The decomposition of N₂O₅ is a first-order reaction. If 50% decomposes in 30 minutes, what is the rate constant?
For first-order: k = 0.693/t₁/₂ = 0.30693 = 0.0231 min⁻¹ ≈ 0.023 min⁻¹
In the reaction A → Products, doubling [A] increases rate by 4 times. The order of reaction is:
If doubling concentration increases rate by 4 times (2²), reaction is second order
Which factor does NOT affect the rate constant k of a reaction?
Rate constant k is independent of reactant concentration; it depends on T, nature of reactants, and catalyst
For a reaction with Eₐ = 50 kJ/mol and A = 2 × 10¹³ s⁻¹ (Arrhenius pre-exponential factor), calculate k at 300K (R = 8.314 J/mol·K)
k = A·exp(-Eₐ/RT) = 2 × 10¹³ × exp(-850000.314×300) = 2 × 10¹³ × exp(-20.03) ≈ 3.4 × 10⁻³ s⁻¹
For an elementary reaction: 2A + B → Products, the rate law is:
For elementary reactions, rate law exponents = stoichiometric coefficients. Rate = k[A]²[B]
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Which statement about potential energy diagrams is CORRECT?
Catalyst lowers Eₐ (forward and reverse) without changing ΔH, reaction enthalpy change
The integrated rate law for second-order reaction is 1/[A] = 1/[A]₀ + kt. If [A]₀ = 0.5 M, k = 0.4 M⁻¹s⁻¹, find [A] after 5 seconds
1/[A] = 2 + 0.4(5) = 2 + 2 = 4; [A] = 41 = 0.25 M
For the reaction: (1) Cl₂ ⇌ 2Cl (fast), (2) Cl + H₂ → HCl + H (slow), (3) H + Cl₂ → HCl + Cl (fast). The overall reaction is:
Adding all steps and canceling intermediates (Cl, H): Cl₂ + H₂ → 2HCl
The half-life of a second-order reaction is 100 s when initial concentration is 0.5 M. What is the rate constant?
For second-order: t₁/₂ = 1/(k[A]₀); 100 = 1/(k × 0.5); k = 0.04 M⁻¹s⁻¹
A reaction has Eₐ = 60 kJ/mol. How many times faster will it be at 327°C compared to 27°C? (R = 8.314 J/mol·K, assume A constant)
Using ln(k₂/k₁) = (Eₐ/R)[(T₂-T₁)/(T₁T₂)]; ln(k₂/k₁) = (860000.314)[(300)/(600×300)] ≈ 6.2; k₂/k₁ ≈ 500
