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

To solve this question, we need to analyze each option concerning the Arrhenius equation and temperature dependence of rate constants.

The Arrhenius equation is given as:

k = $Ae^{-Ea/RT}$

Where:

• \(k\): Rate constant
• \(A\): Frequency factor (also known as pre-exponential factor)
• \(Ea\): Activation energy
• \(R\): Universal gas constant
• \(T\): Temperature in Kelvin

Now, let's examine each statement:

1. Statement A: The Arrhenius equation holds true only for an elementary homogeneous reaction.
   This statement is incorrect. The Arrhenius equation is a general equation that applies to a wide range of reactions, not just elementary homogeneous reactions. It can be used for complex reactions as well.
2. Statement B: The unit of A is same as that of k in Arrhenius equation.
   This statement is correct. The frequency factor \(A\) has the same units as the rate constant \(k\) because they need to match in this equation.
3. Statement C: At a given temperature, a low activation energy means a fast reaction.
   This statement is correct. A lower activation energy \(Ea\) implies less energy is required for the reactants to reach the transition state, resulting in a faster reaction at a given temperature.
4. Statement D: A and Ea as used in Arrhenius equation depend on temperature.
   This statement is incorrect. While the rate constant \(k\) indeed depends on temperature, the frequency factor \(A\) and activation energy \(Ea\) are considered constants at a given temperature span.
5. Statement E: When Ea >> RT, A and Ea become interdependent.
   This statement is incorrect. The pre-exponential factor \(A\) and the activation energy \(Ea\) remain independent parameters, regardless of the relation between \(Ea\) and \(RT\).

From the explanation above, the correct statements are B and C.

Therefore, the correct answer is: B and C Only

Answer 2

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).