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All reactions are of 1st order  At time t = t1 (t1 > 0) \frac{[B]}{[C]} = \alpha . Therefore at time  t = t2 (where t2 \geq t1\frac{[C]}{[D]} = \beta which of the following is correct?

Option: 1

\alpha > \beta


Option: 2

\alpha = \beta


Option: 3

\alpha \beta = 0.4


Option: 4

\alpha + \beta = 0.4


Answers (1)

best_answer

First Order Reaction -

The rate of the reaction is proportional to the first power of the concentration of the reactant.

- wherein

Formula:

R    \rightarrow        P

a                 0

a-x             x

rate[r]=K[R]^{1}

\frac{-d(a-x)}{dt}=K(a-x)

\frac{-dx}{dt}=K(a-x)  [differentiate rate law]

ln \:[\frac{a}{a-x}]=kt \:(Integrated rate law)

Unit of k=sec^{-1}

t_\frac{1}{2}=\frac{0.693}{k}

-

\frac{[B]}{[C]} = \frac{3k_{1}}{8k_{1}}=\frac{3}{8}= \alpha

\frac{[C]}{[D]} = \frac{8k_{2}}{7.5k_{2}}=\frac{8}{7.5}= \beta

\therefore \alpha \beta = 0.4

Therefore, Option(3) is correct.

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