THE PHYSICAL CHEMISTRY OF VISUAL PURPLE 



trated in Fig. 3.5 in which cf> is plotted against the transmissivity for 

 the range of values of If/ 1 from 1-0 to 0-5. The case //// = 1-0 

 corresponds to a final transmission of 100 per cent, i.e. to a solution 

 quite free from absorbing impurities. In this instance the value of </> 

 is invariant and equal to unity, and equation (7) reduces to the form 

 of equation (4). The case /^// = 0-5 represents a final transmission 

 of only 50 per cent, i.e. a density due to impurities of 0-3. Even in 

 such an impure solution as this, however, the change in cf) is quite 

 small, provided the initial density of the solution (i.e. before bleach- 

 ing) is not too high. The maximum variations in (j) over the whole 

 range of a bleaching curve, assuming an initial optical density of 0-5 

 (for example) and various values for the final transmissivity, Ifjl, 

 are as follows: 



General case. By means of the function </>, we may now solve the 

 general case, viz. where not only are light-absorbing impurities 

 present but where also the photo-product absorbs hght of the wave- 

 length used for bleaching. 



Assuming that Beer's and Lambert's laws of light absorption 

 hold for all components, the optical density of the solution at any 

 time, r, is 



loge7 



(x.cl + za'(co — c)l + di, 



(8) 



where zcx.' has been written for aa^ + ^a^ + • • .; a^, a,,, . . ., 

 being the extinction coefficients of the products of bleaching and 

 a, 6, . . ., their stoichiometric relation to visual purple, d^ the density 

 of the impurities present and Cq the visual purple concentration when 

 t = 0. Differentiating (8) with respect to time and rearranging the 

 result, 



dL 



It.dt 



(a/-za7)J 

 73 



(9) 



