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GATE 2024 CH – Question 20

Chemical Reaction Engineering · Reaction rates and kinetics of homogeneous reactions · 1 mark · Multiple choice

The rate of a reaction $A \to B$ is 0.2 mol m$^{-3}$ s$^{-1}$ at a particular concentration $C_{A1}$. The rate constant of the reaction at a given temperature is 0.1 m$^3$ mol$^{-1}$ s$^{-1}$. If the reactant concentration is increased to $10C_{A1}$ at the same temperature, the reaction rate, in mol m$^{-3}$ s$^{-1}$, is

  1. 20
  2. 10
  3. 100
  4. 50

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Correct answer: (A) 20

Explanation

The unit of the rate constant (m³ mol⁻¹ s⁻¹) shows a second-order reaction, $r = kC_A^2$. Then $C_{A1}^2 = \frac{0.2}{0.1} = 2$. At ten times the concentration, $r = 0.1 \times 100 \times 2 = 20$ mol m⁻³ s⁻¹.