Gym · Kinetics

Kinetics: integrated rate laws, half-life, and reading the order

A reaction's ORDER sets its clock. Each drill gives a reaction, its measured order, and its rate constant k (a sourced value), and asks one of three things: how much reactant is left after a time t (apply the order's integrated rate law — [A]₀−kt for zero order, [A]₀e^(−kt) for first, 1/[A]₀+kt for second), what its half-life is (t½ = [A]₀/2k, ln2/k, or 1/k[A]₀), or — given three successive half-lives — what the order must be. Type the numeric answers to three significant figures; pick the order from the menu. The one mistake the drill keeps catching is using the WRONG order's formula, so every diagnostic names which order you slipped into. The arithmetic is machine-checked; the rate law and order are a disclosed model, and k is a sourced measured value.

Model: The rate law and its reaction order are an experimentally determined model — not read off the balanced-equation coefficients. The order and the rate constant k are the sourced data; the integrated rate law and half-life follow exactly from them. The rate constant k is constant over the run (fixed temperature, unchanging conditions), so the integrated rate law and half-life hold throughout. The arithmetic is machine-checked and the answer is reported to 3 significant figures.