Use the Chapman model to explore the behaviour of a model atmosphere consisting of pure 0, at 10 Torr and 298 K that is exposed to measurable frequencies and intensities of UV radiation.
(a) Look up the values of k" k4, and ks in a source such as the CRC Handbook of chemistry and physics or Chemical kinetics and photochemical data for use in stratospheric modeling (the URL is available at the text's web site). The rate constants k, and k3 depend upon the radiation conditions; assume values of 1.0 x 10-8 S-I and 0.016 S-I, respectively. If you cannot find a value for ks' formulate chemically sound arguments for exclusion of the fifth step from the mechanism.
(b) Write the rate expressions for the concentration of each chemical species.
(c) Assume that the UV radiation is turned on at t= 0, and solve the rate expressions for the concentration of all species as a function of time over a period of 4 h. Examine relevant concentrations in the very early time period t < 0.1 s. State all assumptions. Is there any ozone present initially? Why must the pressure be low and the UV radiation intensities high for the production of ozone? Draw graphs of the time variations of both atomic oxygen and very short and another very long for help with using mathematical software to solve systems of differential equations, see M.P. Cady and CA. Trapp, A MathCAD primer for physical chemistry. Oxford University Press (1999) ozone on both the very short and the long timescales what is the percentage of ozone after 4.0 h of irradiation? Hint. You will need a software package for solving a 'stiff' system of differential equations. Stiff differential equations have at least two rate constants with very different values and result in different behaviours on different timescales, so the solution usually requires that the total time period be broken into two or more periods; one may be very short and another very long. For help with using mathematical software
to solve systems of differential equations, see M.P. Cady and CA. Trapp, A MathCAD primer for physical chemistry Oxford University Press (1999).