Rate Constant Units and Eyring Equation Rearranging the Eyring equation leads to the following:

$$\Delta^\ddagger S^\circ = R \ln{\frac{k \times h}{{k_\text{B}}{T}}}+\frac{\Delta^\ddagger H^\circ}{T}$$

where $k$ is the rate constant, $h$ is the Planck constant, $R$ is the universal gas constant, $k_\text{B}$ is the Boltzmann constant, $T$ is temperature, $H$ is enthalpy, and $S$ is entropy. The entropy term should ultimately be in units of $\mathrm{\frac{J}{mol\ K}}$. The right term of the equation will clearly yield the correct units. For the left term, the universal gas constant can be expressed in $\mathrm{\frac{J}{mol\ K}}$, which means that the log term should be dimensionless. For the bottom part of the fraction, the units evaluate to $\mathrm{J}$. For the top part, the Planck constant has units of $\mathrm{J\cdot s}$. To get the top part of the fraction to evaluate to $\mathrm{J}$, the rate constant would have to be in units of $\mathrm{s^{-1}}$. For first order reactions, this is indeed the case. For reactions of higher order, this will never work out to the correct units.

This makes me think that the Eyring equation is simply using the unitless values of these variables. This still leads to some ambiguity about which value of the rate constant to use. Take for instance a second-order reaction in which the rate constant is in units of $\mathrm{M^{-1}\ s^{-1}}$. If we rearrange the units to SI units ($\mathrm{m^3\ mol^{-1}\ s^{-1}}$), the value of the rate constant changes. So is the rate constant $k$ in the Eyring equation simply the value of the rate constant when that rate constant is expressed in certain units? And if so, are the concentration units always expressed in molarity? I kept missing a homework problem because I was converting $k$ from molarity to SI units, which makes me believe this is indeed the case.
Using Transition State Theory (TST) one has to be aware of at least some of the many flaws of it. And may also often lead to wrong assumptions. However, it is a wonderful tool to describe basic kinetics in a theoretical manner.

The most important/ fundamental assumptions are


separation of electron and nuclear movement (comparable to Born-Oppenheimer approximation)
(all possible) transition states (TS) are in equilibrium with the reactants  $$\ce{A + B &lt;=&gt; [AB]^{\ddagger}}\tag1$$
combined Boltzmann statistic for reactants and TS
All molecules that reach the transition state from the reaction coordinate of the reactants will leave the TS to the reaction coordinate of the product(s) - and vice versa 
\begin{align}
\ce{A + B &lt;=&gt; &amp;[AB]^{\ddagger}-&gt;P}\tag{2a}\\
\ce{P &lt;=&gt; &amp;[AB]^{\ddagger}-&gt; A + B}\tag{2b}
\end{align}
at the TS the transition vector can be separated from all other motions and hence may be treated classical as translation


In other words TST reduces a very complicated multidimensional problem to a one-dimensional translation. That implies that all treated molecules must be connected on a potential energy hypersurface with one vector. (Borrowing from the amazing wikipedia)



Hence reactions that are described with TST are of first order by default. One would have to make various adjustments to treat higher orders (and I would assume that not matching units would be of minor concern).