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Integrated Rate Equation
We have already noted that the concentration dependence of rate is called differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by determination of slope of the tangent at point‘t’ in concentration vs time plot. This makes it difficult to determine the rate law and hence the order of the reaction. In order to avoid this difficulty, we can integrate the differential rate equation to give a relation between the directly rate equation to give a relation concentrations at different times and rate constant.
The integrated equation, thus, derived is used for determining the rate constant, k of the reaction. Also as the integrated from yields concentration for all times. It is helpful in calculating the time in which the reactions is 25% or 50% or 90% complete and vice versa.
The integrated rate equations are different for the reactions of different reaction orders.
1. Zero order reaction: A reaction is zero order if its rate is independent of the concentration of reactants or a zero order reaction means that the rate of reaction is proportional to zero power of the concentration of reactants. For a zero order reaction of the form.
R
P
The rate of reaction, rate = d[R]/dt = k[R]0
2. First order reaction: Let us assume a simple hypothetical first order reaction represented as
R
P
If the initial concentration of R is [R]0, k is the rate constant and [R] is conc. At time t then the differential form of the first order reaction will be
-d [R]/dt = k [R]
Rearranging the equation, we get
-d[R]/[R] = kdt
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The integrated equation, thus, derived is used for determining the rate constant, k of the reaction. Also as the integrated from yields concentration for all times. It is helpful in calculating the time in which the reactions is 25% or 50% or 90% complete and vice versa.
The integrated rate equations are different for the reactions of different reaction orders.
1. Zero order reaction: A reaction is zero order if its rate is independent of the concentration of reactants or a zero order reaction means that the rate of reaction is proportional to zero power of the concentration of reactants. For a zero order reaction of the form.
R
The rate of reaction, rate = d[R]/dt = k[R]0
2. First order reaction: Let us assume a simple hypothetical first order reaction represented as
R
If the initial concentration of R is [R]0, k is the rate constant and [R] is conc. At time t then the differential form of the first order reaction will be
-d [R]/dt = k [R]
Rearranging the equation, we get
-d[R]/[R] = kdt
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