Reaction Rates - AP Chemistry

1. If the solution is diluted to twice its original volume by adding more of the same solvent, while the moles of reactants stay constant, how will the initial reaction rate be affected?
   Answer: The rate will decrease by a factor of four. The rate of this reaction depends on the concentrations of both CH₃Br and OH⁻. When the volume of the solvent is doubled, the concentration of each reactant is halved (since concentration = moles/volume). Because the rate law is Rate = k[CH₃Br][OH⁻], the new rate will be Rate' = k([CH₃Br]/2)([OH⁻]/2) = (1/4) k[CH₃Br][OH⁻] = (1/4) original rate. Thus, the rate decreases by a factor of four.
2. In which of the following systems would an increase in pressure cause the greatest increase in reaction rate, assuming all other factors are constant?
   Answer: A reaction between two gases in a container. Increasing the total pressure of a system by decreasing its volume will increase the concentration of all gaseous species. For a reaction between two gases, this increases the concentrations of both reactants, leading to a significant increase in the rate of reaction due to more frequent collisions. Pressure has a negligible effect on the rates of reactions in the liquid or solid phase.
3. The rate of the reaction $A + B \rightarrow C$ is monitored. When the initial concentration of B is doubled while keeping the initial concentration of A constant, the initial rate of reaction doubles. What does this observation imply?
   Answer: The reaction rate is directly proportional to the concentration of B. This question describes a method for determining reaction order, but the core concept tested is the relationship between concentration and rate. The observation that doubling the concentration of B causes the rate to double indicates a direct, first-order relationship between the rate and [B]. This is the definition of direct proportionality. While this means the reaction is first order in B, option A is a more direct and fundamental description of the observed relationship. B is a reactant, not a catalyst. Thermodynamics (D) is unrelated to rate.
4. Which of the following best describes the rate of a chemical reaction?
   Answer: The change in concentration of a reactant or product per unit of time. The rate of a chemical reaction is defined as the change in the amount (usually concentration) of a reactant or product over a specific time interval. The other options describe the reaction yield (B), enthalpy change (C), and activation energy (D), which are distinct concepts from reaction rate.
5. A student measures the concentration of reactant $\text{D}(aq)$ during a reaction: [D] is 0.800 M at 0 s, 0.560 M at 10 s, 0.400 M at 20 s, 0.290 M at 30 s, 0.210 M at 40 s, and 0.155 M at 50 s. Which time interval shows the greatest average rate of disappearance of $\text{D}$?
   Answer: $0\text{–}10\ \text{s}$ Average rate of disappearance = −Δ[D]/Δt. From the data, [D] falls by 0.240 M from 0 to 10 s (0.024 M/s), by 0.160 M from 10 to 20 s, by 0.110 M from 20 to 30 s, by 0.080 M from 30 to 40 s and by 0.055 M from 40 to 50 s. The largest drop is in 0–10 s, so choice A has the greatest average rate. The rate slows as [D] decreases.
6. Which of the following experimental conditions would be expected to produce the fastest rate for the reaction of a 1.0 g sample of zinc metal with 100 mL of hydrochloric acid?
   Answer: Zinc powder and 1.0 M HCl at 25°C To achieve the fastest reaction rate, conditions that favor high collision frequency and energy should be chosen. High surface area (zinc powder vs. strip), high reactant concentration (1.0 M HCl vs. 0.5 M HCl), and high temperature (25°C vs. 15°C) all increase the rate. Option A combines the highest surface area, highest concentration, and highest temperature among the choices, and will therefore result in the fastest reaction rate.
7. Which expression correctly represents the rate of reaction?
   Answer: $\text{Rate} = -\frac{1}{2}\frac{\Delta[\text{NO}]}{\Delta t}$ The rate of reaction is defined to be a unique positive value. For a reactant, the change in concentration is negative, so a minus sign is used. The rate of change of each species is divided by its stoichiometric coefficient. For NO, the coefficient is 2, so the rate is given by $-\frac{1}{2}\frac{\Delta[\text{NO}]}{\Delta t}$. Choices A and D are incorrect because they omit the stoichiometric coefficient for NO and define the rate based on a reactant without normalizing by stoichiometry. Choice C correctly represents the rate in terms of the product NOCl, but the question asks for the correct expression among the choices, and B is a correct representation. C is also correct, but B is offered as an option and is a valid representation of the reaction rate.
