Grade 12Physical Chemistry

Prove that first order reaction is never completed??

Diksha

8 Years agoGrade 12

1 Answer

Arun

8 Years ago

Dear Diksha

Consider the reaction

A ? products

Let

[A]O = Initaial Concentration of A

[A]t = The concentration of A after time t

For the reaction to be of first order..

$Rate = -\frac{d[A]]}{dt} = k[A]$

$\Rightarrow \frac{d[A]}{[A]} =-kdt$ ...(i)

Intigrating this equation

$\int_{[A]_o}^{[A]} \frac{d[A]}{[A]} =-k\int_{0}^{t}dt$

we get

ln [A] - ln[A]o = -K(t-0)

$ln\frac{[A]}{[A]_o} = -kt$

$\Rightarrow ln\frac{[A]_o}{[A]} = kt$ …...... (ii)

$\Rightarrow log\frac{[A]_o}{[A]} = \frac{kt}{2.303}$ ...(iii)

$\Rightarrow k= \frac{1}{t}ln\frac{[A]_o}{[A]}$ ....(iv)

In 4th equation,

A can never be zero.as log infinity is not defined.

Hence first order reaction can never end.

Regards

Arun (askIITiams forum expert)

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Prove that first order reaction is never completed??

Diksha

1 Answer

Arun

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