Question

What is the slope for a first-order reaction plot of \(\log [A]_{0}/[A]_{t}\) vs time \((t)\)?

• A. slope \(=k/2.303\)
• B. slope \(=-k/2.303\)
• C. slope \(=k\)
• D. slope \(=-k\)

Hint:

Rewrite the integrated first order rate equation in the form of a straight line and read off the slope.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The integrated rate equation for a first order reaction can be rearranged into the equation of a straight line.

Step 2: Write the equation
\(k=\dfrac{2.303}{t}\log\dfrac{[A]_0}{[A]_t}\)

Step 3: Rearrange
\(\log\dfrac{[A]_0}{[A]_t}=\dfrac{k}{2.303}\,t\). This has the form \(y=mx\) with \(y=\log\dfrac{[A]_0}{[A]_t}\) and \(x=t\).

Step 4: Compare the options
The slope is \(\dfrac{k}{2.303}\) and it is positive, which matches the first option.

Final Answer:
The slope of the plot is k/2.303. \[ \boxed{\text{(A) }\text{slope }=k/2.303} \]