Question
What is Pseudo first order reaction? Derive integrated rate law equation for zero order reaction
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Answer
pseudo first order reaction:
A reaction which has higher order true rate law but experimentally found to behave as first order are called pseudo first order reaction.
The integrated rate law for zero-order reactions:
For zero$-$order reaction, $A \rightarrow P$
the differential rate law is given by
rate $=-\frac{ d [ A ]}{ A }= k [ A ]_0= k...(1)$
Rearrangement of Eq. $(1)$ gives
$d[A] = -k dt (\because [A]^0= 1)$
Integration between the limits
$[A] = [A]_0at t = 0$ and $[A] = [A]_t$ at $t = t$ gives
$\int_{[A]_0}^{[A]_t} d[A]=-k \int_0^t d t$
or $[A]_t - [A]_0 =-kt$
Hence, $kt = [A]_0- [A]_t ....(2)$
A reaction which has higher order true rate law but experimentally found to behave as first order are called pseudo first order reaction.
The integrated rate law for zero-order reactions:
For zero$-$order reaction, $A \rightarrow P$
the differential rate law is given by
rate $=-\frac{ d [ A ]}{ A }= k [ A ]_0= k...(1)$
Rearrangement of Eq. $(1)$ gives
$d[A] = -k dt (\because [A]^0= 1)$
Integration between the limits
$[A] = [A]_0at t = 0$ and $[A] = [A]_t$ at $t = t$ gives
$\int_{[A]_0}^{[A]_t} d[A]=-k \int_0^t d t$
or $[A]_t - [A]_0 =-kt$
Hence, $kt = [A]_0- [A]_t ....(2)$
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