Equilibrium for a Simple Reaction

FIGURE 20.8 If the time of the measurements is extended (using data from Table 20.1 A), it becomes clear that a first-order plot fits the data better than a second-order plot A straight-line fit is more obvious for the first-order plot over longer periods of time. In experimental kinetics, it is extremely important to extend an experiment to a long enough time that the appropriate straight line—and therefore the correct order of the reaction—is determined conclusively. 

Kinetics describes how reactions proceed, but we should understand from thermodynamics that virtually all reactions do not proceed to completion. Instead, in time a reverse reaction begins to occur, and when the rate of the reverse reaction equals the rate of the forward reaction, net change ceases and the system is at a dynamic equilibrium. Although we have stated previously that thermodynamics and kinetics are separate considerations, the previous statement—that the rate of forward reaction equals the rate of reverse reaction for a system at equilibrium—suggests that there are some connections between kinetics and thermodynamics. 

In our discussion of initial rates, we were implicitly confining ourselves to short periods of time near the beginning of the reaction. That is, we assumed was small. For equilibrium conditions, however, we need to consider a different time regime, that where approaches its maximum value. What this implies is that a reverse chemical process will become important in our understanding of how concentrations are changing. This reverse reaction is an additional consideration that we have so far ignored. 

k is the rate constant for the forward reaction and is the rate constant for the reverse reaction. Furthermore, we will assume that each reaction is first-order 

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