A reaction proceeds through the formation of an intermediate B in an unimolecular reaction A ka B kb C The… · ABC26PH0474
Subject: Physical Chemistry · Chapter: Chemical Kinetics · Topic: Chemical Kinetics – General · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium
A reaction proceeds through the formation of an intermediate B in an unimolecular reaction \[ \mathrm{A} \xrightarrow{\mathrm{k}_{\mathrm{a}}} \mathrm{B} \xrightarrow{\mathrm{k}_{\mathrm{b}}} \mathrm{C} \]
The integrated rate law for this reaction is (a)$[\mathrm{A}]=[\mathrm{A}]_{0} \mathrm{e}^{-\mathrm{k}_{\mathrm{a}} \mathrm{t}}$
(b)$[\mathrm{A}]=[\mathrm{A}]_{0}\left(\mathrm{e}^{-\mathrm{k}_{\mathrm{a}} \mathrm{t}}-\mathrm{e}^{-\mathrm{k}_{\mathrm{b}} \mathrm{t}}\right)$
(c)$[\mathrm{A}]=\frac{[\mathrm{A}]_{0}}{2}\left(1+\frac{\mathrm{k}_{\mathrm{a}} \mathrm{e}^{-\mathrm{k}_{\mathrm{b}} \mathrm{t}}-\mathrm{k}_{\mathrm{b}} \mathrm{e}^{-\mathrm{k}_{\mathrm{a}} \mathrm{t}}}{\mathrm{k}_{\mathrm{a}}-\mathrm{k}_{\mathrm{b}}}\right)$
(d)$[\mathrm{A}]=[\mathrm{A}]_{0}\left(1+\mathrm{e}^{-\mathrm{k}_{\mathrm{a}} \mathrm{t}}-\mathrm{e}^{-\mathrm{k}_{\mathrm{b}} \mathrm{t}}\right)$
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
A decays by simple first order: [A] = [A]₀e^(−k_a t) (a).
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