The rate law and the order of a reaction are often found with the help of its integrated rate equation rather than its differential rate equation. What makes the integrated rate equation useful for this?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → It relates the concentrations measured at different times directly to the rate constant.
The differential rate equation uses the instantaneous rate, which has to be found from the slope of a tangent drawn on the concentration-time plot. That is slow and makes the rate law hard to fix. Integrating it gives an equation in the concentrations at different times, which are measured directly, and the rate constant.
Why the other options are incorrect
Option (2) It gives the instantaneous rate from the slope of the tangent at each point of the concentration-time curve. — Incorrect. Drawing tangents is the difficulty that the integrated equation removes.
Option (3) It shows how the rate constant changes with temperature. — Incorrect. The effect of temperature on k is given by the Arrhenius equation, not by the integrated rate equation.
Option (4) It has the same form for zero order and first order reactions. — Incorrect. The integrated equations are different for different orders: [R] = −kt + [R]0 for zero order and ln[R] = −kt + ln[R]0 for first order.
NCERT (2026-27 edition):
3.3 Integrated Rate Equations – “It is not always convenient to determine the instantaneous rate, as it is measured by determination of slope of the tangent at point ‘t’ in concentration vs time plot … This makes it difficult to determine the rate law and hence the order of the reaction. In order to avoid this difficulty, we can integrate the differential rate equation to give a relation between directly measured experimental data, i.e., concentrations at different times and rate constant.”