Question

If 'x' is the fraction of molecules having energy greater than ${E_a}$ it will be given by
A. $x = - \dfrac{{{E_a}}}{{RT}}$
B . $\ln x = - \dfrac{{{E_a}}}{{RT}}$
C. $x = {e^{E_a/RT}}$
D. None of these

Answer 1

In a given sample, different molecules will have different energies. Some molecules will have energy equal to ${E_a}$ , some molecules will have energy less than ${E_a}$ while remaining molecules will have energy greater than ${E_a}$ . You are asked for the ratio of the number of molecules having energy greater than ${E_a}$ to the total number of molecules.

Complete answer:
The symbol ${E_a}$ represents the energy of activation. You can also call it activation energy. It is the difference between the energy of the transition state and the energy of reactants. In other words, you must provide the reacting molecule with energy equal to activation energy in order to have a fruitful collision. A collision is fruit full when it leads to the formation of a product. Such a collision is called an effective collision.
If 'x' is the fraction of molecules having energy greater than ${E_a}$ it will be given by either $x = {e^{ - E_a/RT}}$ or $\ln x = - \dfrac{{{E_a}}}{{RT}}$
In the above expression, R is the ideal gas constant and T is the temperature. The value of the ideal gas constant is $8.314{\text{ J/mol}}{\text{.K}}$ and the temperature should have a unit of kelvin. Usually, the activation energy is given in kilojoules per mole. You need to convert the unit of activation energy from kilojoules per mole to joules per mole by multiplying it with 1000.

**Hence, the correct option is the option B.

Note:**
Not all the collisions between the reactant molecules leads to the formation of products. Only those collisions are fruitful in which colliding molecules are provided with activation energy.