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For a ZERO-ORDER reaction $A \to \text{products}$, which graph is a STRAIGHT LINE?
A$[A]$ vs $t$, with slope $-k$
B$\ln[A]$ vs $t$, with slope $-k$
C$1/[A]$ vs $t$, with slope $+k$
D$[A]^2$ vs $t$, with slope $-k$
Answer & Solution
Correct answer: A. $[A]$ vs $t$, with slope $-k$
1. For zero order, $\text{rate} = -d[A]/dt = k[A]^0 = k$.
2. Integrate: $-d[A] = k\,dt \Rightarrow [A] = [A]_0 - k\,t$.
3. This is the equation of a STRAIGHT LINE with $[A]$ on the y-axis, $t$ on the x-axis, slope $-k$, and y-intercept $[A]_0$.
4. Option B is the FIRST-order straight-line plot ($\ln[A]$ vs $t$). Option C is the SECOND-order straight-line plot ($1/[A]$ vs $t$). Option D doesn't yield a linear relationship for any standard order.
5. These linear plots are how chemists EXPERIMENTALLY determine the order of a reaction: try plotting each linearisation; the one that gives a straight line tells you the order.
_Source: NCERT Class 12 Chemistry Part 1, Ch 3, §3.3.1 (Zero Order Reactions, integrated form), p. 12._
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