Zero Order Reaction
Chemical Kinetics Class 12 | Rate Laws, Half-Life & Graphs
1. Definition & Rate Law
A Zero Order Reaction is a reaction in which the rate is independent of the concentration of the reactants. The rate remains constant throughout the reaction.
Reaction: $R \rightarrow P$
Rate law: $\text{Rate} = -\frac{d[R]}{dt} = k[R]^0 = k$
Rate law: $\text{Rate} = -\frac{d[R]}{dt} = k[R]^0 = k$
Examples:
- Decomposition of Ammonia ($NH_3$) on a hot Platinum surface at high pressure.
- Decomposition of $HI$ on Gold surface.
- Enzyme catalyzed reactions (at high substrate concentration).
2. Integrated Rate Equation
Since Rate $= -d[R]/dt = k$, we integrate both sides:
$$ \int d[R] = -k \int dt $$ $$ [R] = -kt + I $$At $t=0$, concentration is $[R]_0$, so the integration constant $I = [R]_0$.
$$ [R] = -kt + [R]_0 $$
$$ k = \frac{[R]_0 - [R]}{t} $$
$$ k = \frac{[R]_0 - [R]}{t} $$
3. Half-Life ($t_{1/2}$)
The time at which the concentration of reactant becomes half of its initial value ($[R] = [R]_0/2$).
$$ k = \frac{[R]_0 - [R]_0/2}{t_{1/2}} $$
$$ t_{1/2} = \frac{[R]_0}{2k} $$
Key Point: Unlike first-order reactions, the half-life of a zero-order reaction is directly proportional to the initial concentration of the reactant.
4. Important Graphs
- $[R]$ vs $t$: A straight line with negative slope $= -k$ and intercept $= [R]_0$.
- Rate vs Concentration: A straight line parallel to the concentration axis (horizontal), as rate is constant.
- $t_{1/2}$ vs $[R]_0$: A straight line passing through the origin with slope $= 1/2k$.
5. Time for Completion
Zero order reactions go to completion in finite time.
$$ t_{100\%} = \frac{[R]_0}{k} $$Unit of Rate Constant ($k$): Same as rate of reaction: $mol \cdot L^{-1} \cdot s^{-1}$.
Practice Quiz
Test your concepts on Zero Order Kinetics.
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