Kinetic analysis of the simplest mechanism

These actual concentrations which are present in the solution are related by the equilibrium constant  

The chemistry of the system will determine which is chosen, but usually the change in [A]totai or [C] is monitored when 

But note in the examples in Problems 8.3 and 8.7, the rate is given in terms of an actual concentration of a reactant. In these examples the experimental technique actually measured the actual concentration rather than the total concentration. Care must be taken to distinguish between these two situations. 

Since the reaction is first order in A, a plot of loge[A]total at time, versus t is linear with slope = —kobs = —k2K/( 1 + K), from which kz can be found, provided K is known independently. K=kdk i, and other experiments will be required to determine ki and k, individually. 

Question. Formulate expressions for /cobs for the above mechanism for cases where the overall rate is found by following 

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