Chemical Kinetics Calculator

Equilibrium tells you how far a reaction can go; kinetics tells you how fast it actually gets there — and a reaction that is thermodynamically allowed but kinetically stalled (like diamond turning into graphite, or iron rusting over centuries) is a chemistry fact of life. Kinetics measures how quickly concentration changes, and its central object is the rate law: rate = k[A]ⁿ, where n is the reaction order and k the rate constant. In the sample, a first-order reaction with k = 0.01 s⁻¹ at [A] = 0.5 M runs at 5.000×10⁻³ M/s.

The order says how sensitively the rate leans on concentration. Zero order: rate = k, flat — the reaction is running at capacity for some other reason (a saturated catalyst surface, an enzyme maxed out, light supply), so [A] falls in a straight line until it runs out. First order: rate ∝ [A] — each molecule decays independently of its neighbors; radioactive decay and most thermal decompositions live here. Second order: rate ∝ [A]² — two molecules must collide, so dilution hurts quadratically. The units of k change with the order (M·s⁻¹ for zero, s⁻¹ for first, M⁻¹·s⁻¹ for second), which is why the panel's unit selector follows the order dropdown. The honest experimental test is the method of initial rates: double one concentration at a time and watch the rate stay flat (zero), double (first), or quadruple (second).

The differential rate law describes the slope; the integrated rate law integrates it into an actual [A]-versus-time curve. First order gives a pure exponential: the sample starts at 1.0 M with k = 0.01 s⁻¹, and after t = 100 s holds e⁻¹ = 0.3679 M (36.79% remaining). This is also the classic lab trick for measuring order: plot ln[A] vs t, 1/[A] vs t, or [A] vs t — whichever comes out a straight line announces the order (first, second, or zero respectively).

Only first-order reactions have a concentration-independent half-life, t½ = ln2/k — the sample's k = 0.01 s⁻¹ gives 69.31 s no matter how much material is left. Zero order: t½ = [A]₀/2k shrinks as the supply runs low. Second order: t½ = 1/(k[A]₀) grows as concentration falls — dilution makes second-order reactions drag out their ending. The constancy of first-order half-lives is precisely why radioactive dating works; that story continues on the Nuclear Chemistry page.

Rate constants are not constants — they surrender to temperature: k = A·e^−Ea/RT. The activation energy Ea is the hill molecules must climb before they can react; the fraction that makes it over scales as e^−Ea/RT, and A (the pre-exponential, roughly how often collisions with the right orientation occur) sets the ceiling. The numbers are dramatic: with Ea = 50 kJ/mol at 300 K, Ea/RT ≈ 20, so only about 2 parts in 10⁹ of attempts succeed — yet the sample still yields k ≈ 19.7 s⁻¹ because A = 10¹⁰ s⁻¹ multiplies it back. This sensitivity is the famous rule of thumb that 10 °C of warming roughly doubles a typical reaction's rate, and it is why food keeps in a freezer and milk spoils on a warm counter.

• Order comes from the equation's coefficients. Only for elementary single-step reactions. For anything composite, doubling [A] and watching the rate is the only honest test.
• A catalyst shifts the equilibrium. It lowers Ea, speeding forward and reverse equally — equilibrium arrives sooner, at exactly the same place (see Chemical Equilibrium).
• Bigger k means more product. k is about speed, K about extent. A fast reaction can finish far from complete, and a slow one can be strongly product-favored.
• First-order half-life depends on how much you have. It is the one order where it does not — 69.31 s in the sample, whether starting from 1 M or 0.001 M.

Related tools: Chemical Equilibrium (how far reactions go), Nuclear Chemistry (first-order decay at nuclear scale), and Equation Balancer (the recipes rates are measured against).