Derive the expression for integrated rate law for zero-order reac… - Vidyadip

Question

Derive the expression for integrated rate law for zero-order reaction $A \rightarrow$ Products.

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Answer

Consider a zero order reaction, $A \rightarrow$ Products
The rate of the reaction is, Rate $=\frac{-d[ A ]}{d t}$
By rate law,
$\begin{aligned}
& \text { Rate }=k \times[A]^0=k \\
& \therefore- d [ A ]= k \times dt
\end{aligned}$

If $[A]_0$ is the initial concentration of the reactant $A$ at $t=0$ and $[A]_t$ is the concentration of $A$ present after time $t$, then by integrating above equation,

This is the integrated rate law expression for rate constant for zero order reaction.
$\begin{aligned}
& \therefore k \times t=[A]_0-[A]_t \\
& \therefore[A]_t=-k t+A_0
\end{aligned}$

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