We present a quantum cascade laser-based absorption spectrometer deploying a compact (145 mL volume) segmented circular multipass cell (SC-MPC) with 6 m optical path length. This SC-MPC is embedded into an effective cooling system to facilitate operation at cryogenic temperatures. For CO2, the sample is cooled to 153 K, i.e. close to the sublimation point at 10 mbar. This enables efficient suppression of interfering hot-band transitions of the more abundant isotopic species and thereby enhances analytical precision. As a demonstration, the amount fractions of all three CO2 isotopologues involved in the kinetic isotope exchange reaction of 12C16O2 + 12C18O2⇌ 2·12C16O18O are measured. The precision in the ratios [12C18O2]/[12C16O2] and [12C16O18O]/[12C16O2] is 0.05 ‰ with 25 s integration time. In addition, we determine the variation of the equilibrium constant, K, of the above exchange reaction for carbon-dioxide samples equilibrated at 300 K and 1273 K, respectively.