The rate constants are chosen so that all three reactions have the same half-life at the reference [A]₀. Drag the [A]₀ slider to change only the starting concentration and see how each time course responds.
All three graphs show the same data, transformed differently: [A] itself, ln[A], and 1/[A]. Each reaction order time course plots as a straight line on only one of them.
Straight for zero order, slope −k₀
Straight for first order, slope −k₁
Straight for second order, slope k₂
Half-lives
| Order | Rate constant | Ratio | Depends on [A]₀ as |
|---|
The rate constants are chosen so all three reactions have the same half-life t½ at the reference [A]₀:
Moving the [A]₀ slider does not change these k values.
Each rate law is written for A → B, with −d[A]/dt = k₀, k₁[A] or k₂[A]².
Doubling [A]₀ doubles the zero-order half-life, leaves the first-order one unchanged, and halves the second-order one.
The zero-order reaction runs out at t = [A]₀/k₀. After that [A] stays at zero. Its ln and 1/[A] curves end there, since neither is defined at [A] = 0, and a blue column of × marks shows that time on those two graphs.
The ln graph plots ln[A] with [A] in mM, so each curve starts at ln[A]₀. Raising [A]₀ shifts the first-order line up without changing its slope, which shows that k₁ is the same. With “Plot fraction of A remaining” on, it plots ln([A]/[A]₀), which starts at 0 for every curve.
“Plot fraction of A remaining” replaces [A] with the fraction left, f = [A]/[A]₀, on all three graphs: f, ln f, and 1/f = [A]₀/[A]. Only the first-order fraction left is independent of [A]₀, so first-order curves from different starting concentrations fall on one curve on every graph. Zero- and second-order curves stay separate. The second-order line on the third graph has slope k₂[A]₀, which grows with [A]₀.
The axes stay fixed over the slider's whole range so the curves move as you drag. Switch on “Rescale axes to fit” to zoom in on the current curves.