Question

Calculate the rate constant of first order reaction if the slope of graph of \(\log [A]_{0}/[A]_{t}\) versus time is \(8.5\times 10^{-3}\) \(\text{s}^{-1}\).

• A. \(2.728\times 10^{-2}\) \(\text{s}^{-1}\)
• B. \(2.258\times 10^{-2}\) \(\text{s}^{-1}\)
• C. \(1.132\times 10^{-2}\) \(\text{s}^{-1}\)
• D. \(1.958\times 10^{-2}\) \(\text{s}^{-1}\)

Hint:

For a first order reaction the slope of log([A]0/[A]t) against time equals k divided by 2.303.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The first order integrated rate law is \(\log\dfrac{[A]_{0}}{[A]_{t}}=\dfrac{k}{2.303}\,t\). A plot of \(\log\dfrac{[A]_{0}}{[A]_{t}}\) against \(t\) is a straight line.

Step 2: Use the slope
Slope \(=\dfrac{k}{2.303}\), so \(k=2.303\times\text{slope}\).

Step 3: Calculation
\(k=2.303\times 8.5\times 10^{-3}=1.958\times 10^{-2}\ \text{s}^{-1}\), option (D).

Final Answer:
The rate constant is \(1.958\times 10^{-2}\ \text{s}^{-1}\). \[ \boxed{\text{(D) }1.958\times 10^{-2}\ \text{s}^{-1}} \]