8. In a first-order reaction, the concentration of reactant $\text{H}(aq)$ is 1.00 M at 0 s, 0.50 M at 10 s, 0.25 M at 20 s, 0.125 M at 30 s, and 0.0625 M at 40 s. At which time is the instantaneous rate of disappearance of $\text{H}$ greatest (i.e., where the magnitude of the slope is largest)?
   Answer: At $t=0\ \text{s}$ This question tests understanding of instantaneous reaction rates versus average rates. The instantaneous rate of disappearance at any point equals the magnitude of the slope of the tangent line to the concentration versus time curve at that point. Because the rate of a first-order reaction is proportional to [H], the curve is steepest at t=0s when reactant concentration is highest, giving the greatest instantaneous rate at the beginning. As the reaction proceeds, [H] decreases, the curve becomes less steep, and the instantaneous rate decreases. A common error is thinking the rate is highest when concentration is lowest, but this confuses concentration with rate of change. To find maximum instantaneous rate, identify where the concentration versus time curve has the steepest negative slope, which here is at t=0.
9. Increasing the concentration of reactants in a solution increases the rate of reaction. What is the fundamental reason for this effect according to collision theory?
   Answer: It increases the frequency of collisions between reactant particles. When the concentration of reactants is increased, there are more reactant particles per unit volume. This leads to a higher probability of particles colliding with each other, thus increasing the collision frequency. A higher collision frequency results in a higher frequency of successful, reaction-leading collisions, and therefore a faster reaction rate. Concentration does not affect the kinetic energy of particles (temperature does), nor does it affect the activation energy (a catalyst does).
10. Which of the following correctly compares the initial rate of reaction in the two trials?
    Answer: The rate in Trial 2 will be faster because the powdered solid has a greater surface area for reaction. For reactions involving a solid reactant, the rate is dependent on the surface area of the solid. Grinding the CaCO₃ into a powder significantly increases the surface area available for contact with the HCl solution. This leads to more frequent collisions between reactant particles and thus a faster reaction rate. The mass and concentration being the same does not mean the rates will be the same if another factor like surface area is varied.
11. To investigate the effect of reactant concentration on the rate, a student could measure the initial rate of oxygen production while varying which of the following?
    Answer: The initial concentration of H₂O₂ while keeping the concentration of I⁻ and the temperature constant. To study the effect of a specific reactant's concentration on the reaction rate, one must vary that concentration while holding all other potentially influential factors (like the concentration of other reactants, catalysts, and temperature) constant. Therefore, varying the initial concentration of H₂O₂ while keeping the catalyst (I⁻) concentration and temperature constant is the correct experimental design.
12. What is the rate of formation of C?
    Answer: $0.040 \text{ M/min}$ The stoichiometric ratio between A consumed and C produced is 3:2. Therefore, the rate of formation of C is 2/3 of the rate of disappearance of A. Rate of C = (2/3) * (0.060 M/min) = 0.040 M/min.
13. The reaction $\text{F}(aq) \rightarrow \text{products}$ is followed by measuring $[\text{F}]$ over time. Which statement correctly compares the average rate of disappearance of $\text{F}$ over $0\text{–}20\ \text{s}$ to the average rate over $20\text{–}40\ \text{s}$?
    Answer: The average rate over $0\text{–}20\ \text{s}$ is greater than over $20\text{–}40\ \text{s}$. This question assesses understanding of how reaction rates change over time by comparing two intervals. The average rate of disappearance is calculated as -Δ[F]/Δt for each interval. For typical reactions, the rate is higher early in the reaction when reactant concentration is greater, so the average rate over 0-20s is greater than over 20-40s. This occurs because higher [F] in the early interval leads to more frequent collisions and faster reaction. The magnitude of the concentration change is larger in the first interval, giving a steeper slope and higher rate. A misconception is thinking equal time intervals mean equal rates, or that lower concentration at later times means higher rate. Remember that reaction rate typically decreases as the reaction progresses due to decreasing reactant concentration.
