A Method for the Determination of Rate Coefficients for the Formation of Protonated Monomers and Proton Bound Dimers of Volatile Organic Compounds in Air at Ambient Pressure by Ion Mobility Spectrometry

Rate coefficients (<i>k</i>) for the reactions of hydrated protons and a sample vapor (M) to form protonated monomers (MH⁺(H₂O)_<i>n</i>) and proton bound dimers (M₂H⁺) were determined simultaneously by using ion mobility spectrometry with a tandem drift tube at ambient pressure. In this method, sample vapors were introduced to a first drift region with stepwise reactions: M + H⁺(H₂O)<i>n</i><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mo>→</mml:mo><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mover></mml:math> _MH⁺ (H₂O)_<i>y</i> + (<i>n</i> - <i>y</i>) H₂O and M + MH⁺ (H₂O)<i>y</i><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mo>→</mml:mo><mml:msub><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mover></mml:math> M₂H⁺ + <i>y</i>H₂O. Ions with a drift time between 9 and 18 ms in the first drift region were subsequently mobility analyzed in purified air with the second drift region using a synchronized second ion gate with boxcar averaging. Slope for plots of ion abundance against drift time was fitted by successive approximation between peaks of H⁺(H₂O)_<i>n</i> and MH⁺(H₂O)_<i>y</i> to obtain <i>k</i>₂ until computed and experimental slopes matched within a maximal deviation of 0.01. Values for <i>k</i>₁ were obtained from the experimental baseline slope when adjusted for <i>k</i>₂. Rate coefficients for triethyl phosphate and phenylacetate were determined using this method with <i>k</i>₁ values of 1.14 × 10^-9 ± 1.87 × 10^-10 cm³/s and 0.81 × 10^-9 ± 9.26 × 10^-11 cm³/s and <i>k</i>₂ values of 1.05 × 10^-9 ± 4.13 × 10^-10 cm³/s and 1.07 × 10^-9 ± 1.86 × 10^-10 cm³/s, respectively. Relative error for this method was determined using mobility spectra generated with a COMSOL model and artificial rate coefficients. Rate coefficients were then extracted from the modeled mobility spectra and compared to the original artificial values. Relative error of this method was 10% and should be generally applicable for individual substances with reactions forming protonated monomers and proton bound dimers.