= Conductometric determination of activation energy
A concrete laboratory route to an <Arrhenius plot> is to infer a <rate constant> at each controlled <temperature> from a changing <electrical conductivity>. The Technical University of Munich's <Laboratory Course in Physical Chemistry for Fundamental Studies: Experiments Manual/Activation Energy of a First-Order Reaction> supplies a teaching protocol, rather than a published set of measured <rate constants>.
The manual follows <tertiary amylbromide> conversion, which produces conducting <ions>. A measuring cell connects to a thermostat; an immersed <electrical conductivity> probe also measures solution <temperature>, and a magnetic stirrer mixes it. Use $80\,\mathrm{mL}$ of $80\%$ by volume <ethanol> in <water>, equilibrate, then add $0.5\,\mathrm{mL}$ of <tertiary amylbromide>. Record the baseline before addition and set time zero at addition. Repeat with fresh mixtures at $25$, $30$, and $35\,{}^\circ\mathrm C$, each within $\pm0.5\,{}^\circ\mathrm C$; record for $30$ minutes at the first two <temperatures> and until completion at the last. Clean the cell between runs and keep the added volume fixed. The completed $35\,{}^\circ\mathrm C$ mixture supplies endpoint <electrical conductivity> measurements at the other <temperatures>: one endpoint reading cannot be used unchanged at every <temperature>.<Laboratory Course in Physical Chemistry for Fundamental Studies: Experiments Manual/Activation Energy of a First-Order Reaction>[pp. 82–84, §§8.2.5–8.3.2, and p. 85, §8.5.1: reaction, apparatus, temperatures, endpoint and baseline]{ref}
To see what is inferred from the readout, let $\sigma_0$, $\sigma(t)$, and $\sigma_\infty$ be the baseline, current, and completed-mixture <electrical conductivities> at the same <temperature>. Assume their baseline-subtracted changes are proportional to converted <concentration>. Combining that measurement model with a <first-order reaction> gives
$$
f(t)=\frac{\sigma_\infty-\sigma(t)}{\sigma_\infty-\sigma_0}
=\frac{c(t)}{c_0}=e^{-kt},
\qquad -\ln f(t)=kt.
$$
Thus the <electrical conductivity> increases toward an endpoint, while the remaining <reactant> fraction decreases. Fit $-\ln f$ against time to obtain $k$; then fit $\ln(k/k_{\mathrm{ref}})$ against $1/T$ in <kelvin> to estimate an <apparent activation energy>. This baseline-aware derivation states the measurement assumptions explicitly; it does not infer a <rate constant> from the steepness of a raw conductivity trace alone.
The controls distinguish a faster <chemical reaction> from a larger instrumental response. Measure the actual solution <temperature>, retain the same <solvent> composition and initial <reactant> <concentration>, and compare endpoint and baseline at that <temperature>. As further diagnostic checks, repeat runs and inspect <regression residuals> for departure from a <first-order reaction>. These checks follow from the model: <electrical conductivity> also depends on how <ions> move, a baseline drift can mimic conversion, and a mixing delay can distort early points. Near completion, a small endpoint error produces a large relative error in $f$ and its <natural logarithm>. A successful fit supports an apparent rate model for this <solvent> and interval; it does not directly image a <transition state> or identify a unique <reaction mechanism>. No measured $k$ or $E_a$ is supplied here.
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