Chemical Kinetics and Rate Laws (5E)
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MCAT Chemical and Physical Foundations of Biological Systems › Chemical Kinetics and Rate Laws (5E)
In a stopped-flow experiment modeling detoxification in hepatocytes, an enzyme-mimetic catalyst converts a reactive aldehyde (A) to a less reactive alcohol (P) in aqueous buffer at 25°C: A → P. Initial rates were measured while varying A with catalyst concentration held constant and saturating NADH present. Rates were recorded within the first 5 s to minimize product inhibition.
What is the reaction order with respect to A based on the initial-rate data?
Third order in A, because tripling [A] increases the rate ninefold
Second order in A, because doubling [A] quadruples the rate
First order in A, because doubling [A] doubles the rate
Zero order in A, because doubling [A] does not change the rate
Explanation
This question assesses understanding of reaction order determination from initial rate data. The reaction order with respect to a reactant is determined by how the rate changes when that reactant's concentration changes. When the concentration of A doubles and the rate also doubles, this indicates a linear relationship between [A] and rate. This means the rate is proportional to [A]¹, making it first order in A. Option B correctly identifies this first-order relationship. Option A would be correct if changing [A] had no effect on rate, while option C would require the rate to quadruple when [A] doubles.
In an environmental chemistry study of coastal waters, the degradation of a pollutant (P) is monitored under sunlight. The pollutant reacts with hydroxyl radicals (•OH): P + •OH → products. Using a radical generator, •OH is held constant at a low steady-state value while P is varied. Initial rates are measured immediately after illumination.
Based on the data, what is the order of the reaction with respect to P?
Zero order in P, because the rate is controlled only by light intensity
Second order in P, because tripling [P] increases the rate ninefold
Second order in P, because doubling [P] doubles the rate
First order in P, because tripling [P] triples the rate
Explanation
This question evaluates determination of reaction order from experimental data. The data indicates that when [P] triples, the rate also triples, showing a direct linear relationship between pollutant concentration and reaction rate. This proportionality (rate ∝ [P]¹) defines first-order kinetics with respect to P. Option B correctly identifies this first-order relationship. Option A would require the rate to be independent of [P], while option D would require the rate to increase ninefold when [P] triples, indicating second-order kinetics.
An industrial bioreactor produces lactate from pyruvate using a soluble catalyst. Under conditions where pyruvate remains low and well-mixed, the observed rate law is $\text{rate} = k\text{cat}\text{Pyr}$. During scale-up, an operator doubles the catalyst concentration while keeping temperature, pH, and Pyr constant.
Which change in the initial reaction rate is most consistent with the given rate law?
The initial rate decreases by a factor of 2 because more catalyst lowers activation energy too much
The initial rate increases by a factor of 2 because rate is first order in catalyst
The initial rate is unchanged because rate depends only on temperature through $k$
The initial rate increases by a factor of 4 because rate is second order overall
Explanation
This question tests application of a given rate law to predict changes in reaction rate. The rate law shows that rate is directly proportional to catalyst concentration: rate = k[cat][Pyr]. When catalyst concentration doubles while all other factors remain constant, the rate should also double due to the first-order dependence on [cat]. Option C correctly predicts this doubling of the initial rate. Option B incorrectly suggests rate depends only on temperature, while option D misinterprets the overall reaction order as affecting the catalyst's contribution.
To model oxidative stress, researchers measure the initial rate of a bimolecular scavenging reaction in cytosolic-like buffer at 25°C: R• + GSH → RH + GS•. The radical concentration R• is held constant using a steady photochemical source, while GSH is varied.
Based on the initial-rate data, what is the order of the reaction with respect to GSH?
First order in GSH, because doubling [GSH] doubles the rate
Second order in GSH, because tripling [GSH] triples the rate
Second order in GSH, because doubling [GSH] quadruples the rate
Zero order in GSH, because the rate does not change when [GSH] increases
Explanation
This question evaluates understanding of reaction order from rate data in a radical scavenging reaction. The data shows that when [GSH] doubles, the rate quadruples (increases by a factor of 4). This quadratic relationship indicates the rate is proportional to [GSH]², making the reaction second order in GSH. Option D correctly identifies this second-order relationship. Option B incorrectly suggests first order (linear relationship), while option C confuses the mathematical relationship by stating tripling concentration only triples the rate, which would indicate first order.
To compare two catalysts for the same aqueous reaction (S → P) relevant to drug metabolism, initial rates are measured at 25°C with identical S. Catalyst X gives an initial rate of 0.60 mM·min$^{-1}$, while catalyst Y gives 0.20 mM·min$^{-1}$. Both catalysts are used at the same concentration and do not change the reaction equilibrium.
Which statement best explains the difference in observed initial rates?
Catalyst X likely lowers the activation energy more, increasing the rate constant
Catalyst X must increase reactant concentration over time, which raises the initial rate
Catalyst Y likely lowers activation energy more, but only affects equilibrium, not rate
Catalyst X likely increases $\Delta G^\circ$ of the reaction, driving faster product formation
Explanation
This question tests understanding of how catalysts affect reaction rates. Catalysts increase reaction rates by lowering the activation energy, making it easier for reactants to overcome the energy barrier. Since catalyst X produces a higher initial rate (0.60 mM·min⁻¹) than catalyst Y (0.20 mM·min⁻¹) under identical conditions, catalyst X must lower the activation energy more effectively. Option A correctly identifies this mechanism. Option B incorrectly suggests catalysts change the thermodynamics (ΔG°), which they cannot do. Catalysts only affect kinetics, not equilibrium position.
