While systematically calculating the order of the given reaction, 2A + B → C + D using the data given below, the most appropriate correct sequence of steps (from the below given steps) that should be followed is
| Experiment | [A] (mol L−1) | [B] (mol L−1) | Initial rate of formation of D (mol L−1 min−1) |
| I | 0.1 | 0.1 | 6.00 × 10−3 |
| II | 0.3 | 0.2 | 7.20 × 10−2 |
| III | 0.3 | 0.4 | 2.88 × 10−1 |
| IV | 0.4 | 0.1 | 2.40 × 10−2 |
A. Independently compare the proposed Rate Law equations of experiment II with III, AND of experiment I with IV.
B. Divide the proposed Rate Law equations for experiments I and IV to determine the value of m. Similarly, divide the proposed Rate Law equations for experiments II and III to determine the value of n.
C. Assume the Rate Law equation for the given reaction to be, Rate = k[A]m[B]n
D. Add m and n to calculate the numerical value of order of the reaction.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → C, A, B, D
The order of a reaction is found experimentally by the initial rate method. The rate law is first written with unknown powers, then experiments are compared in pairs in which only one concentration changes, so the change in rate is due to that reactant alone.
(C) comes first: the rate law is assumed with unknown orders m and n:
\( \displaystyle \text{Rate}=k[\mathrm{A}]^m[\mathrm{B}]^n \)
(A) next: the suitable pairs are chosen. In II and III, [A] is the same (0.3); in I and IV, [B] is the same (0.1).
(B) then: the rate equations of each pair are divided.
\( \displaystyle \frac{\text{Rate}_{IV}}{\text{Rate}_{I}}=\frac{2.40\times10^{-2}}{6.00\times10^{-3}}=\left(\frac{0.4}{0.1}\right)^m\ \Rightarrow\ 4=4^m\ \Rightarrow\ m=1 \)
\( \displaystyle \frac{\text{Rate}_{III}}{\text{Rate}_{II}}=\frac{2.88\times10^{-1}}{7.20\times10^{-2}}=\left(\frac{0.4}{0.2}\right)^n\ \Rightarrow\ 4=2^n\ \Rightarrow\ n=2 \)
(D) last: the order of the reaction is m + n = 1 + 2 = 3.
Shortcut: The rate law must be assumed first (C) and the orders added last (D). Only Options (3) and (4) start with C, and choosing the pairs (A) must come before dividing them (B), which leaves Option (3).