Chemical Kinetics and Nuclear ChemistryHard

Question

For the reaction A → Products (order = n), the theoretical time of completion of reaction is

Options

A.Infinite for all values of n.
B.Infinite for n ≥ 1.
C.$\frac{\left\lbrack A_{0} \right\rbrack^{1 - n}}{K(1 - n)}$for n ≠ 1
D.$\frac{\left\lbrack A_{0} \right\rbrack^{1 - n}}{K(1 - n)}$ for n < 1

Solution

$n = 1 \Rightarrow t_{100\%} = \frac{1}{K}.\ln\frac{\left\lbrack A_{0} \right\rbrack}{0} = \text{ Infinite}$

$n \neq 1 \Rightarrow t_{100\%} = \frac{\left\lbrack A_{0} \right\rbrack^{1 - n} - (0)^{1 - n}}{K(1 - n)} = \frac{\left\lbrack A_{0} \right\rbrack^{1 - n}}{K(1 - n)}\text{ if }n < 1 $$$= \text{Infinite if }n > 1$$

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