= Solution
For simultaneous competitive <adsorption>, use the butyric-acid constant inferred in part (c), $b_b\simeq1.21\,\mathrm{m^3\,mmol^{-1}}$, and $C_b=10^6\,\mathrm{mmol\,m^{-3}}$:
$$
\theta_p=\frac{0.36(10^5)}
{1+0.36(10^5)+1.21(10^6)}
\simeq0.0289.
$$
The propionic-acid rate is therefore approximately
$$
\boxed{v_p=2.1\theta_p\simeq0.061\,\mathrm{mmol\,m^{-3}s^{-1}}}.
$$
The abundant, more strongly adsorbing butyric acid occupies most common sites, reducing propionic conversion by roughly a factor of $35$. This calculation follows the requested competitive Langmuir model despite the physical concern about the fitted saturation density noted earlier.
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