Reactor laboratory
Well-mixed batch reaction, fixed temperature, exponential decay and positive concentrations.
Experimental record
Concept figure
Taking a logarithm straightens ideal exponential decay. Cref is a fixed concentration unit used to make the logarithm dimensionless.
Live log-linear model
Model controls
Adjust your model before checking.
The maths
First-order decay: C(t) = C₀ exp(−kt). The fitted line is ln(C/Cref) = ln(C₀/Cref) − kt, with k in s⁻¹.
Initial-rate power law: rate = kCⁿ. Taking logarithms yields ln(rate/rref) = ln(kCrefⁿ/rref) + n ln(C/Cref).
Log-linear fitting minimises squared residuals after the logarithm, so multiplicative measurement errors are more natural than additive errors on the original scale.
For uncorrelated measurements, f = Π xᵢ^pᵢ and u(f) / |f| = √Σ[pᵢu(xᵢ)/xᵢ]².
The largest squared relative contribution dominates the combined standard uncertainty. First-order propagation assumes sufficiently small relative uncertainty.