  The Chandra X-ray Observatory's Cycle 18 Large Program titled "Spiral
galaxies of the Virgo Cluster" will image 52 galaxies with the ACIS-S detector.
Combined with archival data for an additional 22 galaxies, this will represent
the complete sample of 74 spiral galaxies in the Virgo cluster with
star-formation rates $\gtrsim$ 0.3 $M_{\odot}$/yr. Many of these galaxies are
expected to have an active nucleus, signalling the presence of a central black
hole. In preparation for this survey, we predict the central black hole masses
using the latest black hole scaling relations based on spiral arm pitch angle
$\phi$, velocity dispersion $\sigma$, and total stellar mass $M_{\rm
*,galaxy}$. With a focus on intermediate mass black holes ($10^2<M_{\rm
bh}/M_{\odot}<10^5$), we highlight NGC 4713 and NGC 4178, both with $M_{\rm
bh}\approx10^3$-$10^4$ (an estimate which is further supported in NGC 4178 by
its nuclear star cluster mass). From Chandra archival data, we find that both
galaxies have a point-like nuclear X-ray source, with unabsorbed 0.3-10 keV
luminosities of a few times 10$^{38}$ erg/s. In NGC 4178, the nuclear source
has a soft, probably thermal, spectrum consistent with a stellar-mass black
hole in the high/soft state, while no strong constraints can be derived for the
nuclear emission of NGC 4713. In total, 33 of the 74 galaxies are predicted to
have $M_{\rm bh}<(10^5$-$10^6)$ $M_{\odot}$, and several are consistently
predicted, via three methods, to have masses of $10^4$-$10^5\,M_{\odot}$, such
as IC 3392, NGC 4294 and NGC 4413. We speculate that a sizeable population of
IMBHs may reside in late-type spiral galaxies with low stellar mass ($M_{\rm
*,galaxy}\lesssim10^{10}\,M_{\odot}$).
