Question

Following is the graph between $\log t_{1 / 2}$ and log a (a initial concentration) for a given reaction at $27^{\circ} C$

Find the order of reaction.

Answer 1

$t_{1 / 2} \propto \frac{1}{a_{0}^{n-1}}$

$t_{1 / 2}=k \cdot \frac{1}{a_{0}^{n-1}}$

$\log t_{1 / 2}=\log\, k-(n-1) \log\, a_{0}$

slope $=\tan 45^{\circ}=1 \Rightarrow -(n-1)=1$

$\Rightarrow n=0$