Write down a kinetic equation (net rate law) for the concentration change of excited oxygen atoms with time d[0]/dt where t represents time.
Integrate your rate law, to afford an analytical expression showing the actual variation of the excited oxygen atom concentration with time, given that no o* exists prior to t = 0.
HINT: you may find that making assumptions that I and [M] are independent of time to be helpful!
Use the steady-state approximation and your kinetic equation to determine the steady-state concentration
of excited oxygen atoms., and identify under what conditions the actual variation of the excited oxygen
atom concentration corresponds to the steady-state variation.
Then, estimate the minimum illumination time required for the non-steady state and steady-state
concentrations to be identical to within 1%.
Comment on whether the steady-state hypothesis is a good approximation for the atmospheric behaviour of
excited oxygen atoms where the solar intensity changes over periods of hours.
Question A2: The ground state oxygen atom
Write down a kinetic equation (net rate law) for the concentration change of ground-state oxygen atoms
with time, do, where t represents time, neglecting equation (A.2).
Integrate your rate law, to afford an analytical expression showing the actual variation of the ground-state
oxygen atom concentration with time, under conditions of constant irradiation, and that all species M are
present in excess. Make sure you identify appropriate boundary conditions.
Use the steady-state approximation and your kinetic equation to determine the steady-state concentration
of ground-state oxygen atoms.
Then, identify whether the steady-state hypothesis is a suitable approximation to apply to ground-state
oxygen atoms in atmospheric modelling.
Comment on any similarities or differences you have found in the application of the steady-state
approximation for the reactive intermediates (O and O*) considered in Questions A1 and A2.