Mastering Kinetics Graphs
A comprehensive visual guide to Zero, First, Second, and n-th Order reaction graphs.
In chemical kinetics, graphical analysis is the most reliable way to determine the order of a reaction. By plotting different functions of concentration against time, we look for the plot that yields a straight line ($y = mx + c$).
1 Zero Order Reactions
Rate Law: Rate = $k[A]^0 = k$ (Constant rate)
Integrated Rate Equation: $[A] = [A]_0 - kt$
Half-Life ($t_{1/2}$): $t_{1/2} = \frac{[A]_0}{2k}$
Concentration vs. Time
$y = mx + c \implies [A] = -kt + [A]_0$
Rate vs. Concentration
Rate is independent of concentration
2 First Order Reactions
Rate Law: Rate = $k[A]^1$
Integrated Rate Equation: $\ln[A] = \ln[A]_0 - kt$ (or $\log[A] = \log[A]_0 - \frac{kt}{2.303}$)
Half-Life ($t_{1/2}$): $t_{1/2} = \frac{\ln 2}{k} \approx \frac{0.693}{k}$ (Independent of initial concentration)
$\ln[A]$ vs. Time
$y = mx + c \implies \ln[A] = -kt + \ln[A]_0$
Half-life vs. Initial Conc.
Half-life is a constant
Note on Exponential Decay: If you plot plain concentration $[A]$ vs. time $t$ for a first-order reaction, you get an exponential decay curve (not a straight line) represented by $[A] = [A]_0 e^{-kt}$. Radioactive decay strictly follows first-order kinetics.
3 Second Order Reactions
Rate Law: Rate = $k[A]^2$
Integrated Rate Equation: $\frac{1}{[A]} = \frac{1}{[A]_0} + kt$
Half-Life ($t_{1/2}$): $t_{1/2} = \frac{1}{k[A]_0}$
$1/[A]$ vs. Time
$y = mx + c \implies \frac{1}{[A]} = kt + \frac{1}{[A]_0}$
Rate vs. $[A]^2$
Direct proportionality to the square
4 General Formula (n-th Order)
To generalize for any reaction order $n$ (where $n \neq 1$), the half-life dependence on the initial concentration is given by a master equation:
Master Half-Life Relation
$$ t_{1/2} \propto \frac{1}{[A]_0^{n-1}} $$
| Order (n) | Straight Line Plot | Slope | Half-Life Dependency |
|---|---|---|---|
| 0 | $[A]$ vs $t$ | $-k$ | $t_{1/2} \propto [A]_0$ |
| 1 | $\ln[A]$ vs $t$ | $-k$ | $t_{1/2} \propto [A]_0^0$ (Constant) |
| 2 | $1/[A]$ vs $t$ | $+k$ | $t_{1/2} \propto 1/[A]_0$ |
Knowledge Check
10 Practice MCQs on Chemical Kinetics Graphs
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