Which of the following graph(s) are for First Order Reactions?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A and D only
The order of a reaction can be read from the shape of its concentration–time graph, using the integrated rate equations:
First order:
\( \displaystyle \ln[R] = \ln[R]_0 - kt \)
\( \displaystyle \log\frac{[R]_0}{[R]} = \frac{kt}{2.303} \)
A plot of ln[R] against t is a straight line with slope −k and intercept ln[R]0; a plot of log([R]0/[R]) against t is a straight line through the origin with slope k/2.303.
Zero order:
\( \displaystyle [R] = [R]_0 - kt, \qquad \text{Rate} = k[R]^0 = k \)
[R] against t is a straight line with intercept [R]0, and the rate does not change with [R].
(A) ln[R] against t, falling straight line from ln[R]0 — Correct. First order.
(B) Rate against [R], horizontal line — Incorrect. The rate is independent of concentration: zero order.
(C) [R] against t, falling straight line from [R]0 — Incorrect. Zero order.
(D) log([R]0/[R]) against t, rising straight line from the origin — Correct. First order.