The total quenching rate constants of argon atoms in the 4p′[1/2]0, 4p[1/2]0, 4p[3/2]2, and 4p[5/2]2 states (2p1, 2p5, 2p6, and 2p8, respectively, in the Paschen numbering system) by rare gases, H2, D2, N2, CO, NO, O2, F2, Cl2, CO2, NO2, CH4, C2H2, C2H4, C2H6, CF4, CHF3, and SF6 have been determined at room temperature. These four excited states of argon (energy 13.09–13.48 eV) were selectively prepared by two-photon excitation from the ground state using VUV (184–190 nm range) laser pulses. The total quenching rates were deduced from the pressure dependence of the decay times of the excited-state atoms, measured by observing their fluorescence emission intensities in the presence of added reagents. The quenching constants increase from values of ≅0.01×10−10 cm3 atom−1 s−1 for Ne, to ≅0.1×10−10 cm3 atom−1 s−1 for He and Ar, and to very large values, (5–15)×10−10 cm3 atom−1 s−1, for most polyatomic molecules, F2, Cl2, and O2. The quenching mechanisms of the Ar(4p,4p′) atoms are briefly discussed and compared to the reactions of the Ar(4s,4s′) metastable and resonance state atoms, 11.55–11.83 eV, which can serve as a reference.