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Question of 117

Q.(a) A reaction is first order with respect to reactant A and second order with respect to reactant B. Write differential rate equation.

(b) If the rate constant of a reaction is k=3×10⁻⁴ s⁻¹, then what would be the order of reaction?
(c) Match the statements given in Column I with Column II:
Column I:
(i) Mathematical expression for rate of reaction
(ii) Fraction of molecules with energy equal to or greater than activation energy
(iii) Order of complex reaction
(iv) CH₃COOC₂H₅ + H₂O —H⁺→ CH₃COOH + C₂H₅OH
Column II:
(a) The slowest step
(b) Pseudo first order
(c) Rate law
(d) e^(−Ea/RT)
Uttarakhand UbseUttarakhand Board Intermediate (Class 12) 2026Subjective· 4mImportance★★★★★
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(a) −d[A]dt=k[A][B]2-\dfrac{d[A]}{dt} = k[A][B]^{2} (overall order 3). (b) A rate constant with units s−1\text{s}^{-1} means the reaction is first order. (c) (i)–(c), (ii)–(d), (iii)–(a), (iv)–(b).

(a) Differential rate equation. First order in A and second order in B, so the powers are 1 and 2:

Rate=k[A]1[B]2⇒−d[A]dt=k[A][B]2\text{Rate} = k[A]^{1}[B]^{2} \quad\Rightarrow\quad -\frac{d[A]}{dt} = k[A][B]^{2}

(overall order =1+2=3= 1 + 2 = 3).

(b) Order from units of k. The units of the rate constant reveal the order. For a first-order reaction kk has units of time−1\text{time}^{-1}, i.e. s−1\text{s}^{-1}. Since k=3×10−4 s−1k = 3\times10^{-4}\ \text{s}^{-1}, the reaction is first order.

(c) Matching.

  • (i) Mathematical expression for rate of reaction → (c) Rate law.
  • (ii) Fraction of molecules with energy ≥\geq activation energy → (d) e−Ea/RTe^{-E_a/RT} (the Arrhenius/Boltzmann factor).
  • (iii) Order of a complex reaction → (a) The slowest step (the rate-determining step decides the order).
  • (iv) CH3COOC2H5+H2O→H+CH3COOH+C2H5OH\text{CH}_3\text{COOC}_2\text{H}_5 + \text{H}_2\text{O} \xrightarrow{\text{H}^{+}} \text{CH}_3\text{COOH} + \text{C}_2\text{H}_5\text{OH} → (b) Pseudo first order (water is in large excess, so its concentration is effectively constant).

[!NOTE]

OR alternative asked — from the potential-energy plot (Reactants ≈150\approx 150 kJ, peak/activated complex C≈300C \approx 300 kJ, Products ≈100\approx 100 kJ): …

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