Question

For a reaction, the value of rate constant at 300 K is 6.0 ×10⁵ s^-1. The value of Arrhenius factor A at infinitely high temperature is :

• A. 6 × 10⁵ × e^-Ea/300R
• B. e^-Ea/300R
• C. \(\frac{6\times10^{-5}}{300}\)
• D. 6 × 10⁵

Answer 1

The Correct Option is D

Arrhenius Equation

The Arrhenius equation is given by: \[ k = A e^{-\frac{E_a}{RT}} \] where \(k\) is the rate constant, \(A\) is the pre-exponential factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature.

At Infinitely High Temperature

At infinitely high temperature, \(e^{-\frac{E_a}{RT}}\) approaches 1, because the exponential term becomes negligible. Therefore, the rate constant \(k\) approaches the pre-exponential factor \(A\).

Given

The rate constant \(k\) at 300 K is \(6.0 \times 10^5 \, \text{s}^{-1}\).

Conclusion

Therefore, at infinitely high temperature, the Arrhenius factor \(A\) is: \[ \boxed{6 \times 10^5} \]

Answer 2

The relationship between the rate constant (k), Arrhenius factor (A), activation energy (\(E_a\)), gas constant (R), and absolute temperature (T) is given by the Arrhenius equation: $$ k = A e^{-E_a/RT} $$

We are asked to find the value of the Arrhenius factor A. The Arrhenius factor A, also known as the pre-exponential factor, is considered a constant for a given reaction in the context of the basic Arrhenius equation. It represents the frequency of collisions with the proper orientation.

The question asks for the "value of Arrhenius factor A at infinitely high temperature". This phrasing can be interpreted as finding the limit of the rate constant k as the temperature T approaches infinity, because this limit is equal to A. Let's examine the limit of the Arrhenius equation as \( T \rightarrow \infty \): $$ \lim_{T \to \infty} k = \lim_{T \to \infty} \left( A e^{-E_a/RT} \right) $$

As \( T \rightarrow \infty \), the term \( \frac{E_a}{RT} \rightarrow 0 \) (assuming \( E_a \ge 0 \) and R > 0). Therefore, the exponential term \( e^{-E_a/RT} \rightarrow e^0 = 1 \).

Substituting this back into the limit: $$ \lim_{T \to \infty} k = A \times 1 = A $$ Thus, the rate constant approaches the Arrhenius factor A at infinitely high temperature.

We are given that at T = 300 K, the rate constant \( k = 6.0 \times 10^5 \) s⁻¹. So, $$ 6.0 \times 10^5 \text{ s}^{-1} = A e^{-E_a/(R \times 300)} $$ Without knowing the activation energy \(E_a\), we cannot determine A precisely from this equation alone.

However, let's consider the options provided. Option (D) is \( 6 \times 10^5 \). This is the value of k at 300 K. If we assume that the activation energy \(E_a = 0\), then the exponential term \( e^{-E_a/RT} = e^0 = 1 \) for all temperatures. In this specific case, the Arrhenius equation becomes \( k = A \). If \( k = A \), then \( A \) would be equal to the rate constant at any temperature, including 300 K. So, if \( E_a = 0 \), then \( A = k(300 \text{ K}) = 6.0 \times 10^5 \) s⁻¹.

Given the options, it is most likely that the question implies either that the activation energy is zero (or negligible) or that the value given for k at 300 K is intended to be the value of A. The question asks for the value of A, and \( 6 \times 10^5 \) is provided as an option matching the given rate constant. The phrasing "at infinitely high temperature" signifies the condition under which k equals A.

Final Answer: The final answer is \({6 \times 10^5} \)