In the Lindemann theory of unimolecular reaction, it is shown that the apparent rate constant for such a reaction is $k_{a p p} = \frac{k_{1} C}{1 + α C}$ where C is the concentration of the reactant $k_{1}$ and $α$ are constants. Calculate the value of C for which $k_{a p p}$ has 90% of its limiting value at C tending to infinitely large values, given $α = 9 \times 10^{5}$ .

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$10^{- 5} mole /litre$

$5 \times 10^{- 5} mole/itre$

$10^{- 4} mole/litre$

$10^{- 6} mole/litre$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$lim_{c \to \infty} \frac{k_{1} C}{1 + α C} = \frac{k_{1}}{α} = k_{a p p}$

Now, $\frac{9}{10} \times \frac{k_{1}}{α} = \frac{k_{1} C}{1 + α C}$

$\begin{array}{ll} \Rightarrow C = \frac{1}{0.1 α} (0.9) \\ \Rightarrow C = \frac{9}{9 \times 10^{5}} \end{array}$

hence, the correct answer is $10^{- 5} mole /litre$ .

Watch 3-min video & get full concept clarity