Chemical Kinetics

Chemical kinetics helps us to understand how chemical reactions occur basically the rate of reaction. Substances with well defined properties are converted by chemical reactions into other substances with different properties.

For any chemical reaction,chemists try to find out:

  1. the feasibility of the chemical reaction which can be predicted by thermodynamics ( for a reaction to be feasible at constant temperature and pressure, it should be spontaneous and if Gibbs free energy is less than zero ΔG<0).
  2. extent to which a reaction will proceed can be determined by the chemical equilibrium.
  3. speed of a reaction that means time taken by a reaction to reach equilibrium.

Rate of reaction


The speed or the rate of the reaction is defined as the change of the concentration of a reactant or product in unit time.

For example:

  • some reactions like ionic reactions occur very fast, precipitation of silver chloride.
  • on the other hand, some reactions are very slow, the rusting of iron in presence of air and moisture.

Consider a reaction:     R → P,

  •  In this reaction, one mole of reactant R produced the one mole of product P.
  • So, the Rate of disappearance of R = Decrease in concentration of R/time taken = -Δ[R]/Δt.(-Δ[R],Here negative sign indicates that the decrement of the concentration of the reactant.
  • and Rate of appearance of P = Increase in the concentration of P/time taken = +Δ[P]/Δt.

 

Unit of Rate of reaction = mol/L/sec.However, in gaseous state ,when the concentration of the gases is expressed in terms of pressure, then the units of the rate of reaction becomes atm/sec.

Factors affecting the Rate of Reaction


  • Depends upon the concentration

The rate of chemical reaction at a given specific temperature depends upon the concentration of reactants and products. Thus,Rate Law  represents the rate of reaction in terms of concentration of reactants. It is also called as rate expression and rate equation.

  •  Depends upon the Rate expression and rate constant

As the rate of reaction decreases, when the concentration of reactants decreases and increases, when the concentration of reactants increases. So,the rate of reaction depends upon the concentration of reactants.

For example:

Consider the equation,           aA + bB   → cC + dD

                                   where a,b,c,d are the stoichiometric coefficients of reactants and products.

The rate of reaction for this reaction is,

        Rate ∝ [A]^x   [B]^y

                                 where exponents x and y may or may be equal to the stoichiometric coefficients (a and b) of the reactants.  

The above equation can be written as,  Rate = K [A]^x  [B]^y 

which is equal to,        -d[R]/dt = K[A]^x [B]^y

This foam of equation is called as Differential rate equation. Where K is the rate constant.

Thus, the Rate Law can be defined as the molar concentration of reactants  with each raised to the power which is may or may be equal to the stiochoimetric coefficients of the reactants in the balanced chemical equation.    

  • Order of a Reaction

In the rate equation,      Rate  = K [A]^x  [B]^y

Sum of these exponents i.e, x + y in gives the overall order of reaction whereas the x and y represent the order with respect to the reactants A and B.

Hence, the sum of the powers of concentration of the reactants in the rate law is called the orders of that reaction. 

Order of the reaction can be 0,1,2,3 and also even fraction.

  • Molecularity of a reaction

The number of the reacting species taking part in the elementary reaction, which must collide simultaneously in order to bring out a chemical reaction is called molecularity of the reaction.

(Elementary reactions are those which completes in one step.)

For example:

  1.       Decomposition of ammonium nitrate,      NH4NO2 → N2 + 2H2O

This reaction is a uni-molecular reaction, as there is only one reacting species.

2.      Dissociation of hydrogen iodide,             2HI → H2 + I2

This is a Bi-molecular reaction involve simultaneously collision between species.

3.       2NO + O2 → 2NO2

Trimolecular or termolecular reactions  involve simultaneous collisions between three reacting species.

Integrated Rate Equations


The integrated rate equations are different for the reactions of different reaction orders.

  • Zero Order Reaction

Zero order reaction means that the rate of the reaction is proportional to zero power of the concentration of reactants.

Consider the reaction,     R → P

Rate = – d[R]/dt = K[R]^0,  as any quantity raised to zero is unity

So,  Rate = – d[R]/dt = K[R] × 1

d[R] = – Kdt

Integrating both sides, [R] = -Kt + I ,   where I is the constant of integration

Now, at t=0, the concentration of the reactant R = [R]0, where [R]0 is the initial concentration of the reactant.

substituting in the above equation,  [R]0 = -K × 0 + I

Graph of Zero order reaction
Image Source:

[R]0  = I

substituting the value of I in the equation,   [R] = -Kt + [R]0

comparing with equation of a straight line, y =mx + c , then [R] against t, we get a straight line with the slope -K and intercept equal to [R]0.

After simplifying the equation, we get,   K = [R]0 – [R]/t  

zero order reactions are so uncommon but they occur only at the special conditions. Some enzymes catalyzed reactions and reactions which occur on metal surfaces. The decomposition of gaseous ammonia on a hot platinum surface is a zero order reaction.

  • First order Reaction

In first order reactions, the rate reaction is proportional to the first power of the concentration  of the reactant R.

For Example,        R → P

Rate = -d[R]/dt = K[R]       or           d[R]/[R] = -Kdt

Integrating the above equation, we get

In [R] = -Kt + I

Again I, is the constant of integration and its value can be determine easily.

When t = 0, R = [R]^0, where [R]^0 is the initial concentration of the reactant.

Then, equation can be written as In [R]^0 = -K × 0 + I

In [R]^0 = I

Graph of second order reaction
Image source:

substituting the value of I in equation,   In [R] = -Kt + In[R]0

At time t1 the above equation becomes,  In [R]1 = -Kt1 + In[R]0

At time t2 the equation becomes,              In [R]2 = -Kt2 + In[R]0

Where, [R]1 and [R]2 are the concentrations of the reactants at time t1 and t2,

Subtracting the two equations, In[R]1 – In[R]2 =-Kt1 –  (-Kt2)

K = 1/(t2 -t1) In [R]1/In[R]2

The equation can be written as, In [R]/ In[R]0 = -Kt

Taking antilog of both sides, [R] = [R]0 e^-Kt

comparing the equation with y =mx + c, the plot of In[R] against t, we get a straight line with slope = -k and intercept equal to in[R]0

The first order rate equation can also be written in the foam, K= 2.303 /t log [R]0/[R]

log[R]0/[R] = Kt/2.303.

For example the Hydrogenation of ethene is an example of first order reaction.

All natural and artificial radioactive decay of unstable nuclei take place by first order kinetics.

 

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