Question

For a first order reaction with rate constant 'k', the slope of the line obtained by plotting log ([R\(_0\)] [R]) vs time is

• A. (k 2.303)
• B. k \(\times\) 2.303
• C. (-k 2.303)
• D. (2.303 k)
• E. (-2.303 k)

Hint:

For a first-order reaction, a plot of log([R\(_0\)]/[R]) vs. time gives a straight line with a positive slope of k/2.303.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The integrated rate law for a first-order reaction is \(k = \frac{2.303}{t} \log \frac{[R_0]}{[R]}\).

Step 2: Detailed Explanation:
Rearrange the integrated rate law to the form of a straight line (y = mx + c): \[ \log \frac{[R_0]}{[R]} = \frac{k}{2.303} \times t \] Here, \(y = \log ([R_0]/[R])\), \(x = t\) (time), slope \(m = \frac{k}{2.303}\), and intercept \(c = 0\).

Step 3: Final Answer:
The slope of the plot is \(k / 2.303\).