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Standard XII

Chemistry

First Order Reaction

Reaction A ...

Question

Reaction $A + B \to C + D$ follows following rate law rate $= k = [A]^{\frac{1}{2}} [B]^{\frac{1}{2}}$ . Starting with initial conc. of one mole of $A$ and $B$ each, what is the time taken for amount of $A$ of become $0.25$ mole? Given $k = 2.31 \times 10^{- 3} s e c^{- 1}$ .

300 s e c .

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600 s e c .

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900 s e c .

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1300 s e c .

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Solution

The correct option is D $1300 s e c .$
For $\frac{1}{2}$ order:
$\frac{1}{a^{- \frac{1}{2}}} = \frac{1}{a_{0}^{- \frac{1}{2}}} - \frac{k t}{2}$
$\frac{k t}{2} = \sqrt{a_{0}} - \sqrt{a}$
$t = \frac{2 (\sqrt{a_{0}} - \sqrt{a})}{k}$
Using $a = 0.25$ and $a_{0} = 1$ and $k = 2.31 \times 10^{- 3} s e c^{- 1}$
We get $t = 1300 s e c$

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Reaction A+B→C+D follows following rate law rate =k=[A]12[B]12. Starting with initial conc. of one mole of A and B each, what is the time taken for amount of A of become 0.25 mole? Given k=2.31×10−3sec−1.

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