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Characteristics of Equilibrium Constant

Reaction A+...

Question

Reaction $A + B ⟶ C + D$ follows rate law, $r = k {[A]}^{1 / 2} {[B]}^{1 / 2}$ starting with $1 M$ of $A$ and $B$ each. What is the time taken for concentration of $A$ become $0.1 M$ ?
[Given $2.303 \times 10^{- 2} s e c^{- 1}$ ].

A

10 s e c

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B

100 s e c

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C

1000 s e c

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D

434 s e c

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Solution

The correct option is B $100 s e c$
The rate constant is $2.303 \times 10^{- 2} s e c^{- 1}$ . The overall reaction order is 1.

$t = \frac{2.303}{k} l o g \frac{a}{a - x}$
$t = \frac{2.303}{2.303 \times 10^{- 2}} l o g \frac{1}{0.1} = 100$

Hence, the time taken to consume 90% of concentration is 100 sec.

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