In the Lindemann theory of unimolecular reactions, it is shown that the apparent rate constant for such a reaction is kapp =\frac{k_{1} C}{1 + k_{2} \textrm{ } C}, where C is the concentration of the reactant, k1 and k2 are constants (k2 = 9 × 105). The value of C for which kapp has 90% of its limiting value at C tending to infinitely large is

Engineering

Chemistry

Reaction Mechanism and Molecularity

Question

In the Lindemann theory of unimolecular reactions, it is shown that the apparent rate constant for such a reaction is k_app = $\frac{k_{1} C}{1 + k_{2} C}$ , where C is the concentration of the reactant, k₁ and k₂ are constants
(k₂ = 9 × 10⁵). The value of C for which k_app has 90% of its limiting value at C tending to infinitely large is

5 × 10^–5 M

10^–5 M

10^–4 M

10^–6 M

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$k_{aap} = \frac{k_{1} C}{1 + k_{2} C}$

$∵ c \to \infty, k_{app} = \frac{k_{1} C}{k_{2} C} = \frac{k_{1}}{k_{2}}$

Putting value of k_app

$k_{1} \times \frac{0 .9}{k_{2}} = \frac{k_{1} C}{1 + k_{2} C}$

$\frac{C k_{2}}{0 .9} = 1 + k_{2} C$

C k₂ = 0.9 + 0.9 C k₂
0.1 C k₂ = 0.9
C k₂ = 9

$C = \frac{9}{k_{2}} = \frac{9}{9 \times 10^{5}} = 10^{- 5}$