The temperature dependence of a reaction rate can be represented by the Arrhenius equation

\[K =Ae^{-E_a/RT}\]

The pre-exponential factor \(A\) is called the frequency factor and \(E_a\) is the energy of activation. The unit of \(E_a\) is J/mol or Kcal/mol.

The rate constants at two different temperatures are related as

\[log\frac{K_2}{K_1} = \frac{E_a}{2.303R}\left[\frac{T_2 – T_3}{T_1T_2}\right]\]

Log K versus 1/T gives a linear graph with negative slope. The reactant molecules collide with each other to cross over an energy barrier existing between the reactants and products. If the value of the difference in the internal energies of reactants and product is positive, the reaction is exothermic and if it is negative, the reaction is endothermic. If the temperature is raised the kinetic energy of the molecules increases which causes increase in (i) number of collisions (ii) number of molecules halving higher energy than threshold energy. For every 10°C rise in temperature, the increase in kinetic energy is about 3.3%. So the increase in number of collisions is about \(\sqrt{3.3}\) . , i.e., 1.8%. Hence the rate of reaction must increase only by about 1.8%. For every 10°C rise in temperature, the rate of reaction increases by 100%, i.e., two times If the rate of reaction is doubled for every rise of 10 K temperature, the rate of reaction increased for rise of temperature from 30°C to 80°C is 32 times. The activation energy does not depend on the concentration. The ratio of the rate constants at two different temperatures (preferably 35°C and 25°C) is known as temperature coefficient. If the activation energy is zero, then all the collisions will be fruitful and the reaction is 100% complete.

For a reaction for which the activation energies of forward and backward reactions are equal

energy is neither absorbed nor liberated

The correct answer is option 3. energy is neither absorbed nor liberated.

Let us analyze the given statement: "For a reaction for which the activation energies of forward and backward reactions are equal."

The activation energy (\(E_a\)) is the minimum energy required for a reaction to occur. For a reaction, we have:

\(E_{a, \text{forward}}\): Activation energy for the forward reaction.

\(E_{a, \text{backward}}\): Activation energy for the backward reaction.

If \(E_{a, \text{forward}} = E_{a, \text{backward}}\), it implies that the energy barrier to convert reactants to products is the same as the barrier to convert products back to reactants.

Implications for Reaction Energetics

Thermodynamic Considerations:

The difference in activation energy between the forward and backward reactions is related to the enthalpy change (\(\Delta H\)) of the reaction. For a reaction:
\(\Delta H = E_{a, \text{forward}} - E_{a, \text{backward}}\)

If \(E_{a, \text{forward}} = E_{a, \text{backward}}\), then:

\(\Delta H = 0\)

Energy Absorption or Release:

A \(\Delta H = 0\) means there is no net energy change in the reaction. Neither energy is absorbed nor released during the reaction because the energy required to form the activated complex from reactants is exactly balanced by the energy released when the activated complex converts back to reactants.

Given that the activation energies of the forward and backward reactions are equal, the reaction does not involve a net absorption or release of energy. Therefore, the correct answer is energy is neither absorbed nor liberated.