Derive integrated rate law for a zero-order reaction A Product .

Question

Derive integrated rate law for a zero-order reaction
A $\longrightarrow$ Product
.

✓

Answer

The integrated rate law for zero order reaction:
For zero order reaction,
$
A \rightarrow P
$
The differential rate law is given by,
$
\text { Rate }= d [ A ]= k [ A ]^0= k
$
Rearrangement of Eq. (i) gives,
$
d [ A ]=- kdt
$
Integration between the limits.
$[A]=[A]_0$ at $t=0$ and $[A]=[A]_t$ at $t=t$ gives,
$
\begin{aligned}
& \int_{[A]_0}^{[A]^t} d[A]=-k \int_0^t d t \\
& \operatorname{or}[ A ]_{ t }-[ A ]_0=-k t
\end{aligned}
$
or $[ A ]_{ t }-[ A ]_0=- kt$
Hence, $k t=[A]_0-[A]_t$
$
k =\frac{[A]_0-[A]_t}{t}
$

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