Read the passage carefully and answer the Questions.
The decomposition of \( N_2O_5 (g) \) is given as
\( N_2O_5 (g) → 2NO_2(g) +\frac{1}{2}O_2(g) \)
The above reaction is found to be of first order.
Predict the intercept for the plot of \( \log\frac{[N_2O_5]_o}{[N_2O_5]} \) versus time
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → zero
The integrated rate equation of a first order reaction can be rearranged to the form of a straight line, y = mx + c:
\( \displaystyle k = \frac{2.303}{t}\log\frac{[\mathrm{R}]_0}{[\mathrm{R}]} \)
\( \displaystyle \log\frac{[\mathrm{R}]_0}{[\mathrm{R}]} = \frac{k}{2.303}\,t + 0 \)
So a plot of \( \log([\ce{N2O5}]_0/[\ce{N2O5}]) \) against t is a straight line with slope k/2.303 and intercept zero: at t = 0, [R] = [R]0 and log 1 = 0, so the line passes through the origin.
Why the other options are incorrect
Option (1) 2.303 k — Incorrect. This is not a feature of the plot; neither the slope nor the intercept has this value.
Option (2) 2.303/k — Incorrect. This factor appears in the expression for t (\( t = \frac{2.303}{k}\log\frac{[\mathrm{R}]_0}{[\mathrm{R}]} \)), not as an intercept.
Option (4) k/2.303 — Incorrect. This is the slope of the line, not its intercept.
NCERT (2026-27 edition):
First Order Reactions – …
