Variability in hydraulic properties and various mechanisms resulting in rate‐limited mass transfer influence field scale solute transport in aquifers. In this study analytical expressions are presented for the expected value and variance of the mass flux for a solute undergoing a nonequilibrium sorption reaction controlled by first‐order kinetics. The uncertainty in the mass flux, expressed through the variance, stems from finite solute injection volumes compared to the hydraulic conductivity integral scale. Two‐dimensional numerical simulations are performed under statistically identical conditions to the ones assumed in the derivation of the analytical results. Two cases of variability in the log hydraulic conductivity are considered (σY2= 0.1 and σY2= 1.0). The analytical model and the numerical simulations yield comparable predictions of the mass flux statistics for both variability cases. Comparing conservative and kinetically sorbing solute an apparent effect of sorption kinetics is to lower the discrepancy between the analytical model and the simulations due to increased spreading of the solute resulting from rate‐limiting mass