  Trapping molecular ions that have been sympathetically cooled with
laser-cooled atomic ions is a useful platform for exploring cold ion chemistry.
We designed and characterized a new experimental apparatus for probing chemical
reaction dynamics between molecular cations and neutral radicals at
temperatures below 1 K. The ions are trapped in a linear quadrupole
radio-frequency trap and sympathetically cooled by co-trapped, laser-cooled,
atomic ions. The ion trap is coupled to a time-of-flight mass spectrometer to
readily identify product ion species, as well as to accurately determine
trapped ion numbers. We discuss, and present in detail, the design of this ion
trap time-of-flight mass spectrometer, as well as the electronics required for
driving the trap and mass spectrometer. Furthermore, we measure the performance
of this system, which yields mass resolutions of $m/\Delta{}m \geq 1100$ over a
wide mass range, and discuss its relevance for future measurements in chemical
reaction kinetics and dynamics.
