  Using the 16$\mu$m peakup imager on the Infrared Spectrograph (IRS) on
Spitzer, we present a serendipitous survey of 0.0392 deg$^{2}$ within the area
of the NOAO Deep Wide Field Survey in Bootes. Combining our results with the
available Multiband Imaging Photometer for Spitzer (MIPS) 24$\mu$m survey of
this area, we produce a catalog of 150 16$\mu$m sources brighter than 0.18 mJy
(3$\sigma$) for which we derive measures or limits on the 16/24$\mu$m colors.
Such colors are especially useful in determining redshifts for sources whose
mid infrared spectra contain strong emission or absorption features that
characterize these colors as a function of redshift. We find that the 9.7$\mu$m
silicate absorption feature in Ultraluminous Infrared Galaxies (ULIRGs) results
in sources brighter at 16$\mu$m than at 24$\mu$m at z $\sim$ 1--1.8 by at least
20%. With a threshold flux ratio of 1.2, restricting our analysis to $>5\sigma$
detections at 16$\mu$m, and using a $3\sigma$ limit on 24$\mu$m non-detections,
the number of silicate-absorbed ULIRG candidates is 36. This defines a strong
upper limit of $\sim$920 sources deg$^{-2}$, on the population of
silicate-absorbed ULIRGs at z $\sim$ 1--1.8. This source count is about half of
the total number of sources predicted at z $\sim$ 1--2 by various
phenomenological models. We note that the high 16/24$\mu$m colors measured
cannot be reproduced by any of the mid-IR spectral energy distributions assumed
by these models, which points to the strong limitations currently affecting our
phenomenological and theoretical understanding of infrared galaxy evolution.
