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GATE 2023 CY – Question 46

Physical Chemistry · Kinetics and Reaction Dynamics: Elementary, parallel, opposing, and consecutive reactions. Steady state approximation. Mechanism of complex reactions. Unimolecular reactions. Potential energy surface and classical trajectories, Concept of saddle points, Transition state theory: Eyring equation, thermodynamic aspects. Kinetics of polymerization. Catalysis concepts and enzyme catalysis. Kinetic isotope effects. Fast reaction kinetics: relaxation and flow methods. Diffusion controlled reactions. Kinetics of unimolecular and bimolecular photophysical processes, Quantum yield calculation, static and dynamic quenching. · 2 marks · Multiple choice

In $P_2\xrightleftharpoons[k_1]{I_a}2Q\xrightarrow{k_2}R$, $I_a$ is absorbed light intensity and the first-step quantum yield is one. The steady-state Q concentration is ______.

  1. $\sqrt{I_a/(k_1+k_2)}$
  2. $\sqrt{I_a[P_2]/(k_1+k_2)}$
  3. $I_a/(k_1+k_2)$
  4. $I_a[P_2]/(k_1+k_2)$

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Correct answer: (A) $\sqrt{I_a/(k_1+k_2)}$

Explanation

Photodissociation produces 2Q at a rate 2Ia, because Ia already counts absorbed photons and the quantum yield is one. Both recombination channels consume Q in pair events, at combined rate 2(k1+k2)[Q]². Balance production and loss to obtain **[Q]=√[Ia/(k1+k2)], A**. Multiplying Ia by [P2] again would double-count absorption.