The positron lifetime method has been used to study orthopositronium formation and quenching in argon, nitrogen, oxygen and mixtures of these gases. Quenching rates were found to be proportional to pressure for all gases and gas mixtures, except commercial grade argon. Highly quenched orthopositronium lifetimes were observed in pure argon and the formation fraction of positronium was estimated as 0.40±0.04. The quenching rate in oxygen was found to be (2.3 ± 0.3) × 10 7 sec -1 atm -1 . This rate holds for oxygen concentration greater than 2% in oxygen-argon mixtures. A constant quenching rate (2.51 ± 0.05) × 10 5 sec -1 atm -1 was obtained for lower oxygen concentrations; this rate is not significantly different from the quenching rate (2.42 ± 0.07) × 10 5 sec -1 atm -1 obtained for nitrogen-argon mixtures containing less than 10% nitrogen.