Write equations of the following:
$(i)$ The integrated rate equation for a zero-order reaction.
$(ii)$ The integrated rate equation for a first-order reaction.
$(i)$ The integrated rate equation for a zero-order reaction.
$(ii)$ The integrated rate equation for a first-order reaction.
(N/A) For a zero-order reaction $A \rightarrow P$,the rate is given by $Rate = -\frac{d[A]}{dt} = k[A]^0 = k$.
Integrating this,we get $[A] = -kt + [A]_0$,where $[A]_0$ is the initial concentration.
For a first-order reaction $A \rightarrow P$,the rate is given by $Rate = -\frac{d[A]}{dt} = k[A]$.
Rearranging and integrating,we get $\ln[A] = -kt + \ln[A]_0$,which can also be written as $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$.
Integrating this,we get $[A] = -kt + [A]_0$,where $[A]_0$ is the initial concentration.
For a first-order reaction $A \rightarrow P$,the rate is given by $Rate = -\frac{d[A]}{dt} = k[A]$.
Rearranging and integrating,we get $\ln[A] = -kt + \ln[A]_0$,which can also be written as $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$.
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