  We present measurements of thermalized collisional rate coefficients for
ultra-cold $^7$Li and $^{87}$Rb colliding with room-temperature He, Ne, N$_2$,
Ar, Kr, and Xe. In our experiments, a combined flowmeter and dynamic expansion
system, a vacuum metrology standard, is used to set a known number density for
the room-temperature background gas in the vicinity of the magnetically trapped
$^7$Li or $^{87}$Rb clouds. Each collision with a background atom or molecule
removes a $^7$Li or $^{87}$Rb atom from its trap and the change in the atom
loss rate with background gas density is used to determine the thermalized loss
rate coefficients with fractional standard uncertainties better than 1.6 % for
$^7$Li and 2.7 % for $^{87}$Rb. We find consistency -- a degree of equivalence
of less than one -- between the measurements and recent quantum-scattering
calculations of the loss rate coefficients [J. Klos and E. Tiesinga, J. Chem.
Phys. 158, 014308 (2023)], with the exception of the loss rate coefficient for
both $^7$Li and $^{87}$Rb colliding with Ar. Nevertheless, the agreement
between theory and experiment for all other studied systems provides validation
that a quantum-based measurement of vacuum pressure using cold atoms also
serves as a primary standard for vacuum pressure, which we refer to as the
cold-atom vacuum standard.
