  [Abridged] We combine new CO(1-0) line observations of 24 intermediate
redshift galaxies (0.03 < z < 0.28) along with literature data of galaxies at
0<z<4 to explore scaling relations between the dust and gas content using PAH
6.2 $\mu$m ($L_{6.2}$), CO ($L'_{\rm CO}$), and infrared ($L_{\rm IR}$)
luminosities for a wide range of redshifts and physical environments. Our
analysis confirms the existence of a universal $L_{6.2}-L_{\rm CO}$ correlation
followed by normal star-forming galaxies (SFGs) and starbursts (SBs) at all
redshifts. This relation is also followed by local ULIRGs that appear as
outliers in the $L_{6.2}-L_{\rm IR}$ and $L_{\rm IR}-L'_{\rm CO}$ relations
from the sequence defined by normal SFGs. The emerging tight ($\sigma \approx
0.26$ dex) and linear ($\alpha = 1.03$) relation between $L_{6.2}$ and $L_{\rm
CO}$ indicates a $L_{6.2}$ to molecular gas ($M_{\rm H_2}$) conversion factor
of $\alpha_{6.2} = M_{\rm H2}/L_{6.2} = (2.7\pm1.3) \times \alpha_{\rm CO}$,
where $\alpha_{\rm CO}$ is the $L'_{\rm CO}$ to $M_{\rm H_2}$ conversion
factor. We also find that on galaxy integrated scales, PAH emission is better
correlated with cold rather than with warm dust emission, suggesting that PAHs
are associated with the diffuse cold dust, which is another proxy for $M_{\rm
H_2}$. Focusing on normal SFGs among our sample, we employ the dust continuum
emission to derive $M_{\rm H_2}$ estimates and find a constant $M_{\rm
H_2}/L_{6.2}$ ratio of $\alpha_{6.2} = 12.3 \ M_{\rm H_2}/{\rm L}_{\odot}$
($\sigma\approx 0.3$ dex). We propose that the presented $L_{6.2}-L'_{\rm CO}$
and $L_{6.2}-M_{\rm H_2}$ relations will serve as useful tools for the
determination of the physical properties of high-$z$ SFGs, for which PAH
emission will be routinely detected by the James Webb Space Telescope.
