Reactant Concentration and Time

Using calculus, it is possible to develop integrated rate equations relating reactant concentration to time. We now examine several such equations, starting with first-order reactions. 

For the decomposition of N205 and other first order reactions of the type 

Because In a/b = In a — In b, the first-order equation can be written in the form 

A first-order reaction plot I ho rate constant for a first-order reaction can be determined from the slope of a plot of ln[A] versus time. The reaction illustrated, at 67°C. 

Comparing this equation with the general equation of a straight line, y = b + mx (b = -intercept, m = slope) 

For the decomposition of N2O5 and other first-order reactions of the type A-------------------------- products rate = fc[A] 

Comparing this equation with the general equation of a straight line, 

It follows that the rate constant is 0.35/min the integrated first-order equation for the decomposition of N2O5 is 

For the first-order decomposition of N2O5 at 67°C, where k = 0.35/min, calculate 

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THE RELATION BETWEEN REACTANT CONCENTRATION AND TIME Review Questions... 

Figure 9.2 (a) Linear relation between logarithm of reactant concentration and time for a first-order reaction, b) Influence of reactant concentration on rate for a first-order reaction, (c) Rate of an enzyme-catalyzed reaction as a function of substrate concentration. 

Next, we examine the relationship between reactant concentration and time for three types of reactions zero-order, first-order, and second order. The half-life, which is the time required for the concentration of a reactant to decrease to half of its initial value, is useful for distinguishing between reactions of different orders. (13.3)... 

Integrated Rate Laws Specify the Relationship Between Reactant Concentration and Time 723... 

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