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.

Identify the false statement from the following:

A reaction with high activation energy proceeds rapidly when temperature is lowered

The correct answer is option 4. A reaction with high activation energy proceeds rapidly when temperature is lowered.

Let us delve into each statement with detailed explanations to identify the false statement:

1. Threshold energy is the minimum energy possessed by the colliding molecules for converting into products.

Threshold Energy is the minimum energy required by colliding reactant molecules to overcome the activation energy barrier and convert into products. It represents the energy needed to reach the transition state, where bonds are broken and formed. The threshold energy must be met or exceeded by the colliding molecules for a successful reaction to occur. This concept is consistent with the collision theory of chemical reactions. This statement is correct.

2. Activation energy is the difference in threshold energy and average kinetic energy of reactants.

Activation Energy (E_a) is the energy barrier that must be overcome for a reaction to proceed. It is the difference between the threshold energy (the energy required to reach the transition state) and the average kinetic energy of the reactants. If the reactants have enough kinetic energy to overcome this activation barrier, the reaction can proceed. The activation energy can be thought of as the energy needed to bring the reactants from their average kinetic energy to the energy required for the reaction. This statement is correct.

3. The activation energy for a specific reaction depends primarily on the nature of the reactants.

Nature of Reactants: The activation energy of a reaction is influenced by the specific properties of the reactants, such as their bond strengths, molecular structures, and the nature of the chemical bonds involved. Different reactants will require different amounts of energy to overcome the activation barrier due to their unique characteristics. For different reactants, the energy needed to reach the transition state (activation energy) will vary based on how easily they can achieve the necessary molecular configurations for the reaction to occur. This statement is correct.

4. A reaction with high activation energy proceeds rapidly when temperature is lowered.

Effect of Temperature: According to the Arrhenius equation (\(k = A e^{-\frac{E_a}{RT}}\)), the rate constant \(k\) of a reaction increases with an increase in temperature. This is because higher temperatures provide more kinetic energy to the molecules, increasing the number of molecules that can overcome the activation energy barrier. For reactions with high activation energy, the barrier is steep, meaning that fewer molecules at lower temperatures have enough energy to reach this barrier. Consequently, the reaction rate decreases when the temperature is lowered, not increases. This statement is incorrect because a reaction with high activation energy would slow down, not speed up, when the temperature is reduced.

Thus, the false statement is option 4. A reaction with high activation energy proceeds rapidly when temperature is lowered.

This is because lowering the temperature decreases the number of molecules with sufficient energy to overcome the high activation energy barrier, thus slowing the reaction rate.