COLLISION THEORY

The first theory to explain the mechanism of chemical reaction was the collision theory. According to this theory the reactant molecules collide and due to this collision, some structural rearrangement occurs which is responsible for chemical reaction.

However, if each collision leads to reaction then number of molecules reacting per c.c. per second should be equal to frequency. But the number of molecules reacting per c.c. per second much less than the collision frequency. Further more while rate of a reaction increases by 100% to 200% for 10⁰C rise in temperature, collision frequency increases by only 2% to 3% for the same change in temperature. Hence all collision may not lead to reaction. It was at this time; Arrhenius introduced the concept of activation energy. According to which for a molecule to react, it must have energy equal to or greater than activation energy (E). These molecules are called active molecules. Collision between active molecules are fruitful and lead to reaction where as collision between passive molecules are fruitless.

Now, according to Boltzmann’s distribution law, if n₀ is the total number of molecules, out of which n_E molecules have energy greater or equal to E, then—

n_E = n₀ e^{- E/RT}

Hence, if Z is the total number of collisions per c.c. per second, out of which Z_E is the number of collisions between activated molecules, then---

Z_E = Z e^{- E/RT}

Hence number of molecules reacting per c.c. per second is proportional to Z_E. This is collision theory.

Test of this theory was made from kinetic study of the decomposition of HI.

2HI <========> H₂ + I₂

If, Z is the collision frequency, then since each collision involves two molecules, number of molecules reacting per c.c. per second is---

 – dn/dt = 2 Z e^{- E/RT}

Now from kinetic theory----

Z = (1/√2) Π σ² C_a n²

Where,

σ = Collision diameter

C_a = Average velocity

n = Number of molecules per c.c.

So,

 – dn/dt = 2 (1/√2) Π σ² C_a n² e^{- E/RT} ----- (1)

Now, we calculate the rate in another way.

For the above reaction rate----

 – dc/dt = K₂C²

Where,

K₂ = 2 nd order rate constant

C = Molar concentration

N = Avogadro number

But, C = (n x 10³)/N

Or, – dc/dt = - (10³/N) dn/dt

Hence, - (10³/N) dn/dt = K₂ [(n x 10³)/N]²

Or, - dn/dt = K₂ (10³/N) n² ----- (2)

Comparing (1) and (2), we get---

K₂ (10³/N) n² = √2 Π σ² C_a n² e^{- E/RT}

Or, K₂ = √2 Π (N/10³) σ² C_a e^{- E/RT}

Or, K₂ = A e^{- E/RT}

[Where, A = √2 Π (N/10³) σ² C_a and it is known as frequency factor.]

LIMITATIONS OF THE THEORY

Though collision theory explains many reactions very well, it fails to explain many other cases. Thus, in many cases, the observed rate constant is much different from A e^{- E/RT}. The cases where it is greater than A e^{- E/RT} are chain reaction. However, the cases where it is less than A e^{- E/RT} are explained on the basis of orientation of molecules during collisions. If the collisions are not perfect oriented than collisions between active molecules also may not lead to reaction. In these aspects the expression for rate constant K is now written as—

K = P A e^{- E/RT}

Where P is known as steric factor or probability factor, generally its value is less than 1 (excepting chain reaction).

Another defect of collision theory is that it does not consider the entropy change for the reaction. Actually, probability factor is related with entropy change, which can be shown below.

For reversible reaction, the forward and backward rate constant K₁ and K₂ can be written as---

K₁ = P₁ A₁ e^{- E}₁^/RT

K₂ = P₂ A₂ e^{- E}₂^/RT

Or, K₁/K₂ = [(P₁ A₁) / (P₂ A₂)] e^{- (E}₁^{- E}₂^)/RT

But, K₁/K₂ = Equilibrium constant (K)

So, K = [(P₁A₁) / (P₂A₂)] e^{- (E}₁^{- E}₂^)/RT ----- (3)

Again, from Vant Hoff’s isotherm----

ΔG = - RT ln K

Or, K = e^{- ΔG/RT}

Putting, ΔG = ΔH – TΔS

K = e^{- ΔH/RT} e^ΔS/R ----- (4)

Comparing (3) and (4), we get---

[(P₁A₁)/(P₂A₂)] = e^ΔS/R

Thus, probability factor is related with entropy change of the reaction. This factor has not been maintained in collision theory.