Questions & explanations
1. What is the significance of the steric factor in collision theory?
- It represents the fraction of molecules that have energy greater than the activation energy.
- It accounts for the requirement of proper orientation during collisions.
- It is always equal to 1 for all chemical reactions.
- It is the ratio of the actual rate to the rate predicted by the Arrhenius equation.
Answer: It accounts for the requirement of proper orientation during collisions.
The steric factor (often denoted as p) is a correction factor that accounts for the need for proper orientation when molecules collide. Even if colliding molecules have sufficient energy, an incorrect orientation may prevent bond formation, making the effective collision less likely. Option A describes the exponential factor in the Arrhenius equation, not the steric factor. Option C is false because many reactions, especially those involving large or complex molecules, have steric factors much less than 1. Option D is incorrect; the steric factor is part of the pre-exponential factor, not a ratio of actual to predicted rates.
2. According to the collision theory of chemical reactions, which of the following conditions is necessary for a reaction to occur?
- All collisions between reactant molecules lead to product formation.
- The colliding molecules must possess a minimum energy (equal to or greater than the activation energy) and have proper orientation.
- The rate of reaction is directly proportional to the activation energy of the reaction.
- Increasing the temperature decreases the number of collisions per second.
Answer: The colliding molecules must possess a minimum energy (equal to or greater than the activation energy) and have proper orientation.
Collision theory states that for a reaction to occur, reactant molecules must collide with energy at least equal to the activation energy and with correct orientation. Not all collisions are effective; only those meeting both criteria lead to product formation. Option A is incorrect because many collisions lack sufficient energy or proper orientation. Option C is wrong because rate is inversely related to activation energy, not directly proportional. Option D is false; increasing temperature increases the number of collisions.
3. Which of the following statements correctly distinguishes order from molecularity?
- Order can be zero, but molecularity cannot be zero
- Molecularity can be fractional, but order cannot
- Order is determined experimentally, while molecularity is a theoretical concept based on the reaction mechanism
- Order is applicable only to elementary reactions, while molecularity applies to complex reactions
Answer: Order is determined experimentally, while molecularity is a theoretical concept based on the reaction mechanism
Order of a reaction is an experimental quantity obtained from the rate law; it can be zero, fractional, or integer. Molecularity is a theoretical concept defined only for elementary steps and is always a positive integer. The other statements are false: molecularity cannot be fractional, order can be zero, and order applies to both elementary and complex reactions while molecularity only to elementary steps.
4. Which of the following statements correctly defines activation energy?
- The minimum energy required by the reactants to form the activated complex.
- The energy released when the products are formed from the reactants.
- The total energy of the activated complex.
- The difference in energy between the products and the reactants.
Answer: The minimum energy required by the reactants to form the activated complex.
Activation energy is the minimum energy that reacting molecules must possess to form the activated complex (transition state) and proceed to products. The other options describe the enthalpy change of the reaction (option B and D) or the total energy of the activated complex (option C), which are not correct definitions of activation energy.
5. In an energy profile diagram for an exothermic reaction, the activation energy (Ea) is represented by the difference in energy between:
- Products and reactants.
- Activated complex and reactants.
- Activated complex and products.
- Reactants and products.
Answer: Activated complex and reactants.
The activation energy is the energy barrier from the reactants to the top of the energy hill, i.e., the difference between the energy of the activated complex and the energy of the reactants. Option A and D refer to the overall energy change of the reaction, and option C refers to the activation energy of the reverse reaction.
6. A catalyst increases the rate of a reaction by:
- Decreasing the activation energy and providing an alternative pathway.
- Increasing the frequency factor.
- Increasing the temperature of the system.
- Increasing the activation energy.
Answer: Decreasing the activation energy and providing an alternative pathway.
A catalyst works by offering a different reaction pathway with a lower activation energy, so a larger fraction of molecules have sufficient energy to react. Option B is not the primary mechanism, option C is incorrect because the catalyst does not raise the temperature, and option D would slow the reaction.
