  Using the far-infrared emission, as observed by the Herschel Virgo Cluster
Survey (HeViCS), and the integrated HI and CO brightness, we infer the dust and
total gas mass for a magnitude limited sample of 35 metal rich spiral galaxies
in Virgo. The CO flux correlates tightly and linearly with far-infrared fluxes
observed by Herschel. Molecules in these galaxies are more closely related to
cold dust rather than to dust heated by star formation or to optical/NIR
brightness. We show that dust mass establishes a stronger correlation with the
total gas mass than with the atomic or molecular component alone. The
dust-to-gas ratio increases as the HI deficiency increases, but in highly HI
deficient galaxies it stays constant. Dust is in fact less affected than atomic
gas by weak cluster interactions, which remove most of the HI gas from outer
and high latitudes regions. Highly disturbed galaxies, in a dense cluster
environment, can instead loose a considerable fraction of gas and dust from the
inner regions of the disk keeping constant the dust-to-gas ratio. There is
evidence that the molecular phase is also quenched. This quencing becomes
evident by considering the molecular gas mass per unit stellar mass. Its
amplitude, if confirmed by future studies, highlights that molecules are
missing in Virgo HI deficient spirals, but to a somewhat lesser extent than
dust.
