= Solution
At <chemical equilibrium>, the forward and reverse event rates are equal, rather than both reactions stopping:
$$
k_1[\mathrm{cis}]_{\rm eq}=k_{-1}[\mathrm{trans}]_{\rm eq}.
$$
For the dilute-solution <concentration> model,
$$
\boxed{K_{\rm eq}=\frac{[\mathrm{trans}]_{\rm eq}}{[\mathrm{cis}]_{\rm eq}}=\frac{k_1}{k_{-1}}.}
$$
The ratio is dimensionless because both <concentrations> and both <rate constants> have matching units. An exact thermodynamic <equilibrium constant> uses activities; here the common standard <concentration> and ideal-solution activity coefficients cancel.
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