  The James Webb Space Telescope's Medium Resolution Spectrometer (MRS), will
offer nearly 2 orders of magnitude improvement in sensitivity and >3X
improvement in spectral resolution over our previous space-based mid-IR
spectrometer, the Spitzer IRS. In this paper, we make predictions for
spectroscopic pointed observations and serendipitous detections with the MRS.
Specifically, pointed observations of Herschel sources require only a few
minutes on source integration for detections of several star-forming and active
galactic nucleus lines, out to z$=$3 and beyond. But the same data will also
include tens of serendipitous 0$\lesssim$z$\lesssim$4 galaxies per field with
infrared luminosities ranging $\sim10^6-10^{13}$L$_{\odot}$. In particular, for
the first time and for free we will be able to explore the
$L_{IR}<10^{9}L_{\odot}$ regime out to $z\sim3$. We estimate that with
$\sim$100 such fields, statistics of these detections will be sufficient to
constrain the evolution of the low-$L$ end of the infrared luminosity function,
and hence the star formation rate function. The above conclusions hold for a
wide range in potential low-$L$ end of the IR luminosity function, and
accounting for the PAH deficit in low-$L$, low-metallicity galaxies.
