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  • Which of the following shows the expression of  half life period of second order reaction?                &

Which of the following shows the expression of  half life period of second order reaction?

                                        \mathrm{A \longrightarrow B}

(Where initial concentration of A is [A]0 and rate constant is K)

Option: 1

\mathrm{\frac{0.693}{K }}


Option: 2

\mathrm{\frac{1}{K [A]_0}}


Option: 3

\mathrm{\frac{[A]_0}{2K }}


Option: 4

none of above


Answers (1)

best_answer

As we have learnt,

Expression for Second Order Kinetics -

\mathrm{\mathbf{\frac{1}{[A]}\: =\: kt\: +\: \frac{1}{[A_{o}]}}}
 

Half-life(t1/2): We know that the half-life for a reaction is the time when the concentration of the reactant(A) is half of its initial value.
Thus, at time t = t1/2, A = Ao/2
From equation (i) we have:

\mathrm{t\: =\: \frac{1}{k}\left [ \frac{1}{A}\: -\: \frac{1}{A_{o}} \right ]}

\mathrm{\Rightarrow t_{1/2}\: =\: \frac{1}{k}\left [ \frac{1}{A_{o}/2}\: -\: \frac{1}{A_{o}} \right ]}

\mathrm{Thus,\: \mathbf{t_{1/2}\: =\: \frac{1}{kA_{o}}}}

Therefore, option(2) is correct

Posted by

HARSH KANKARIA

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