How it Works
Chemists rarely know a reaction's rate law in advance — it has to be measured. The method of initial rates does this by running several trials, each starting from a different concentration [A]₀, and clocking only the instantaneous rate right at t=0 of each one, before any product buildup complicates the picture. Because rate₀ = k[A]₀ⁿ, plotting ln(rate₀) against ln([A]₀) turns the exponent n — the reaction order — into the slope of a straight line. Run two or more trials at different starting concentrations and switch the view to "Method of initial rates" to watch that slope emerge from the point cloud.
A single trial's full concentration-versus-time decay carries the same information in a different form. Integrating the rate law −d[A]/dt = k[A]ⁿ for each candidate order predicts a different quantity that should vary linearly with time: [A] itself for zero order, ln[A] for first order, or 1/[A] for second order. Toggle the linearization view to try each transformation of the same trial's decay data — only the correct one will straighten into a line, and its R² will sit close to 1.000 while the other two curve visibly away from their fitted lines.
This 2D companion renders the same synthetic-kinetics engine as the 3D version through a plain HTML5 canvas: a particle panel where the reactant population visibly thins during each timed trial, and a plot panel with a live least-squares fit line — no WebGL required.
Method of initial rates: ln(rate₀) = ln k + n·ln[A]₀ (slope = n)
Integrated (linear) forms — n=0: [A]=[A]₀−kt · n=1: ln[A]=ln[A]₀−kt · n=2: 1/[A]=1/[A]₀+kt
Half-life — n=0: t½=[A]₀/2k · n=1: t½=ln2/k (constant) · n=2: t½=1/(k[A]₀)
Frequently Asked Questions
What is the "order" of a chemical reaction?
The order of a reaction with respect to a reactant is the exponent on that reactant's concentration in the experimentally determined rate law, rate = k[A]ⁿ. The overall order is the sum of all such exponents. Order is not read off the balanced equation — it must be measured.
What is the method of initial rates?
The method of initial rates measures the instantaneous rate at the very start of several separate trials, each begun at a different initial concentration [A]₀. Plotting ln(rate₀) against ln([A]₀) gives a straight line whose slope is the reaction order n.
Why does plotting ln[A] vs time give a straight line only for a first-order reaction?
Integrating −d[A]/dt = k[A] gives ln[A] = ln[A]₀ − kt, which is linear in t with slope −k. For a zero-order or second-order reaction, ln[A] is a curved function of time, so only the truly first-order case produces a straight line here.
Why is the half-life of a first-order reaction independent of the starting concentration?
For a first-order reaction t½ = ln2/k, a formula with no [A]₀ term — halving the amount always takes the same amount of time no matter how much you started with. This constant half-life is a hallmark of first-order kinetics.
What is R² and why do chemists use it to identify reaction order?
R² measures how closely points follow a straight line, from 0 (no relationship) to 1 (a perfect line). Because real data always carries noise, chemists fit all three integrated-rate-law transformations to the same decay data and pick the order whose R² sits closest to 1.