Question

Calculate rate constant of a first order reaction having pre-exponential factor $1.6\times10^{-13}\text{s}^{-1}$. ($E_{a}/2.303RT=21$)}

• A. $1.6\times10^{-13}$
• B. $3.2\times10^{-13}$
• C. $3.2\times10^{-8}$
• D. $1.6\times10^{-34}$

Hint:

When dealing with Arrhenius equations, remember that $e^{-x}$ is mathematically equivalent to $10^{-x / 2.303}$. Therefore, $e^{-E_a/RT} = 10^{-E_a/2.303RT}$. You can plug the given exponent directly onto a base 10!

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Arrhenius equation relates the rate constant ($k$) to the pre-exponential factor ($A$) and activation energy ($E_a$).

Step 2: Formula Application:
$\log k = \log A - \frac{E_a}{2.303RT}$

Step 3: Explanation:
Given $A = 1.6 \times 10^{-13}$ and $\frac{E_a}{2.303RT} = 21$. $\log k = \log(1.6 \times 10^{-13}) - 21$ $\log k = (\log 1.6 - 13) - 21$ $\log k = 0.2041 - 34 = -33.7959$ $k = \text{antilog}(-33.7959) = 1.6 \times 10^{-34}$ s$^{-1}$.

Step 4: Final Answer:
The rate constant is $1.6 \times 10^{-34}$ s$^{-1}$. (Note: Please check if there was a typo in your provided options, as the calculated value is $10^{-34}$).