Question

In the equation $k = P{Z_{AB}}{e^{\dfrac{{ - {E_a}}}{{RT}}}}$ , what is the term used for describing P?

Answer 1

Hint: We need to know that the activation energy is the minimum energy required to overcome the potential energy barrier or for the reaction to proceed to completion. A reaction will only occur if the reaction has sufficient energy to overcome the potential energy barrier.
The rate of the reaction can be found out by the formula:
$rate = P{Z_{AB}}{e^{\dfrac{{ - {E_a}}}{{RT}}}}$
Where, ZAB is the collision frequency of reactants, A and B is the fraction of molecules having activation energies greater than or equal to Ea and P is the probability steric factor. Ea is the activation energy.

Complete answer:
The probability steric factor denoted by ‘P’ is defined as the ratio between the experimental and theoretical rate constants as predicted by the collision theory. It can also be defined as the ratio between pre-exponential factor and the collision frequency. Usually, the steric factor becomes lower as the complexity of the reactions increases. Sometimes the steric factor is also greater than unity. The deviations from unity can be because of: the molecules being non-spherical, the kinetic energy not delivered to the right spot, presence of solvent, etc.
The solvent cage has an effect on the reactant molecules, when the collision theory is applied to reactions in solutions, because of which the pre-exponential factor becomes too large. If the value of P is greater than unity can be because of favourable entropic contributions.
The steric factor P cannot be accurately measured without performing trajectory or scattering calculations.
Commonly, the steric factor is also known as the Frequency Factor.
In chemical kinetics, the rate of the reaction can be affected by:
Reactant concentration
Temperature
Reactant states
Catalysts.
Consider a reaction $A + B \to AB$
The rate of this reaction can be calculated as the number of active collisions. Mathematically can be represented as:
$rate = P{Z_{AB}}{e^{\dfrac{{ - {E_a}}}{{RT}}}}$
Where,
P= Probability factor
E= activation energy
T= Temperature (in kelvin)
R = gas constant

Note:
As we know that the Arrhenius equation is also used to determine the rate of the reactions. The Arrhenius equation can be given as $rate = A{e^{\dfrac{{ - {E_a}}}{{RT}}}}$
Where, A = Pre exponential factor and Ea is the Activation energy
If rate constants are provided at two different temperature the Arrhenius equation can be modified as:
\[\ln \left( {\dfrac{{{k_1}}}{{{k_2}}}} \right) = \dfrac{{{E_a}}}{R}\left( {\dfrac{1}{{{T_2}}} - \dfrac{1}{{{T_1}}}} \right)\]