For an elementary reaction : $A + 2 B ⟶ C$ when 1 M A was taken with 10^-4 M B, time taken for B to reduce to half was found to be 10 seconds. Calculate t_1/2 when 1 M A is reacted with 10^-5 M B.
[t_1/2 = time for B to reduce to 50% of original]

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1 second

100 seconds

20 seconds

10 seconds

answer is C.

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Detailed Solution

Here,

$\begin{array}{l} - \frac{1}{2} \frac{d [B]}{d t} = K \cdot [B]^{2} \cdot [A] \\ t_{1 / 2} \propto [B]_{0}^{- 1} \\ \frac{10}{t_{1 / 2}} = {(\frac{10^{- 6}}{10^{- 4}})}^{- 1} \\ \Rightarrow t_{1 / 2} = 100 \sec \end{array}$

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