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Grade: 12
        Prove that first order reaction is never completed??
10 months ago

Answers : (1)

Arun
14827 Points
							
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)

10 months ago
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