Chemegate
Home/Practice Tests/PYQ Archive/Reaction Engineering

GATE 2025 Chemical Engineering, Q31 · Reaction Engineering

The correct answers are A. For S ≪ K_m, the reaction is apparent first-order in S.; B. For S ≫ K_m, the reaction rate is nearly independent of S.; D. K_m is independent of the total enzyme concentration..

Question

Consider an enzymatic reaction that follows Michaelis-Menten kinetics. Let Km,K_{m}, S, and VmaxV_{max} denote the Michaelis constant, substrate concentration, and maximum reaction rate, respectively. Which of the following statements is/are TRUE?

  • A. For S ≪Km,\ll K_{m}, the reaction is apparent first-order in S.
  • B. For S ≫Km,\gg K_{m}, the reaction rate is nearly independent of S.
  • C. For S =Km,= K_{m}, the rate of reaction equals Vmax.V_{max}.
  • D. KmK_{m} is independent of the total enzyme concentration.

Official answer: A. For S ≪Km,\ll K_{m}, the reaction is apparent first-order in S.; B. For S ≫Km,\gg K_{m}, the reaction rate is nearly independent of S.; D. KmK_{m} is independent of the total enzyme concentration.

Why

GATE 2025 official key: (A, B, D). v =Vmax⋅S/(Km+S):= V_{max}\cdot S/(K_{m}+S): for S≪Km,v≈(Vmax/Km)SS\ll K_{m}, v\approx (V_{max}/K_{m})S (first order); for S≫Km,v≈VmaxS\gg K_{m}, v\approx V_{max} (zero order, independent of S); at S=Km,v=Vmax/2S=K_{m}, v=V_{max}/2 (not Vmax,V_{max}, making C false); KmK_{m} is an intrinsic kinetic constant independent of enzyme loading.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

Reaction Engineering Topic Guide →More Reaction Engineering PYQs →Take the Full GATE 2025 Test →