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For A_2 + B_2 rightleftharpoons 2AB, E_a for forward and backward reaction are 180 and 200mathrm~kJ~mol^-1 respectively. If catalyst lowers E_a for both reaction by 100mathrm~kJ~mol^-1, which of the following statement is correct?

Solution & Explanation

### Related Formula Delta H = E_a(f) - E_a(b) ### Core Logic A catalyst accelerates both forward and backward path steps symmetrically by carving a lower activation energy profile route. * Uncatalyzed values: Delta H = 180 - 200 = -20mathrm~kJ~mol^-1. * Catalyzed values: E_a(f)' = 80mathrm~kJ~mol^-1 and E_a(b)' = 100mathrm~kJ~mol^-1, leading to Delta H' = 80 - 100 = -20mathrm~kJ~mol^-1. Thermodynamic parameters (Delta H, Delta G, Delta S) depend strictly on the initial and final energy states of reactants and products, meaning they are completely unaltered by the presence of a catalyst. ### Pattern Recognition Catalysts alter only kinetic properties (rate, activation barriers). They have zero impact on equilibrium positions or thermodynamic state parameters like Delta G or Delta H. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Chemical Kinetics

Reference Study Guides

More Chemical Kinetics Previous-Year Questions — Page 5

Q39 2025 Reaction Mechanism and Rate Law
The reaction mathrmA_2 + mathrmB_2 ightarrow 2 AB follows the mechanism mathrm A _ 2 xrightarrow [ mathrm k _ - 1 ]mathrm k _ 1 mathrm A + mathrm A text (fast) mathrm A + mathrm B _ 2 xrightarrow mathrm k _ 2 mathrm A B + mathrm B text (slow) mathrm A + mathrm B ightarrow mathrm A B text (fast) The overall order of the reaction is :
  • A. 1.5
  • B. 3
  • C. 2.5
  • D. 2

Solution

### Related Formula textRate = k cdot [textReactants]^textorder ### Core Logic The slowest elementary step controls the net kinetic pathway rate law : textRate = k_2[mathrmA][mathrmB2] quad dots textEquation (1) Since [mathrmA] behaves as a transient intermediate species, replace it using the prior fast equilibrium step : frack_1k-1 = frac[mathrmA]^2[mathrmA2] implies [mathrmA]^2 = left(frack_1k-1 ight) [mathrmA2] [mathrmA] = sqrtfrack_1k-1 cdot [mathrmA2]^1/2 Substitute [mathrmA] back into Equation (1) : textRate = k_2 sqrtfrack_1k-1 cdot [mathrmA2]^1/2[mathrmB2] Sum of powers determining overall order: textOrder = frac12 + 1 = 1.5 Hence, Option (1) is correct. ### Pattern Recognition Whenever a fast initial step dissociates a molecule into matching independent halves, it always injects a fractional order component of 0.5 relative to that parent species. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Chemical Kinetics

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