Q18. For a reaction, X → Products
Group I contains three plots of reactant concentrations as functions of
time, where x = concentration of reactant X at time t; x0 = concentration of
reactant X at initial time, t = 0. Group II gives a list of different orders of
reaction. Match the plots with the order of the reaction.
(A) (P) – (1), (Q) – (2), (R) – (3)
(B) (P) – (3), (Q) – (2), (R) – (1)
(C) (P) – (2), (Q) – (3), (R) – (1)
(D) (P) – (2), (Q) – (1), (R) – (3)
Concentration-time plots help identify reaction orders in chemical kinetics by matching graph shapes to zero, first, or second-order integrated rate laws. Group I shows three distinct plots of reactant X concentration [X] vs. time t (initial [X] at t=0), while Group II lists matching orders: (P) Zero order, (Q) First order, (R) Second order.
Plot Descriptions
The image displays three unlabeled plots in Group I:
- Plot (i): Straight line with negative slope from high [X] at t=0 to lower [X]—linear decrease.
- Plot (ii): Exponential decay curve, starting steep then flattening—concentration halves predictably.
- Plot (iii): Curve bending upward sharply, concentration drops slowly at first then accelerates inversely.
These shapes derive from integrated rate laws: zero order ([X] = [X]_0 – kt, linear), first order (ln[X] linear, [X] exponential), second order (1/[X] linear, hyperbolic [X]).
Option Analysis
A: (i)-(P), (ii)-(Q), (iii)-(R)
Straight line (i) matches zero order (P)—rate independent of [X]. Exponential curve (ii) matches first order (Q)—rate proportional to [X]. Hyperbolic curve (iii) matches second order (R)—rate proportional to [X]^2. This is correct.
B: (i)-(P), (ii)-(Q), (iii)-(R) (duplicate of A)
Matches correctly as above.
C: (i)-(Q), (ii)-(R), (iii)-(P)
Incorrect: Linear (i) is zero, not first (Q); exponential (ii) is first, not second (R); hyperbolic (iii) is second, not zero (P).
D: (i)-(P), (ii)-(R), (iii)-(Q)
Incorrect: Exponential (ii) is first, not second (R); hyperbolic (iii) is second, not first (Q).
Correct Matching
- (i) → Zero order (P): [X] vs t linear
- (ii) → First order (Q): [X] vs t curved exponentially
- (iii) → Second order (R): [X] vs t concave up
Answer: A
