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.

Which of the following statement is wrong?

Increase in the rate of reaction with increase in temperature is due to increase in collision frequency.

The correct answer is option 3. Increase in the rate of reaction with increase in temperature is due to increase in collision frequency.

Let us delve into each statement to understand why the identified statement is incorrect:

1. The Arrhenius equation expressing the effect of temperature on the rate constant of a reaction is \( k = A e^{-\frac{E_a}{RT}} \).

Arrhenius equation is a fundamental expression in chemical kinetics. It describes how the rate constant (\( k \)) of a reaction depends on temperature (\( T \)), the activation energy (\( E_a \)), and the pre-exponential factor (\( A \)).

\( k \) is the rate constant.

\( A \) is the pre-exponential factor or frequency factor, which includes factors like collision frequency and orientation of molecules.

\( E_a \) is the activation energy, which is the energy barrier that must be overcome for the reaction to proceed.

\( R \) is the gas constant.

\( T \) is the absolute temperature in Kelvin.

The term \( e^{-\frac{E_a}{RT}} \) represents the fraction of molecules that have enough energy to overcome the activation barrier at a given temperature.

This statement correctly represents the Arrhenius equation, so it is accurate.

2. The temperature coefficient of a reaction is the ratio of rate constants differing by 10°C preferably 25°C and 35°C.

Temperature Coefficient (\( Q_{10} \)) is a measure of how the rate of a reaction changes with a 10°C change in temperature. It is defined as:

\(Q_{10} = \frac{k_{T+10}}{k_T}\)

where \( k_{T+10} \) is the rate constant at temperature \( T + 10^\circ \text{C} \) and \( k_T \) is the rate constant at temperature \( T \).

While the ratio is indeed calculated over a 10°C temperature change, the specific temperatures (like 25°C and 35°C) mentioned in the statement are not universally standardized and can vary.

Although the general idea is correct, the statement’s reference to "preferably 25°C and 35°C" can be misleading since \( Q_{10} \) is not tied to specific temperatures but rather to a 10°C difference.

3. Increase in the rate of reaction with increase in temperature is due to increase in collision frequency.

According to collision theory, an increase in temperature does lead to more frequent collisions between reactant molecules because the kinetic energy of the molecules increases.

However, the primary reason for the increase in reaction rate with temperature is not just the increase in collision frequency but also the increased number of molecules that have sufficient energy to overcome the activation energy barrier. Higher temperatures provide more molecules with the energy needed to reach the transition state.The exponential term in the Arrhenius equation shows that the rate constant increases more significantly with temperature due to this effect, rather than just the frequency of collisions.

This statement is incorrect because it oversimplifies the effect of temperature by focusing only on collision frequency rather than the combined effect of increased kinetic energy and overcoming the activation energy barrier.

4. The rate of chemical reaction depends on the nature of chemical reactants because the threshold energy level differs from one reaction to another.

The nature of reactants affects the rate of reaction because different reactants have different bond strengths, molecular structures, and intrinsic activation energies. These factors influence how easily reactants can reach the transition state and form products. The threshold energy (or activation energy) is different for each reaction based on the reactants' characteristics, affecting the rate at which the reaction proceeds. This statement accurately reflects how the nature of reactants influences reaction rates through the concept of activation energy.

Thus, the incorrect statement is: 3. Increase in the rate of reaction with increase in temperature is due to increase in collision frequency. This statement is incomplete because it does not consider the primary reason for the increase in reaction rate, which is the increase in the fraction of molecules that have enough energy to overcome the activation energy barrier.