
C_A =Concentration of A
k= Rate constant or velocity constant
The unit of rate constant is   concentration per unit time i.e. mole liter^-1 sec^-1. The rate of reaction can be written by using the concentration of product which increases as
reaction proceeds in forward direction.
R= dP/dt = kCA
Hence the rate of reaction can write as;
R=-dC_A/dt= dP/dt = kC_A
This representation if rate of reaction with respect to the concentration of reactant and product is
called as rate equation.
For a reaction which involve more than one reactant like;
A + B--------> C+D
The rate of reaction can be written as;
R=-dC_A/dt=-dC_B/dt
= dC_c/dt = dC_D/dt= k C_A C_B
If more than one mole of reactants and products involve in reaction; the rate equation is divided by
the Stoichiometric coefficient of reactant and product molecules. For example;
aA + bB------------> pP+qQ
Or      r= k [A]^a [B]^b
The rate consent or velocity constant defined as the fraction of reactant A that reacts per unit
time. If the concentration of reactant A taken as unit [A]=1 ,
Since R= k[C_A]
Rate of reaction=k
Hence at a given temperature, the rate constant of a reaction involving a single reactant is equal to the rate of the reaction when the concentration of the reactant is unity.
There is a large variation in the rate of different chemical reactions due to various factors. Let’s discuss some key factors which affect the rate of reaction;
a) Nature of reacting species:  Since any chemical reaction involves the cleavage of chemical bonds in reactant molecules, hence the strength of bonds present in reactant molecules affect the rate of
reaction. If there are strong bonds in a reactant molecule, it will require a large amount of energy to break these bonds and under conditions the reaction proceeds slowly and rate of reaction decreases. While in case of ionic reactions; reaction precedes instantaneously due to the presence of ions. For example; reaction of strong base NaOH with strong acid HCl occurs at room
temperature and form salt and water.
NaOH +HCl ----------> NaCl +HOH
However the formation of ammonia from nitrogen and hydrogen will take million years in the absence of catalyst and completed 15 % in the presence of catalyst (Iron with Molybdenum)
N₂+3H_{2 ------------>}2NH₃                 
b)Concentration of reactant: According to rate equation; the rate of reaction is directly proportional to
the concentration of reactant molecules, hence as the concentration of reactant molecules increases the rate of reaction also increases. This is because of number of effective collision between reactant molecules which increases with increasing the concentration of reactant molecules.
For example; the process of rusting enhanced in rainy season due to the high concentration of water vapor in atmosphere which is a main reactant in rusting process.
c) Effect of temperature : The effect of temperature on the rate of reaction ca be batter explain by using the temperature coefficient which is ratio of rate constant  at two different temperature
differ by 10 °C represented by Tc.
Tc = K_(T+10)/K_T
In general the value of temperature coefficient is 2-3 , it means by increasing the temperature by 10 °C the rate of reaction increases by two to three times. As the temperature increases, the fraction of activated molecules increases, hence effective collisions increases.
At the same time as the temperature, molecules acquire activation energy to cross the energy barrier and form product.
  
c) Effect of catalyst: The foreign substances which can increase the rate of reaction and regenerate
at the end of reaction are known as catalyst. For example iron acts as catalyst in Haber’s process for the production of ammonia by using nitrogen and hydrogen gas.
d) Effect of surface area of reacting molecules:  Generally heterogeneous reaction occurs at the
surface by absorption process; hence the rate of reaction is directly proportional to surface area of reacting molecules. That is the reason; reactions with small particle size of reacting molecules precede fast compare to lump of reactant.
e) Effect of radiation:  Some reactions are affected by radiant energy just like thermal energy. Such reactions are called as photochemical reactions. For example the formation of HCl by using hydrogen and chlorine gas is an example of photochemical reaction.
The rate of reaction is defined as the amount of reactant consumed in given time interval or amount of product produced in given time. The rate of reaction is directly proportional to the active mass of reactant molecules. Hence for the given reaction;
A +B-----------> P
The rate of reaction=R α [A] [B]
R=k [A][B]
Where
k= Rate constant or velocity constant
[A], [B] = active mass of reactants
The dimensional of;
                          Rate of reaction = mole liter-1 sec-1
                          Concentration of reactant =mole liter-1
Hence the dimensional of rate constant for given reaction will be;
aA +bB +….   -------------> Product
Mole liter-1 sec-1 = k [mole liter-1]^a [mole liter-1]^b…..
k= [(liter/mole) ^{{(a+b+….)-1}}] x [Sec^-1]
Order of reaction: The order of reaction defined as the number of molecules whose concentration
determines the rate of the chemical reaction at a given temperature. Or batter defined as the sum of the powers to which the concentration terms raised in order to determine the rate of reaction.
Thus if the rate equation is R= k[A] , the order of reaction will be one and reaction termed as first order reaction. 
Similarly the rate equation for different order of reaction is;
R = k[A]⁰ ; Zero order reaction
R = k [A]² or R=k [A] [B] ; Second order reaction
R = k [A]³ or R=k [A] [B] [C] ; Third order reaction and so on.
The order of reaction is an experimental determined quantity can be zero, whole number or fractional.
First order reaction: The rate of reaction is depends only on the one power of reactant. Hence for the
given reaction;
Where                            
                                k= Rate constant
                                t=Time
                                 a= Initial concentration of reactant
                              (a-x) = Concentration of reactant at the time t
  


The radioactive decay is an example of first order reaction; hence the rate of reaction varies as the concentration of one molecular species only. For example the radioactive deacy process of radioactive an element A;
A----------->P
Suppose the initial concentration of A = N₀
At time t the amount remains=  N.
Hence the rate of change of A to P with time dt will be directly pereportional to the
intial concentration of reactent A .
Here λ is called as the velocity constant of the nuclear decay, also known radioactive constant or dacay  constant which defined as the fraction of the total number of atoms of the radioactive substances  at any time which disintegrated per second.
The half life period of a radioactive substance defined as the time during which half the amount of a given radioactive sample disintegrates.  So at half life period the initial concentration of A that is N₀ becomes half so N=N₀/2
The rate equation for radioactive decay is
At half life period N=N₀/2