PHOTOCHEMISTRY 267 



The various competing reactions may be quite complicated. There 

 may be a reverse reaction or a side reaction involving the same reactants, 

 or one reaction may follow closely on the heels of another and a whole 

 series of successive reactions may occur. In actual practice the slowest 

 reaction in the series is the one measured and there may be many steps 

 in the complete reaction which proceed at an immeasurably rapid rate. 

 In case two reactions are proceeding at approximately the same rate the 

 situation becomes quite confused. When one reaction is considerably 

 slower than any of the others, it can be made the object of experimental 

 investigation. 



Order of Reaction. — In studying reaction rates it is desirable to express 

 the concentration as a function of the time. A graph in which concen- 

 tration c is plotted against time t may be extrapolated within reasonable 

 limits. Often the relationship between concentration and time can be 

 expressed with mathematical formulas. The rate of a first-order reaction 

 is directly proportional to the concentration as given by the following 

 formula : 



-|=.-c • (8) 



In the integrated form this equation becomes 



- In c = kt + C (9) 



and integrating between limits, the form (10) is obtained: 



1 2.303 , ci ,.^. 



It will be noted that formula (9) is of such a nature that when the 

 logarithm of the concentration is plotted against time, a straight line is 

 produced. In fact, one of the best ways to determine whether a reaction 

 is of the first order is to plot the logarithm of the concentration against 

 the time. If a straight line is produced, the reaction is first order, and 

 the slope of the line multiplied by 2.303 gives at once the specific reaction 

 rate or velocity constant. When this constant is known, the concentra- 

 tion at any time may be calculated. 



In a second-order reaction the rate of the reaction depends on the 

 product of the concentration of two reacting substances. If the initial 

 concentrations are designated respectively by a and h and the amount 

 reacting by x, the following mathematical formula applies : 



-^ = k{a - x){b - x) ill) 



On integration this equation becomes 



t{a — 0) a {h — X) 

 This equation is of such a nature that when log b(a — x)/a(h — x) is plotted 

 against time, a straight line is produced and the slope of the line multi- 



