The hydrodynamically thinned diffusion layer at a sinusoidally rocking disc is approximately uniform and can be expressed in terms of a diffusion layer thickness, with D, the diffusion coefficient of the redox active species, v, the kinematic viscosity, Θ, the total rocking angle (here 90 degrees), and f, the rocking frequency (ranging here from 0.83 to 25 Hz). For the one-electron oxidation of 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) in aqueous carbonate buffer pH 9.5, it is shown that there is quantitative agreement between the expression for the diffusion layer thickness and experimental data. Next, for seven primary alcohols, the catalytic TEMPO-mediated oxidation mechanism is investigated under rocking disc conditions. Chemical rate constants are evaluated (by varying the diffusion layer thickness) employing the DigiElch4.F simulation package. Trends in the chemical rate constants (compared with DFT calculations) suggest enhanced reactivity for methanol versus higher primary alcohols and for aromatic versus non-aromatic primary alcohols. Rocking disc voltammetry allows quantitative mechanistic analysis in the laminar flow regime.