Equation: [A] = [A₀]×e^(-k×t)
Half-life: —
Equilibrium: —
First-Order Kinetics — Linearized Analysis
Normal form: [A] = [A₀] · e−kt
Linearized: ln[A] = −k · t + ln[A₀]
Plot: ln[A] vs t → slope = −k, intercept = ln[A₀]
Linearized: ln[A] = −k · t + ln[A₀]
Plot: ln[A] vs t → slope = −k, intercept = ln[A₀]
In a first-order reaction, rate = k[A]. Taking the natural log gives a straight line:
ln[A] = −kt + ln[A₀]. A linear fit on ln[A] vs t yields k from the slope and A₀ from eintercept.
Chemical Example
2N₂O₅(g) → 4NO₂(g) + O₂(g)k ≈ 3.7 × 10⁻⁵ s⁻¹ at 25 °C
Also: radioactive ¹⁴C decay (t½ = 5 730 yr)
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| Model | Equation | k | A₀ (M) | R² |
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