Question

Consider the following statements related to temperature dependence of rate constants. Identify the correct statements,
A. The Arrhenius equation holds true only for an elementary homogeneous reaction.
B. The unit of A is same as that of k in Arrhenius equation.
C. At a given temperature, a low activation energy means a fast reaction.
D. A and Ea as used in Arrhenius equation depend on temperature.
E. When Ea >> RT. A and Ea become interdependent.
Choose the correct answer from the options given below :

• A. A, C and D Only
• B. B, D and E Only
• C. B and C Only
• D. A and B Only

Hint:

The Arrhenius equation \( k = A e^{-E_a/RT} \) is fundamental to understanding the temperature dependence of reaction rates. Remember that a lower activation energy leads to a faster reaction, and the pre-exponential factor has the same units as the rate constant. In its basic form, \( A \) and \( E_a \) are considered temperature-independent.

Answer 1

The Correct Option is C

The Arrhenius equation describes the temperature dependence of the rate constant \( k \) of a chemical reaction: \[ k = A e^{-E_a/RT} \] where: 
\( k \) is the rate constant 
\( A \) is the pre-exponential factor or frequency factor 
\( E_a \) is the activation energy 
\( R \) is the gas constant 
\( T \) is the absolute temperature 
Let's analyze each statement: 

A. The Arrhenius equation holds true only for an elementary homogeneous reaction. The Arrhenius equation is experimentally found to be applicable to both elementary and complex reactions, although for complex reactions, the 'activation energy' may be an overall parameter that does not correspond to a single energy barrier. Thus, statement A is false. 

B. The unit of A is the same as that of k in the Arrhenius equation. The exponential term \( e^{-E_a/RT} \) is dimensionless. Therefore, the unit of \( A \) must be the same as the unit of \( k \) for the equation to be dimensionally consistent. The unit of \( k \) depends on the order of the reaction. So, the unit of \( A \) also depends on the order of the reaction and is the same as that of \( k \). Thus, statement B is true. 

C. At a given temperature, a low activation energy means a fast reaction. The term \( -E_a/RT \) in the exponent shows that a smaller value of \( E_a \) (lower activation energy) leads to a larger value of \( k \) (rate constant), which implies a faster reaction rate. Thus, statement C is true. 

D. A and Ea as used in Arrhenius equation depend on temperature. In the simple Arrhenius theory, both the pre-exponential factor \( A \) and the activation energy \( E_a \) are considered to be temperature-independent. However, in more advanced treatments (like collision theory with temperature-dependent collision frequency or transition state theory with temperature-dependent entropy of activation), \( A \) can have a weak temperature dependence (typically proportional to \( T^n \) where \( n \) is a small integer or fraction), and \( E_a \) can also exhibit slight temperature dependence. For basic applications of the Arrhenius equation, they are usually treated as temperature-independent. The provided solution states they are temperature-independent, so we consider statement D as false in the context of the basic Arrhenius equation. 

E. When Ea >> RT. A and Ea become interdependent. There is no inherent interdependence between \( A \) and \( E_a \) arising solely from the condition \( E_a >> RT \). \( A \) relates to the frequency of collisions (or the frequency factor related to the entropy of activation in transition state theory) and the orientation factor, while \( E_a \) is the energy barrier that must be overcome for the reaction to occur. These parameters are fundamentally independent. Thus, statement E is false. 

The correct statements are B and C. Therefore, the correct option is (3).