14. If the rate of disappearance of N₂O₅ is measured to be $4.0 \times 10^{-5} \text{ M/s}$ at a certain time, what is the rate of appearance of NO₂ at the same time?
    Answer: $8.0 \times 10^{-5} \text{ M/s}$ The rate of appearance of NO₂ is related to the rate of disappearance of N₂O₅ by the stoichiometry of the balanced equation. The ratio is 4 moles of NO₂ produced for every 2 moles of N₂O₅ consumed. Therefore, the rate of appearance of NO₂ is (4/2) times the rate of disappearance of N₂O₅. Rate of NO₂ = (4/2) (4.0 x 10⁻⁵ M/s) = 2 (4.0 x 10⁻⁵ M/s) = 8.0 x 10⁻⁵ M/s.
15. How is the instantaneous rate of disappearance of N₂O expected to change over the first minute of the reaction?
    Answer: The rate will decrease as the concentration of N₂O decreases. The rate of this reaction is proportional to the concentration of the reactant, N₂O. As the reaction proceeds, N₂O is consumed, so its concentration decreases. Consequently, the instantaneous rate of the reaction, which depends on this concentration, will also decrease over time. The rate is highest at the beginning (initial rate) and slows down as reactants are used up.
16. A catalyst is added to a reaction mixture. Which of the following is the most accurate statement about the effect of the catalyst?
    Answer: The catalyst increases the rate of the reaction by providing an alternative reaction pathway with a lower activation energy. A catalyst increases the rate of a chemical reaction by providing an alternative mechanism, or pathway, that has a lower activation energy. It is not consumed in the overall reaction (A). It does not affect the equilibrium position or the total yield of product (C). Temperature, not a catalyst, is what increases the kinetic energy of molecules (D).
17. What is the rate of consumption of O₂?
    Answer: $2.5 \times 10^{-4} \text{ M/s}$ From the balanced equation, 5 moles of O₂ are consumed for every 4 moles of NO that are formed. The ratio of the rate of consumption of O₂ to the rate of formation of NO is 5/4. Rate of O₂ consumption = (5/4) Rate of NO formation = (5/4) (2.0 x 10⁻⁴ M/s) = 2.5 x 10⁻⁴ M/s.
18. The rate of this reaction is most commonly increased by which of the following changes?
    Answer: Increasing the partial pressure of reactant A. Reaction rates are generally increased by increasing the concentration of reactants. For a gas-phase reaction, increasing the partial pressure of a reactant is equivalent to increasing its concentration. This leads to more frequent collisions between reactant molecules, increasing the reaction rate. Increasing product concentration (A) would favor the reverse reaction. Decreasing temperature (B) slows down reaction rates. Adding an inert gas at constant volume decreases the mole fraction of reactants but does not change their partial pressures, so it has no effect on the rate (D).
19. A reaction is monitored by measuring $[\text{E}]$ as a function of time. Based on the slope of the curve, during which interval is the rate of disappearance of $\text{E}$ the smallest (slowest)?
    Answer: $40\text{–}50\ \text{s}$ This question tests understanding of reaction rates by asking for the interval with the smallest (slowest) rate. The rate of disappearance corresponds to the slope of the concentration versus time curve - a gentler slope indicates a slower rate. In typical reactions, the rate decreases over time as reactant concentration decreases, so the slowest rate usually occurs in the latest time interval. The 40-50s interval would have the smallest rate because [E] is lowest at this point, resulting in fewer collisions and the gentlest slope. Students often confuse low concentration with low rate, but it's actually the low concentration that causes the low rate, not the concentration itself that is the rate. To find the slowest rate, look for the interval where the concentration changes least steeply, typically occurring late in the reaction.
20. A student observes that dropping an effervescent tablet into hot water causes it to dissolve and fizz much faster than dropping it into cold water. This observation demonstrates that the reaction rate is dependent on which factor?
    Answer: Temperature The only significant difference between the two experiments described is the temperature of the water. The increased rate of fizzing (which is CO₂ gas production from a reaction) in hot water compared to cold water directly demonstrates the effect of temperature on reaction rates. Higher temperatures lead to faster reactions.

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