Question

Calculate rate constant of a first order reaction having pre exponential factor \(1.6 \times 10^{13} \mathrm{~s}^{-1}\).

\[ \left(\mathrm{E}_{\mathrm{a}} / 2.303 \mathrm{RT}=21\right) \]

• A. \(1.6\times 10^{-13}\)
• B. \(3.2\times 10^{-13}\)
• C. \(3.2\times 10^{-8}\)
• D. \(1.6\times 10^{-8}\)

Hint:

Use k = A e^(-Ea/RT) and convert the exponent into a power of 10 using the given Ea/2.303RT.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Arrhenius equation: \(k=A\,e^{-E_{a}/RT}\), or \(\log k=\log A-\dfrac{E_{a}}{2.303RT}\).

Step 2: Substitute
\(\log k=\log(1.6\times10^{13})-21\).

Step 3: Calculation
\(k=1.6\times10^{13}\times10^{-21}=1.6\times10^{-8}\text{ s}^{-1}\).

Final Answer:
The rate constant is 1.6 x 10^-8 per second. \[ \boxed{\text{(D) }1.6\times10^{-8}} \]