Rate of Reaction and Rate Laws — Part 2: Integrated rate laws, half-life and mechanism: visual lesson, ISC Class 12 Chemistry

Lesson

Concentration and time

Part 2 — how concentration changes with time, and the steps by which reactions happen.

In this lesson you will

Use the integrated rate equation for a zero-order reaction and interpret its graph
Derive the integrated rate equation and half-life of a first-order reaction
Solve problems on rate constant, half-life and time for a given fraction to react
Distinguish order from molecularity and write the rate law from the slowest step of a mechanism

Concept

Zero-order reactions

Rate $= -\dfrac{d[\ce{R}]}{dt} = k$ . Integrating from $[\ce{R}]_0$ at $t = 0$ : $[\ce{R}] = [\ce{R}]_0 - kt$ . Half-life $t_{1/2} = [\ce{R}]_0/2k$ (proportional to the initial concentration). Examples: decomposition of NH₃ on hot platinum at high pressure; some enzyme reactions at saturation; H₂ + Cl₂ photochemical reaction.

[\ce{R}] = [\ce{R}]_0 - kt, \qquad k = \frac{[\ce{R}]_0 - [\ce{R}]}{t}, \qquad t_{1/2} = \frac{[\ce{R}]_0}{2k}

Table of features of a zero-order reaction
Feature	Zero order
Straight-line plot	[R] against t
Slope	−k
Unit of k	mol L⁻¹ s⁻¹
Half-life	Proportional to [R]₀

Diagram

Zero order on a graph

Zero order: straight line, slope −k

k = 0.02 mol L⁻¹ min⁻¹ in this example.

A plot of $[\ce{R}]$ against $t$ is a straight line with intercept $[\ce{R}]_0$ and slope $-k$ ; the reaction stops when the reactant is used up.

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