Can a reaction have a fractional or even zero order?

Yes. Fractional orders often arise from complex multi-step mechanisms, and zero order occurs when the rate is limited by something other than reactant concentration, such as a saturated catalyst surface, so the rate stays constant until a reactant is nearly exhausted.

Why is the half-life of a first-order reaction independent of concentration?

For first-order kinetics the rate is directly proportional to concentration, so the fractional decrease per unit time is constant; the time to fall to half is therefore the same regardless of the starting amount, which is why radioactive decay has a fixed half-life.

Reaction Rate Laws

A rate law expresses how the speed of a reaction depends on the concentrations of its reactants, and its integrated form predicts how those concentrations evolve in time.

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Definition

A reaction rate law is an empirical equation relating the instantaneous rate of a reaction to the concentrations of reactants, each raised to a power that defines its order, with a temperature-dependent rate constant.

Scope

This topic covers the empirical determination of rate laws: the definition of reaction rate, the concepts of order and molecularity, the rate constant, and methods such as initial rates and isolation for finding orders. It develops the integrated rate equations for zero-, first-, and second-order reactions, the corresponding half-lives, and the analysis of reversible, parallel, and consecutive reactions. The reconstruction of mechanisms from rate laws and the theoretical origin of rate constants are treated in separate topics.

Core questions

How is reaction order determined experimentally from concentration-time data?
What are the integrated rate equations and half-lives for the common reaction orders?
How do molecularity and order differ, and why need they not coincide?
How are parallel and consecutive reactions analyzed kinetically?

Key concepts

Reaction rate and rate constant
Order and molecularity
Integrated rate equations
Half-life and characteristic time
Method of initial rates and isolation

Key theories

Integrated rate laws: Integrating the differential rate law for a given order yields explicit concentration-time relationships, linear plots that identify the order, and characteristic half-lives that are constant for first-order reactions but concentration-dependent otherwise.
Determination of order by isolation and initial rates: By holding all but one reactant in large excess, or by measuring rates at the very start before products accumulate, the dependence on each reactant can be isolated and the overall rate law assembled.

Clinical relevance

Rate laws set the design equations for chemical reactors, predict the decomposition and shelf life of drugs and reagents, govern the timing of dosing and clearance in pharmacokinetics, and quantify the persistence of pollutants in environmental systems.

History

Wilhelmy's 1850 study of sucrose inversion gave the first quantitative rate law; Guldberg and Waage's law of mass action in the 1860s connected rates to concentrations, and van't Hoff systematized order and molecularity in his 1884 studies of chemical dynamics.

Key figures

Ludwig Wilhelmy
Cato Maximilian Guldberg
Peter Waage

Seminal works

atkins2018
laidler1987

Frequently asked questions

Can a reaction have a fractional or even zero order?: Yes. Fractional orders often arise from complex multi-step mechanisms, and zero order occurs when the rate is limited by something other than reactant concentration, such as a saturated catalyst surface, so the rate stays constant until a reactant is nearly exhausted.
Why is the half-life of a first-order reaction independent of concentration?: For first-order kinetics the rate is directly proportional to concentration, so the fractional decrease per unit time is constant; the time to fall to half is therefore the same regardless of the starting amount, which is why radioactive decay has a fixed half-life.