PHOTOCHEMISTRY 21 



For relatively simple reactions (Kassel, 1932; Laidler, 1950) this can be 

 done by solving simultaneously the differential rate equations for the 

 individual steps. In general, the resulting solution cannot be obtained in 

 terms of simple functions, and the analysis demands a mathematical 

 skill which the average photochemist does not possess. As a result 

 it has become conventional among students of kinetics to use approx- 

 imate methods to deduce the over-all rate equation from a postulated 

 mechanism. 



STEADY-STATE APPROXIMATION 



The most generally applicable of these simple methods is the so-called 

 "steady-state approximation." A steady state may be defined as a con- 

 dition in which the rates of change of the concentrations of the several 

 intermediates are very small compared to the rates of change of the con- 

 centrations of the reactants and products. This condition is realizable 

 whenever the ratio of the concentrations of the intermediates to the con- 

 centrations of the reactants is very much less than unity. When this 

 condition is not attained, the method is not applicable; however, it should 

 not then be necessary since the (larger) concentrations of the intermedi- 

 ates could be measured by experimental means. In no reaction is the 

 steady state attained instantaneously. However, the time required for 

 its attainment is usually a negligibly small fraction of the half time of the 

 reaction. The steady-state approximation consists in setting the rates 

 of change of each of the intermediates equal to zero and in solving simul- 

 taneously the resulting algebraic equations. This process can be 

 explained most easily by outlining the details of two well-known examples. 



Examples. The decomposition of hydrogen iodide is a classic example 

 (Warburg, 1916; Bonhoeffer and Farkas, 1928) of a carefully studied and 

 thoroughly understood photochemical reaction. Although this reaction 

 is so simple that it is not necessary to use the steady-state approximation 

 method in its analysis, it will serve to introduce the fundamentals of this 

 procedure. Gaseous hydrogen iodide strongly absorbs light of wave 

 length 3000 A or shorter. It is nonfluorescent, and its absorption spec- 

 trum is continuous, showing no vibrational or rotational structure. It 

 follows from these observations that the primary act is one of direct 

 optical dissociation, 



HI 4- /iv ^ H + I. 



The secondary steps must be reactions of hydrogen and of iodine atoms. 

 They may combine to form hydrogen iodide or molecular hydrogen and 

 iodine, or more probably they may react with hydrogen iodide: 



I + HI^l2+ H, 

 H 4- HI-^ H2 + I. 



The first of these tw^o reactions can be ruled out since it is strongly endo- 



