Discussion

NO_x formation via the Zel'dovich mechanism.

Nitric oxide formation by electrical discharge is thought to be via the Zel'dovich mechanism. At high temperatures the gas mixture heated by the discharge is thought to be in chemical equilibrium, with the equilibrium concentration of NO, ([NO]_equil.(T)) decreasing as the temperature decreases (figure 6). If the gas mixture maintained chemical equilibrium as it cooled to ambient temperature, then the quantity of NO formed would be insignificant as [NO]_equil. at 300 K is very low. However, the time constant for the rate at which the gas approaches chemical equilibrium (tau_equil.(T)) is also very strongly dependent on temperature, and increases as the gas cools. For example, from (figure 6), at 3000K, 500 mbar, tau_equil. = 10^-3 s, therefore if the gas is cooling sufficiently slowly that tau_cooling > 5×10^-3 s the NO concentration follows the equilibrium NO concentration as the gas cools. When the gas has cooled to the extent that tau_equil. is approximately equal to tau_cooling, the equilibrium NO concentration for this temperature is "frozen out". Further cooling of the gas results in the rate of approach to chemical equilibrium being much slower than the rate of cooling of the gas, so the NO concentration no longer follows the equilibrium NO concentration below this freeze out temperature, T_{freeze out}, ie.

where T_{freeze out} is determined by the condition such that,

The number of NO molecules produced by the discharge is simply the volume of gas heated to the freeze out temperature multiplied by [NO]_{freeze out}.

Any NO₂ production has either been thought to be insignificant, or due to conversion of NO to NO₂ after the gas has cooled to well below the freeze out temperature: the total number of NO_x molecules produced has therefore been taken as the amount of NO formed by the Zel'dovich mechanism.