7. Which of the following is an example of a pseudo-first-order reaction?
- Decomposition of hydrogen peroxide (2H₂O₂ → 2H₂O + O₂)
- Acid-catalyzed hydrolysis of ethyl acetate (CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH)
- Reaction of nitric oxide with oxygen (2NO + O₂ → 2NO₂)
- Formation of phosgene (CO + Cl₂ → COCl₂)
Answer: Acid-catalyzed hydrolysis of ethyl acetate (CH₃COOC₂H₅ + H₂O → CH₃COOH + C₂H₅OH)
In the acid-catalyzed hydrolysis of ethyl acetate, water is present in large excess, so its concentration remains effectively constant throughout the reaction. The rate then depends only on the concentration of ethyl acetate, making it appear as a first-order reaction, i.e., a pseudo-first-order reaction.
8. For the reaction A → products, the following data were obtained:
Experiment 1: [A] = 0.10 M, initial rate = 2.0 × 10⁻³ M/s
Experiment 2: [A] = 0.20 M, initial rate = 4.0 × 10⁻³ M/s
Experiment 3: [A] = 0.40 M, initial rate = 8.0 × 10⁻³ M/s
The order of the reaction with respect to A is:
- Zero
- First
- Second
- Third
Answer: First
When the concentration of A is doubled (from 0.10 M to 0.20 M), the initial rate also doubles (from 2.0 × 10⁻³ to 4.0 × 10⁻³ M/s). Similarly, doubling again (to 0.40 M) doubles the rate again (to 8.0 × 10⁻³ M/s). This linear relationship between concentration and rate indicates a first-order reaction.
9. For a reaction, the rate constant at 500 K is 1.0 × 10⁻⁴ s⁻¹ and at 600 K is 1.0 × 10⁻³ s⁻¹. Given R = 8.314 J mol⁻¹ K⁻¹, the activation energy (Ea) is approximately:
- 57.4 kJ mol⁻¹
- 28.7 kJ mol⁻¹
- 114.8 kJ mol⁻¹
- 5.74 kJ mol⁻¹
Answer: 57.4 kJ mol⁻¹
Using the two-point form: log₁₀(k₂/k₁) = (Ea/(2.303R))(1/T₁ – 1/T₂). Here, k₂/k₁ = 10, so log₁₀ = 1. 1/T₁ – 1/T₂ = 1/500 – 1/600 = 0.0003333 K⁻¹. Thus Ea = (1 × 2.303 × 8.314) / 0.0003333 ≈ 57,440 J mol⁻¹ = 57.4 kJ mol⁻¹. The other values arise from common calculation errors like halving or doubling.
10. The molecularity of a reaction is defined as:
- The sum of the exponents of concentration terms in the rate law
- The number of molecules taking part in the rate-determining step of an elementary reaction
- The total number of molecules whose concentrations change during the reaction
- The sum of the stoichiometric coefficients of the balanced chemical equation
Answer: The number of molecules taking part in the rate-determining step of an elementary reaction
Molecularity refers to the number of reactant molecules that collide in the rate-determining step of an elementary reaction. It is always a positive integer. The exponents in the rate law define order, not molecularity. Stoichiometric coefficients do not necessarily reflect the mechanism.
11. For a first-order reaction, the time required for the concentration of a reactant to decrease from 0.1 M to 0.025 M is 40 minutes. What is the rate constant of the reaction?
- 0.0347 min⁻¹
- 0.0693 min⁻¹
- 0.0173 min⁻¹
- 0.1386 min⁻¹
Answer: 0.0347 min⁻¹
For a first-order reaction, k = (2.303/t) log([A]₀/[A]). Here [A]₀ = 0.1 M, [A] = 0.025 M, t = 40 min. log(0.1/0.025) = log(4) = 0.6021. k = (2.303/40) × 0.6021 = (0.057575) × 0.6021 ≈ 0.0347 min⁻¹. The other options would correspond to different time or concentration changes.
12. For a zero-order reaction, the half-life (t₁/₂) is:
- Directly proportional to the initial concentration
- Inversely proportional to the initial concentration
- Independent of the initial concentration
- Directly proportional to the square of the initial concentration
Answer: Directly proportional to the initial concentration
For a zero-order reaction, t₁/₂ = [A]₀ / (2k). Thus, the half-life is directly proportional to the initial concentration. For a first-order reaction, half-life is independent of concentration. The other options describe relationships that do not hold for zero-order reactions.