The present invention relates to a process for purifying a gas mixture G-0 comprising dinitrogen monoxide, at least comprising the contacting of the gas mixture G-0 with a solvent mixture (I) at least comprising 50% by weight of water based on the overall solvent mixture (I), the pH of the solvent mixture (I) being in the range from 3.5 to 8.0, the desorption of a gas mixture G-1 from a composition (A), the contacting of the gas mixture G-1 with a solvent mixture (II) at least comprising 50% by weight of water based on the overall solvent mixture (II), the pH of the solvent mixture (II) being in the range from 2.0 to 8.0, and the desorption of a gas mixture G-2 from a composition (B), the pH being based in each case on a measurement with a glass electrode, and to the use of gas mixtures obtainable by a process according to the invention as oxidizing agents for olefins.