Investigation of the Equilibrium N₂O₄ ⇌ 2NO₂ by Electron Diffraction:  Molecular Structures and Effective Temperature and Pressure of the Expanding Gas with Implications for Studies of Other Dimer−Monomer Equilibria

Gas-phase electron-diffraction patterns are obtained from jets that are expanded into a vacuum. Knowledge of the effective temperature of the sample in the diffraction zone is essential for reliable analyses of any equilibria that may exist between different species and for an understanding of the vibrational properties of the molecules. Knowledge of the effective pressure is also essential for analyses of equilibria in which the number of molecules changes during reaction. The temperature and pressure dependence of the equilibrium N 2 O 4 ⇌ 2NO 2 was studied to investigate these matters. The diffraction experiments fall into two sets: (1) those with nozzle temperatures of 104, 25, 2, −12, −25, and −35 °C with the sample bath temperature constant at −43 °C and (2) those with the nozzle temperature constant at −12 °C and bath temperatures of −26, −36, and −43 °C. The amount of N 2 O 4 was found to range from 76.3 (29)% with the bulk sample at −43 °C and the nozzle tip at −35 °C to zero with the nozzle tip at 104 °C. Analysis of the temperature dependence of the equilibrium reveals that effective temperature in the diffraction zone is satisfactorily represented by the formula T = aT nt, where T nt is the nozzle-tip temperature and a = 0.980 (σ = 0.098). Thus, for T nt = 300 K one has T = 294 K (σ = 29); however, there is evidence that the magnitude of the uncertainty is too conservative and that a more likely figure is 10−15 K. A similar analysis of the effective pressure based on the formula P t = bP bs, where P bs is the vapor pressure of the bulk sample determined by the temperature of the sample bath, led to a plausible but very imprecise value for b: 0.56 (148). The values of both a and b are in principle dependent on nozzle geometry, but in view of its imprecision the matter is moot for b . Our value for a should be applicable to most gas-phase electron-diffraction nozzles in current use, i.e., nozzles having a ratio of capillary length to diameter greater than 10−15. It should also be applicable to the separate components of gaseous system and to equilibria that become established in the nozzle system. The structures of the molecules are in excellent agreement with those measured earlier. Results ( r a /Å; ∠ α /deg) with estimates of 2σ uncertainties are as follows. N 2 O 4 at T nt = −35 °C: r (N O) = 1.191 (1), r (N−N) = 1.774 (5), ∠O N O = 134.8 (4). NO 2 at T nt = 104 °C: r (N O) = 1.199 (1), ∠O N O = 134.8 (4).