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For questions about the definition and usage of units of measurement.
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Units of rate constant (cycles per second vs radians per second) in Eyring equation
In the Eyring equation (EE),
$$k = \frac{k_\mathrm B T}{h} \exp\left(\frac{-\Delta G_{\mathrm f}}{RT}\right),$$
the units of $k$ are $\mathrm{s^{-1}}$. … For instance, in expressions for damped oscillations of the form $\exp[(\mathrm{i} \omega - k)t]$, where $\omega$ is by definition in $\frac{\mathrm{rad}}{\mathrm{s}}$ and $k$ has to bear units providing …