Zero and First Order Reactions — Core Principles

Core Principles

Zero and first-order reactions are fundamental concepts in chemical kinetics, describing how reaction rates depend on reactant concentrations. A zero-order reaction proceeds at a constant rate, entirely independent of the reactant's concentration.

Its integrated rate law is $[A]_t = [A]_0 - kt$, and a plot of $[A]_t$ vs. time yields a straight line with slope $-k$. The half-life ($t_{1/2} = [A]_0 / 2k$) is directly proportional to the initial concentration.

The rate constant $k$ has units of mol L$^{-1}$ s$^{-1}$. Examples include enzyme-saturated reactions or surface-catalyzed reactions.

A first-order reaction has a rate directly proportional to the first power of the reactant's concentration. Its integrated rate law is $ln([A]_t/[A]_0) = -kt$ (or $2.303 \log([A]_t/[A]_0) = -kt$), and a plot of $ln[A]_t$ vs.

time gives a straight line with slope $-k$. Crucially, its half-life ($t_{1/2} = 0.693/k$) is constant and independent of the initial concentration. The rate constant $k$ has units of s$^{-1}$. Radioactive decay is a classic example.

Understanding these distinctions, including their integrated rate laws, half-life expressions, and graphical representations, is vital for NEET.

Important Differences

vs First-Order Reactions

Aspect	This Topic	First-Order Reactions
Rate Law	Rate = $k[A]^0 = k$	Rate = $k[A]^1 = k[A]$
Integrated Rate Law	$[A]_t = [A]_0 - kt$	$\ln([A]_t/[A]_0) = -kt$ or $2.303 \log([A]_t/[A]_0) = -kt$
Units of Rate Constant ($k$)	Concentration/Time (e.g., mol L$^{-1}$ s$^{-1}$)	Time$^{-1}$ (e.g., s$^{-1}$)
Half-life ($t_{1/2}$)	$t_{1/2} = [A]_0 / 2k$ (depends on initial concentration)	$t_{1/2} = 0.693 / k$ (independent of initial concentration)
Graphical Plot for Linearity	$[A]_t$ vs. $t$ (slope = $-k$)	$\ln[A]_t$ vs. $t$ (slope = $-k$)
Effect of Doubling [A]	Rate remains unchanged	Rate doubles

Zero-order reactions have a constant rate, independent of reactant concentration, with a half-life directly proportional to the initial concentration. Their rate constant units are concentration per time. In contrast, first-order reactions have a rate directly proportional to the reactant concentration, and their half-life is constant, independent of the initial concentration. Their rate constant units are inverse time. These differences are critical for identifying reaction order and solving related numerical problems in NEET.