Half-life of a first-order reaction is 30 minutes. What fraction of reactant remains after 90 minutes?
A 2 1 B 4 1 C 8 1 D 16 1
After 90 min = 3 half-lives, remaining = (2 1 8 1
The rate constant of a reaction increases from 4 × 10⁻³ s⁻¹ to 8 × 10⁻³ s⁻¹ when temperature increases from 300K to 310K. Calculate activation energy (R = 8.314 J/mol·K)
A 50.4 kJ/mol B 60.8 kJ/mol C 75.2 kJ/mol D 85.6 kJ/mol
Using ln(k₂/k₁) = (Eₐ/R)(T₂-T₁)/(T₁T₂); ln(2) = (Eₐ/8.314)(93000 10
Which of the following statements about collision theory is INCORRECT?
A Molecules must collide with proper orientation B All collisions lead to reaction C Collision frequency increases with temperature D Only collisions with energy ≥ Eₐ are effective
Not all collisions are effective; only those with proper orientation and sufficient energy lead to reaction
For a zero-order reaction, the integrated rate law is [A] = [A]₀ - kt. If [A]₀ = 0.5 M and k = 0.02 M·s⁻¹, find time when [A] = 0
A 15 s B 20 s C 25 s D 30 s
0 = 0.5 - 0.02t; t = 0.0 5
Consider the mechanism: (1) A + B ⇌ C (fast equilibrium), (2) C + D → E + F (slow). Which is the rate-determining step?
A Step 1 B Step 2 C Both steps D Cannot be determined
The slowest step in a mechanism is the rate-determining step (RDS), which is step 2
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The rate law for a reaction is Rate = k[A]¹[B]⁰. If [B] is doubled and [A] is halved, how does the rate change?
A Increases by factor of 2 B Decreases by factor of 2 C Remains same D Increases by factor of 4
Rate depends only on [A] (order = 1 w.r.t. A). Halving [A] decreases rate by factor of 2. [B] has no effect
At 25°C, the rate constant is 3 × 10⁻² s⁻¹ and at 35°C it is 6 × 10⁻² s⁻¹. What is the temperature coefficient (Q₁₀) for this reaction?
A 1.5 B 2 C 3 D 4
Q₁₀ = k(T+10)/k(T) = (6 × 10⁻²)/(3 × 10⁻²) = 2. For typical reactions, Q₁₀ = 2-3
The decomposition of N₂O₅ is a first-order reaction. If 50% decomposes in 30 minutes, what is the rate constant?
A 0.023 min⁻¹ B 0.035 min⁻¹ C 0.052 min⁻¹ D 0.069 min⁻¹
For first-order: k = 0.693/t₁/₂ = 0.30 693
In the reaction A → Products, doubling [A] increases rate by 4 times. The order of reaction is:
A Zero B First C Second D Third
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?
A Temperature B Concentration of reactants C Nature of reactants D Presence of catalyst
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)
A 2.3 × 10⁻² s⁻¹ B 1.8 × 10⁻¹ s⁻¹ C 3.4 × 10⁻³ s⁻¹ D 5.1 × 10⁻² s⁻¹
k = A·exp(-Eₐ/RT) = 2 × 10¹³ × exp(-8 50000
For an elementary reaction: 2A + B → Products, the rate law is:
A Rate = k[A][B] B Rate = k[A]²[B] C Rate = k[A][B]² D Rate = k[A]³[B]
For elementary reactions, rate law exponents = stoichiometric coefficients. Rate = k[A]²[B]
Which statement about potential energy diagrams is CORRECT?
A Higher activation energy means faster reaction B An exothermic reaction has ΔH > 0 C Activation energy is always greater than ΔH D Catalyst changes activation energy but not ΔH
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
A 0.2 M B 0.25 M C 0.1 M D 0.15 M
1/[A] = 2 + 0.4(5) = 2 + 2 = 4; [A] = 4 1
For the reaction: (1) Cl₂ ⇌ 2Cl (fast), (2) Cl + H₂ → HCl + H (slow), (3) H + Cl₂ → HCl + Cl (fast). The overall reaction is:
A Cl₂ + H₂ → 2HCl B 2Cl₂ + H₂ → 2HCl + Cl C H₂ + Cl₂ → 2HCl D Cl + H₂ → HCl + H
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?
A 0.04 M⁻¹s⁻¹ B 0.02 M⁻¹s⁻¹ C 0.2 M⁻¹s⁻¹ D 0.01 M⁻¹s⁻¹
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)
A 100 times B 256 times C 500 times D 1000 times
Using ln(k₂/k₁) = (Eₐ/R)[(T₂-T₁)/(T₁T₂)]; ln(k₂/k₁) = (8 60000
