Consider a first order decomposition process $A_{3} \to \frac{3}{2} A_{2}$
A plot of the concentration of $A_{3}$ and $A_{2}$ versus time is shown below. At time , the percentage of the reaction decomposed is

75%

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50%

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40%

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30%

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Solution

The correct option is C 40%
At time $= t$ $[A_{2}] = [A_{3}]$
For given reaction
$A_{3} \to \frac{3}{2} A_{2}$
$A t t = 0 y 0$
$A t t = t y - x \frac{3}{2} x$
$y - x = \frac{3}{2} x$
$[A_{2}]_{t = 0} = y = \frac{5}{2} x$
$[A_{2}]_{t} = \frac{3}{2} x$
$%$ of decomposition
$\frac{[A_{2}]_{t = 0} - [A_{2}]_{t}}{[A_{2}]_{t = 0}} \times 100 = 40 %$

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