A lab investigates a two-reactant process relevant to protein crosslinking: A + B → products. Initial rates are measured at 25°C. In Trial 1, A = 0.10 M and B = 0.10 M gives rate = 1.0×10$^{-3}$ M·s$^{-1}$. In Trial 2, A is doubled to 0.20 M while B remains 0.10 M, giving rate = 2.0×10$^{-3}$ M·s$^{-1}$. In Trial 3, A remains 0.10 M while B is doubled to 0.20 M, giving rate = 4.0×10$^{-3}$ M·s$^{-1}$.
Based on these data, what is the order with respect to B?
First order in B, because doubling [B] doubles the rate
Third order in B, because doubling [B] increases the rate eightfold
Zero order in B, because changing [B] does not affect the rate when [A] is fixed
Second order in B, because doubling [B] quadruples the rate
Explanation
This question tests determination of reaction order using the method of initial rates. Comparing trials 1 and 3, when [B] doubles from 0.10 to 0.20 M while [A] remains constant, the rate increases from 1.0×10⁻³ to 4.0×10⁻³ M·s⁻¹, a fourfold increase. This quadratic relationship (rate ∝ [B]²) indicates second-order kinetics with respect to B. Option C correctly identifies this second-order dependence. The data also shows first-order in A (doubling [A] doubles the rate), giving an overall rate law of rate = k[A][B]².
A researcher measures a nonenzymatic rearrangement of a metabolite (M) in aqueous buffer. The rate constant is determined at two temperatures: $k_1 = 1.0\times10^{-3}\ \text{s}^{-1}$ at 298 K and $k_2 = 4.0\times10^{-3}\ \text{s}^{-1}$ at 318 K. Concentrations and solvent composition are unchanged.
How does increasing temperature from 298 K to 318 K most directly affect the rate constant $k$ for this reaction?
$k$ is unchanged because temperature affects rate only through reactant concentrations
$k$ changes only if a catalyst is added, not with temperature
$k$ increases because a larger fraction of collisions have energy $\ge E_a$
$k$ decreases because higher temperature reduces the fraction of molecules above the activation energy
Explanation
This question assesses understanding of temperature effects on rate constants according to the Arrhenius equation. Higher temperature increases the kinetic energy of molecules, resulting in a larger fraction of collisions having energy equal to or greater than the activation energy (Ea). This leads to more successful reactions per unit time, increasing the rate constant k. The data shows k increasing from 1.0×10⁻³ to 4.0×10⁻³ s⁻¹ with temperature increase. Option B correctly explains this through collision theory. Option A incorrectly reverses the temperature effect, while option C wrongly suggests k is temperature-independent.
A clinical lab evaluated decomposition of a disinfectant (D) used on medical devices: $D \rightarrow$ products. The reaction was run at constant temperature and pH. The initial rate was measured at two initial concentrations.
Data:
D = 0.30 M, rate = $9.0\times10^{-5}$ M/s
D = 0.60 M, rate = $9.0\times10^{-5}$ M/s
Based on the data, what is the order of the reaction with respect to D?
First order, because decomposition is typically unimolecular
Second order, because doubling [D] should double the rate but does not due to error
Cannot be determined without time-course data
Zero order, because the initial rate is unchanged when [D] doubles
Explanation
This question assesses understanding of chemical kinetics and rate laws. Zero-order reactions have rates independent of reactant concentration, often due to saturation or external limitations. In the data, doubling [D] from 0.30 M to 0.60 M keeps the rate at $9.0×10^{-5}$ M/s. Option B is correct because this constancy indicates zero order in D. Option A is incorrect as first order would double the rate. When evaluating rate laws, look for rate invariance with concentration changes. Remember zero-order half-life depends linearly on initial concentration, unlike other orders.
A researcher proposes the elementary step $2A + B \rightarrow P$ for a key oxidative reaction in mitochondria. Initial-rate data at constant temperature show that doubling A increases the rate by a factor of 4, while doubling B increases the rate by a factor of 2.
Based on the data, which rate law is most consistent with the observed kinetics?
$\text{rate}=k[A]^2[B]^2$
$\text{rate}=k[A]^2[B]$
$\text{rate}=k[A][B]$
$\text{rate}=k[A]^4[B]$
Explanation
This question assesses understanding of chemical kinetics and rate laws. For elementary steps, the rate law matches molecularity, but must be verified empirically. Data showing doubling [A] quadruples rate (order 2 in A) and doubling [B] doubles rate (order 1 in B) supports rate = $k[A]^2$[B]. Option B is correct as it matches the observed scalings. Option C is incorrect as it implies order 2 in B, which would quadruple rate on doubling [B]. When evaluating, match exponents to observed rate factors. Always confirm if the step is elementary before assuming rate law from stoichiometry.
A lab examines a bimolecular association relevant to receptor-ligand binding under dilute conditions: $A + B \rightarrow AB$. The empirical rate law is $\text{rate}=kAB$. In a new run, both A and B are doubled while temperature is constant.
Which factor most influences the reaction rate after doubling both reactants?
The rate doubles because only one reactant concentration matters
The rate is unchanged because association reactions are diffusion-limited
The rate quadruples because the rate is proportional to the product $[A][B]$
The rate increases 8-fold because doubling concentrations doubles collision energy
Explanation
This question assesses understanding of chemical kinetics and rate laws. For rate = k[A][B], doubling both scales rate by 2×2=4. The combined concentration increases multiply to quadruple the rate. Option B is correct because it predicts quadrupling from the product [A][B]. Option A is incorrect as it assumes only one matters. When changing multiple, multiply factors. This models collision frequency in bimolecular reactions.