Reaction Order Calculator: Zero, First & Second-Order Kinetics Compared

simulator beginner ~8 min
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t½ = 6.93 s — first-order decay, independent of [A]₀

For first-order kinetics with k = 0.1 s⁻¹, the half-life is ln(2)/0.1 = 6.93 s regardless of initial concentration. After 100 s, only 0.005% of the original reactant remains.

Formula

[A] = [A]₀ − kt (zero order)
[A] = [A]₀ × exp(−kt) (first order)
1/[A] = 1/[A]₀ + kt (second order)

Three Fundamental Patterns

Every simple reaction falls into one of three kinetic orders, each with a distinct concentration-time profile. Zero-order reactions consume reactant at a constant rate — the concentration drops linearly until it hits zero. First-order reactions show exponential decay with a constant half-life. Second-order reactions slow down dramatically as reactant is consumed, with concentration following a 1/(1 + kt[A]₀) curve.

Integrated Rate Laws

The integrated rate laws transform differential rate equations into algebraic expressions relating concentration to time. For first order, [A] = [A]₀ exp(−kt) — the same exponential decay seen in radioactive decay and pharmacokinetics. For second order, 1/[A] = 1/[A]₀ + kt gives a hyperbolic concentration profile that approaches zero asymptotically but never quite reaches it.

Half-Life Diagnostics

The dependence of half-life on initial concentration is a powerful diagnostic. If halving [A]₀ does not change t½, the reaction is first-order. If t½ halves when [A]₀ doubles, it is zero-order. If t½ doubles when [A]₀ halves, it is second-order. This simulation lets you verify these relationships interactively.

Visual Comparison

The canvas plots all three integrated rate laws simultaneously, highlighting the selected order. The characteristic diagnostic plot (the one that gives a straight line for the chosen order) is shown alongside the concentration vs time curve. You can immediately see why plotting ln[A] vs t is the test for first-order kinetics — it linearizes the exponential decay.

FAQ

What is reaction order?

Reaction order describes how the rate depends on concentration. For a reaction with rate = k[A]ⁿ, n is the order: n=0 means rate is constant, n=1 means rate is proportional to concentration, n=2 means rate is proportional to concentration squared. Order is determined experimentally, not from stoichiometry.

How do you determine reaction order experimentally?

Use the method of integrated rate laws: plot [A] vs t (linear = zero order), ln[A] vs t (linear = first order), or 1/[A] vs t (linear = second order). Alternatively, the method of initial rates compares rate changes when concentration is varied systematically.

Why does half-life depend on order?

For zero order, t½ = [A]₀/(2k) — proportional to initial concentration. For first order, t½ = ln(2)/k — independent of concentration. For second order, t½ = 1/(k[A]₀) — inversely proportional. This difference is a useful diagnostic for reaction order.

Can reaction order be fractional?

Yes. Complex reactions with multiple elementary steps often show fractional orders like 1.5 or 0.5. For example, the thermal decomposition of acetaldehyde is order 1.5, reflecting its free-radical chain mechanism.

Sources

Embed

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