Chemical Kinetics || Lec # 3 || Zero Order Reaction || First Order Reaction || Dr. Rizwana

Zero-order reactions are defined by a rate that does not depend on the concentration of the reactant. In practical terms, that means the rate law for a reactant A converting into products is constant: the rate equals k, and the concentration of A decreases linearly with time. The lecture derives this by starting from the rate as the negative change in reactant concentration over time, then setting up the proportionality constant k. Because the reaction is “zero order,” the concentration term in the rate expression effectively has an exponent of zero, so k carries the entire rate dependence.

To connect the math to measurable behavior, the lecture introduces the standard concentration-change setup: let x represent the amount of product formed after time t, so the concentration of A at time t becomes (a − x) when the initial concentration is a. Since x increases as time passes, the concentration of A falls accordingly. Solving the resulting differential relationship yields the zero-order integrated form in which x grows linearly with time, matching the expectation of a straight-line concentration–time relationship. The lecture also emphasizes units: for zero-order kinetics, k has units of mol dm⁻³ s⁻¹, consistent with rate being concentration per unit time.

Examples of zero-order behavior are given to anchor the concept in real chemistry. Decomposition of ammonia on a tungsten filament is cited as a zero-order example, and decomposition of hydrogen iodide into hydrogen and iodine on a gold surface is also presented as zero-order. These surface- and condition-dependent systems are typical places where the rate can become independent of bulk reactant concentration.

First-order reactions, by contrast, depend on the concentration of only one reactant. The lecture defines first-order kinetics as a rate law where the rate equals k[A], so the rate decreases as A is consumed. Using the same style of concentration tracking—x as product formed and (a − x) as remaining reactant concentration—the lecture shows that the rate is inversely tied to how much A remains. The differential equation rearranges into a logarithmic integrated form, producing the familiar relationship between time and reactant concentration: ln(a/(a − x)) is proportional to kt.

The lecture then turns to half-life, a key first-order concept. Half-life is the time required for the reactant concentration to drop to half its initial value. By substituting the condition that the remaining reactant is a/2, the lecture arrives at the standard result t₁/₂ = 0.693/k (with 0.693 coming from ln 2). It also notes that half-life can be used with any first-order reaction by plugging in the appropriate k value.

Finally, the lecture describes how first-order kinetics appear on plots. When ln[A] is plotted against time, the result is a straight line. The slope magnitude relates to k, and the sign of the slope reflects whether the logarithmic reactant term is decreasing over time. Thermal decomposition of H2O and N2O5 is listed as an example set for first-order behavior, with the lecture closing by previewing second- and third-order reactions for the next session.