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Standard XII

Chemistry

Arrhenius Equation

The reaction ...

Question

The reaction $A + B \to C + D$ follows the following rate law rate $= K {[A]}^{\frac{1}{2}} {[B]}^{\frac{1}{2}}$ . Starting with the initial concentration of $1 M$ A and B each. What is the time taken for concentration A to become $0.25 M$ .

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Solution

Step 1: Analyzing given data
Rate law $= K {[A]}^{\frac{1}{2}} {[B]}^{\frac{1}{2}}$
The initial concentration of A $= 1 M$
The concentration of A after some time $= 0.25 M$
Step 2: Calculating Time for concentration A to become $0.25 M$
Order of reaction from rate law is given by the sum of the power of the reactant
Therefore, Order $= \frac{1}{2} + \frac{1}{2} \Rightarrow 1$
It will require two half times for the concentration of A to become $0.25$
Therefore, $t_{\frac{1}{2}} = \frac{0.693}{K}$ $K = 2.303 \times 10^{- 3}$
$t_{\frac{1}{2}} = \frac{0.693}{2.303 \times 10^{- 3}} \times 2 \Rightarrow 600 \sec$
Therefore, the time required for the concentration of A to become $0.25 M = 600 \sec$

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