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We use a suite of cosmological zoom galaxy formation simulations and dustradiative transfer calculations to explore the use of the monochromatic$850~\mu m$ luminosity (L$_{\rm \nu,850}$) as a molecular gas mass (M$_{\rmmol}$) estimator in galaxies between $0 < z < 9.5$ for a broad range of masses.For our fiducial simulations, where we assume the dust mass is linearly relatedto the metal mass, we find that empirical L$_{\rm \nu,850}$-M$_{\rm mol}$calibrations accurately recover the molecular gas mass of our model galaxies,and that the L$_{\rm \nu,850}$-dependent calibration is preferred. We argue themajor driver of scatter in the L$_{\rm \nu,850}$-M$_{\rm mol}$ relation arisesfrom variations in the molecular gas to dust mass ratio, rather than variationsin the dust temperature, in agreement with the previous study of Liang et al.Emulating a realistic measurement strategy with ALMA observing bands that aredependent on the source redshift, we find that estimating S$_{\rm \nu,850}$from continuum emission at a different frequency contributes $10-20\%$ scatterto the L$_{\rm \nu,850}$-M$_{\rm mol}$ relation. This additional scatter arisesfrom a combination of mismatches in assumed T$_{dust}$ and $\beta$ values, aswell as the fact that the SEDs are not single-temperature blackbodies.Finallywe explore the impact of a dust prescription in which the dust-to-metals ratiovaries with metallicity. Though the resulting mean dust temperatures are$\sim50\%$ higher, the dust mass is significantly decreased for low-metallicityhalos. As a result, the observationally calibrated L$_{\rm \nu,850}$-M$_{\rmmol}$ relation holds for massive galaxies, independent of the dust model, butbelow L$_{\rm \nu,850}\lesssim10^{28}$ erg s$^{-1}$ (metallicities$\log_{10}({\rm Z}/{\rm Z}_{\odot})\lesssim -0.8$) we expect galaxies maydeviate from literature observational calibrations by $\gtrsim0.5$ dex.

On the Interpretation of Far-infrared Spectral Energy Distributions. I: The 850 $\mu$m Molecular Mass Estimator