Parallel reaction, Concept of activation energy and collision theory of Bimolecular reaction

Parallel reaction

The reaction in which reactant molecules react in more than one way at same or different conditions to give different proportions of product is known as parallel reaction. In this reaction one of the product is formed in large amount which is known as major product. The other product formed is known as minor product. This type of reaction takes place in organic chemistry. For example:Nitration of phenol.

Let 'a' mole/l be the initial concentration of HNO₃ and 'b' mole/l be that of phenol. After time 't', 'x' mole/l of product is formed. So the concentraion of HNO₃ left unreacted at time 't' be (a-x) mole/l and that of phenol be (b-x) mole/l.

Therefore the rate of formation of o-nitrophenol is

\(\frac{d(o-nitrophenol)}{dt}\) = k₁(a-x)(b-x).......(i)

And the rate of formation of p-nitrophenol is

\(\frac{d(p-nitrophenol)}{dt}\) = k₂(a-x)(b-x).........(ii)

Thus, the rate of reaction in terms of reactant (\(\frac{dx}{dt}\) is obtained by adding equation (i) and (ii),

\(\frac{dx}{dt}\) = (k₁+ k₂)(a-x)(b-x)...........(iii)

Dividing equation (i) by (ii), we get,

\(\frac{d(o-nitrophenol)}{d(p-nitrophenol)}\) = \(\frac{k_1(a-x)(b-x)}{k_2(a-x)(b-x)}\)

= \(\frac{k_1}{k_2}\)..............(iv)

Concept of activation energy

Energy profile diagram

The additional energy required to cause the chemical reaction is known as activation energy.

Significance of activation energy

1. Higher the E_alower the rate of reaction i.e very few reacting molecules can cross the energy barrier to give the products.
2. Lower the E_a, faster is the rate of reaction i.e large number of reacting molecules can cross the top energy barrier to give the products.
3. When E_a= 0, reaction is very very fast.

Effect of temperature on rate of reaction:

In most of the reaction, the rate of reaction rises on increasing the temperature. This can be explained on the basis of following facts:

1. On the basis of colliision theory when temperature increases the number of effective collision increases. So, the rate of reaction also increases.
2. When temperature is increased, the fraction of molecules having energy equal to or greater than threshold energy increases. Thus rate of reaction also increases.

The effect of temperature on the rate of reaction can be explained quantitatively with the help of Arrhenius equation which is expressed as,

k = A e^{-\(\frac{E_a}{RT}\)}...........(i)

where, k = rate constant of a reaction

A= a constant for collision factor or frequency factor

E_a= Activation energy

R = gas constant

T = Absolute temperature

Taking \(\ln\) on both sides

\(\ln\) k = \(\ln\) A -\(\frac{E_a}{RT}\) \(\ln\) e where \(\ln\) e = 1

= \(\ln\) A -\(\frac{E_a}{RT}\)

or 2.303 \(\log\) k = 2.303 \(\log\) A -\(\frac{E_a}{RT}\)

or, \(\log\) k = -\(\frac{E_a}{2.303RT}\) + \(\log\) A...........(ii)

This equation is similar to the equation of straight line y = mx + c

If we plot the graph between \(\log\) k verses \(\frac{1}{T}\) a straight line is obtained with slope = -\(\frac{E_a}{2.303R}\) and intercept = \(\log\) A

From above graph A and E_acan be determined

Here, intercept = \(\log\) A

A = e^intercept

and slope =-\(\frac{E_a}{2.303R}\)

E_a= 2.303× (-slope)

Alternatively, E_aof the reaction can be determined as follows:

If the reaction is carried in two different temperature. Let k₁be the rate constant of reaction at temperature T, and k₂be the rate constant of reaction at temperature T₂. Then equation (ii) can be written as

\(\log\) k₁=-\(\frac{E_a}{2.303RT_1}\) + \(\log\) A..........(iii)

and \(\log\) k₂ =-\(\frac{E_a}{2.303RT_2}\) + \(\log\) A........(iv)

Subtracting equation (iii) from (iv) we get

\(\log\) k₂- \(\log\) k₁=-\(\frac{E_a}{2.303RT_2}\) + \(\log\) A. +\(\frac{E_a}{2.303RT_1}\) -\(\log\) A

\(\log\) \(\frac{k_2}{k_1}\) = \(\frac{E_a}{2.303R}\) (\(\frac{T_2 - T_1}{T_1 T_2}\)) .........(v)

By knowing the value of k₁and k₂at two different temperature T₁and T₂the value of activation energy can be determined.

Collision theory of Bimolecular reaction

According to this theory reactant molecules are converted into products only when they collide to each other. All collisions do not lead to product formation. The collision that lead to the product formation is called effective collision. For a collision to be effective reactant molecules must collide with sufficient amount of energy i.e energy equals to or greater than threshold energy.

k is the specific reaction rate constant

z is the total number of collisions per sec per unit volume and,

f is the fraction of molecules that are activated by collision

then, k = zf.......(i)

Now, according to kinetic theory of gases, the fraction of molecules that are activated is given by,

f = \(\frac{n =e^{-\(\frac{E_a}{RT}\)}

So, equation (i) becomes,

k = z e^{-\(\frac{E_a}{RT}\)}............(iii)

Later it was realized that not all the collisions between the activated molecules can give product in a reaction. But only those that collide with proper orientation. So, equation (iii) is modified as

k = p z e^{-\(\frac{E_a}{RT}\)}............(iv)

Where p is probabilistic or steric factor that measures proper orientation between colliding molecules.

References

Prutton, S. H. Maron and C. Principles of Physical Chemistry . Oxford and IBH Pub. Co, 1992.

wikipedia. n.d. <https://en.wikipedia.org/wiki/Rate_equation>.

wikipedia. n.d. <https://en.wikipedia.org/wiki/Collision_theory>.