Practice of Kinetics (Comprehensive Chemical Kinetics, Volume 1)

388 TREATMENT OF EXPERIMENTAL DATAship between [A] and the physical property used to follow the disappearance ofA cannot be determined with any accuracy. For example, suppose we follow aphysical property whose value 4t at time t is linearly related to the concentrationof A, [A], thuswhere A and p are constants. The initial and final values of the physical property4, 4o and cPm, are given byand40 = ACAIO+P4m = Pif all the A originally present disappears. Therefore,and clearly, in a simple case, CI can be calculated from the observed value of 4at any time and the observed or calculated values of 4o and 4m. It sometimeshappens that it is not possible to determine the values of 4o and/or with anyaccuracy. In such cases, special methods of treating the data have been devisedand it is with these procedures that the present section is concerned.(i) Reactions of the type -d[A]/dt = k[A]For such reactionsand so, if the value of the physical property employed is related to [A] by eqn. (80),we obtainGuggenheim’s method.’ For any particular run, consider a pair of values of 4, q5t,and 4t,+z, observed at the two times t, and t,+t as indicated by the subscripts.Then,