THEORY

Reaction

                   O2 + O + (M)  -->  O3 + (M)                                   (1)

O Atoms are Formed by Photolysis of O2

                   O2 + hu (193nm)   -->   2O                                      (2)

The Rate of O3 Formation is:

                  d[O3] / dt = k1[O2][M][O]                                          (3)

The Rate of Consumption of O Atoms:

                  d[O] / dt = -k[O2][M][O]                                            (4)

Pseudo-first Order Conditions are Satisfied

 Since    [O] << [O2], [M]

                     d[O] / dt = -k'[O]      where,                                     (5)

                      k' = k1[O2][M]                                                        (6)

Integrating Equation 5:

                      [O] = [O]o e-k't                                                        (7)

From Reaction 1

                      [O3] = [O]o - [O]                                                    (8)

Combining Equations 7 and 8

                      [O3] = [O]o(1 - e-k't)                                               (9)

From Beer - Lambert  Law

                      I = Ioexp(- s [O3]L)                                               (10)

  L - Length of Reactor

  s = Absorption Cross Section

Since s [O3]L << 1

                      I = Io - Io s [O3]L                                                  (11)
 

PMT Converts Light Intensity into Voltage According to:

                      V = -a . I                                                               (12)

 a  -  PMT Conversion Factor

Substituting for I into Equation 12

                       V(t) = -aIo + aIosL[Oo](1 - e-k't)                          (13)

Simplifying Equation 13:

                        Voltage = B + A(1- e-k't )                                      (14)

The Parameters A, B, and k' are Evaluated from  Non-linear Fits of Equation 14 to
Experimental Profiles Using Standard Software