Question

In a first order reaction, a straight line is obtained when plotting

• A. [R] vs t
• B. ln[R] vs t
• C. 1/[R] vs t
• D. 1/ln[R] vs t

Hint:

Zero order: [R] vs t is linear. First order: ln[R] vs t is linear. Second order: 1/[R] vs t is linear.

Answer 1

The Correct Option is B

Step 1: Concept
The integrated rate law for a first-order reaction is $\ln[R] = -kt + \ln[R]_0$.

Step 2: Analysis
This equation is in the form of a straight line, $y = mx + c$, where $y = \ln[R]$, $m = -k$, and $x = t$.

Step 3: Reasoning
Plotting $[R]$ vs $t$ gives an exponential decay, while $1/[R]$ vs $t$ gives a straight line only for second-order reactions.

Step 4: Conclusion
A plot of $\ln[R]$ against time $t$ yields a straight line with a slope of $-k$. Final Answer: (B)