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GATE 2023 CY – Question 57

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 select

Two enzyme-catalysis reactions I and II have identical y-intercepts in Lineweaver–Burk plots, but slope I is twice slope II. Initial enzyme concentrations are equal. Given $1/v=1/v_{max}+(K_M/v_{max})(1/[S])$, with rate v, maximum rate $v_{max}$, Michaelis constant $K_M$, and substrate concentration [S], select correct statements.

  1. I and II have the same turnover number
  2. I and II have identical Michaelis constants
  3. I has twice the Michaelis constant of II
  4. I and II have identical elementary-step rates

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Correct answer: (A) I and II have the same turnover number; (C) I has twice the Michaelis constant of II

Explanation

The intercept 1/vmax is shared, so both have the same vmax. Equal initial enzyme concentrations then imply equal kcat=vmax/[E]0, A true. Slope KM/vmax doubles in I, so KM, I=2KM, II, C true. Neither equality of KM nor equality of all microscopic step rates follows. **Select A, C**.