Characteristics

In a zero-order reaction: rate = k (constant), independent of concentration.

Why zero order occurs:

• Catalyst surface saturation (Langmuir-Hinshelwood at high pressure)
• Rate determined by a step that doesn't involve the reactant (e.g., light intensity in photochemical reactions)
• Enzyme saturation (Michaelis-Menten at high substrate concentrations → zero order in substrate)

Classic Example

$2\text{NH}_3(g) \xrightarrow{\text{Pt surface, high P}} \text{N}_2(g) + 3\text{H}_2(g)$

At high pressure: all Pt surface sites occupied → rate = k (zero order in $NH_{3}$) At low pressure: fewer sites occupied → rate ≈ k[$NH_{3}$] (first order)

Key Features of Zero-Order Kinetics

1. [A] vs t graph: Straight line; slope = −k; intercept = [A]_{0}
2. Rate: Constant = k throughout
3. Half-life: t_{1}/{2} = [A]{0}/(2k) — proportional to [A]_{0}
4. Each successive half-life: Shorter than the previous (as [A]_{0} decreases)
5. Completion time: t = [A]_{0}/k (finite! Unlike first order)
6. Number of half-lives to completion: Always exactly 2

Worked Example

k = 0.01 mol/(L·s), [A]_{0} = 0.5 M:

$t_{\text{complete}} = \frac{0.5}{0.01} = 50 \text{ s}$

$t_{1/2} = \frac{0.5}{2 \times 0.01} = 25 \text{ s}$

After t = 30 s: [A] = 0.5 − 0.01 × 30 = 0.5 − 0.3 = 0.2 M