The Bolocam Galactic Plane Survey V: HCO+ and N2H+ Spectroscopy of 1.1
  mm Dust Continuum Sources
  We present the results of observations of 1882 sources in the Bolocam
Galactic Plane Survey (BGPS) at 1.1 mm with the 10m Heinrich Hertz Telescope
simultaneously in HCO+ J=3-2 and N2H+ J=3-2. We detect 77% of these sources in
HCO^+ and 51% in N2H+ at greater than 3$\sigma$. We find a strong correlation
between the integrated intensity of both dense gas tracers and the 1.1 mm dust
emission of BGPS sources. We determine kinematic distances for 529 sources (440
in the first quadrant breaking the distance ambiguity and 89 in the second
quadrant) We derive the size, mass, and average density for this subset of
clumps. The median size of BGPS clumps is 0.75 pc with a median mass of 330
M$_{\odot}$ (assuming T_{Dust}=20 K). The median HCO+ linewidth is 2.9 km
s$^{-1}$ indicating that BGPS clumps are dominated by supersonic turbulence or
unresolved kinematic motions. We find no evidence for a size-linewidth
relationship for BGPS clumps. We analyze the effects of the assumed dust
temperature on the derived clump properties with a Monte Carlo simulation and
we find that changing the temperature distribution will change the median
source properties (mass, volume-averaged number density, surface density) by
factors of a few. The observed differential mass distribution has a power-law
slope that is intermediate between that observed for diffuse CO clouds and the
stellar IMF. BGPS clumps represent a wide range of objects (from dense cores to
more diffuse clumps) and are typically characterized by larger sizes and lower
densities than previously published surveys of high-mass star-forming regions.
This collection of objects is a less-biased sample of star-forming regions in
the Milky Way that likely span a wide range of evolutionary states.
