All calculatorsRate Constant Calculator
Compute the rate constant k from either an experimental rate law (rate = k·[A]^m[B]^n[C]^p) or an integrated rate law (0ᵗʰ/1ˢᵗ/2ⁿᵈ order) using concentration–time data. See steps, a mini chart, and a k-magnitude gauge.
Background
For an empirical rate law, the rate constant is k = rate / ∏[X]^order. For a single-reactant integrated rate law: 0ᵗʰ: [A]_t = [A]_0 − kt → k = ([A]_0 − [A]_t)/t; 1ˢᵗ: ln([A]_0/[A]_t) = kt → k = ln([A]_0/[A]_t)/t; 2ⁿᵈ: 1/[A]_t − 1/[A]_0 = kt → k = (1/[A]_t − 1/[A]_0)/t.
How to use this calculator
- Rate experiment: Enter rate, choose units, pick a concentration unit, then provide [A], m (and optionally [B], n; [C], p). Leave unused reactants blank.
- Integrated law: Choose order (0/1/2), enter [A]₀, [A]t, time and units. We apply the correct integrated form automatically.
- Toggle sig-fig rounding, show steps, and visualize with a mini chart + k gauge.
Formula & Equation Used
Rate law: rate = k·[A]^m[B]^n[C]^p → k = rate / ([A]^m[B]^n[C]^p)
Integrated (0th): [A]_t = [A]_0 − kt → k = ([A]_0 − [A]_t)/t
Integrated (1st): ln([A]_0/[A]_t) = kt → k = ln([A]_0/[A]_t)/t
Integrated (2nd): 1/[A]_t − 1/[A]_0 = kt → k = (1/[A]_t − 1/[A]_0)/t
Example Problems & Step-by-Step Solutions
Example 1 — Experimental rate law
rate = 0.0120 M·s⁻¹; [A]=0.100 M (m=1); [B]=0.0500 M (n=2).
k = 0.0120 / (0.100¹ × 0.0500²) = 0.0120 / 0.000125 = 96.0 M⁻²·s⁻¹.
Example 2 — 1ˢᵗ order integrated
[A]₀=0.200 M → [A]t=0.0500 M in t=600 s.
k = ln(0.200/0.0500)/600 = ln(4)/600 = 0.00231 s⁻¹.
Example 3 — 2ⁿᵈ order integrated
[A]₀=50.0 mM → [A]t=25.0 mM in t=2.00 min.
Convert mM to M consistently (or keep mM throughout): k = (1/25.0 − 1/50.0)/2.00 = 0.01 mM⁻¹·min⁻¹ = 1.0×10⁻⁵ M⁻¹·min⁻¹.
Frequently Asked Questions
Q: What units should k have?
It depends on overall order. 1ˢᵗ: time⁻¹; 2ⁿᵈ: (concentration·time)⁻¹; 0ᵗʰ: concentration·time⁻¹; for mixed orders from experiments, k’s units balance the rate law.
Q: Do I need to convert mM to M?
No, just be consistent. This tool carries your chosen concentration unit through the units of k.
Q: Can I include only A in the experiment mode?
Yes. Leave B and C (and their orders) blank to treat the rate law as rate = k·[A]^m.
