![Q.11 Consider a second order reaction, 2A -------->Product The concentration of A is represented as [A]. Which of the following is the CORRECT plot for determining the rate constant for the above reaction?](data:image/svg+xml;base64,PHN2ZyB2aWV3Qm94PSIwIDAgMTkyMCAxMDgwIiB3aWR0aD0iMTkyMCIgaGVpZ2h0PSIxMDgwIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==)
Q.11 Consider a second order reaction, 2A ——–>Product
The concentration of A is represented as [A].
Which of the following is the CORRECT plot for determining the rate constant for
the above reaction?
Correct Answer
For a second-order reaction A → Product, the correct plot to determine the rate constant is 1/[A] vs time, which yields a straight line where the slope equals the rate constant k.
Option Analysis
Each option represents a different graphical test for reaction order using the integrated rate law.
Option (A): log[A] vs time
Shows a curved line for second-order reactions, as this linear plot applies only to first-order kinetics where ln[A] or log[A] decreases linearly with slope = -k/2.303.
Option (B): [A] vs time
Produces an exponential decay curve for second-order reactions, characteristic of first-order decay but not linear; linearity here indicates zero-order kinetics.
Option (C): 1/[A] vs time
Gives a straight line for second-order reactions, derived from the integrated rate law 1/[A]_t = 1/[A]_0 + kt, where slope = k (units: M⁻¹s⁻¹).
Option (D): 1/[A] vs time
Duplicates option (C) based on the description, confirming it as the linear plot for determining k in second-order kinetics.
The correct choice is (C) or (D).
Second Order Reaction Rate Constant Plot Explained
The second order reaction rate constant plot is essential for determining reaction order in chemical kinetics, particularly for CSIR NET aspirants analyzing integrated rate laws. For a second-order reaction like A → Product (rate = k[A]²), plotting 1/[A] vs time produces a linear graph where the slope directly equals the rate constant k. This distinguishes it from zero-order ([A] vs t linear), first-order (ln[A] vs t linear), and confirms second-order behavior through graphical linearity.
Integrated Rate Law Derivation
Start with the second-order differential rate law: -d[A]/dt = k[A]². Integrating from [A]₀ at t=0 to [A]_t at time t yields 1/[A]_t = 1/[A]_0 + kt, a y = mx + c form where m = k. Plotting 1/[A] (y-axis) against time (x-axis) gives a straight line; deviation indicates wrong order.
Why Other Plots Fail
- log[A] vs time curves downward, mimicking first-order but steeper decay.
- [A] vs time shows hyperbolic decay, not linear.
- Only 1/[A] vs time linearity confirms second order and allows k calculation from slope.
CSIR NET Exam Tips
- Practice plotting experimental data: if 1/[A] vs t fits y = mx + c (R² ≈ 1), it’s second order.
- Units verify: k in L mol⁻¹ s⁻¹ or M⁻¹ s⁻¹.
- Common examples include NO₂ decomposition.
- For half-life,
t_{1/2} = 1/(k[A]_0), concentration-dependent unlike first order.
