MCAT Chemical and Physical Foundations of Biological Systems Quiz: 5e Chemical Kinetics Rate Laws

What this quiz covers

This quiz focuses on 5e Chemical Kinetics Rate Laws, giving you a quick way to practice the rules, question types, and explanations that matter most for MCAT Chemical and Physical Foundations of Biological Systems.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. Zero order in A, because doubling [A] does not change the rate
2. First order in A, because doubling [A] doubles the rate (correct answer)
3. Second order in A, because doubling [A] quadruples the rate
4. Third order in A, because tripling [A] increases the rate ninefold

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.

Question 2

1. Zero order in P, because the rate is controlled only by light intensity
2. First order in P, because tripling [P] triples the rate (correct answer)
3. Second order in P, because doubling [P] doubles the rate
4. Second order in P, because tripling [P] increases the rate ninefold

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.

Question 3

1. The initial rate decreases by a factor of 2 because more catalyst lowers activation energy too much
2. The initial rate is unchanged because rate depends only on temperature through $k$
3. The initial rate increases by a factor of 2 because rate is first order in catalyst (correct answer)
4. 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.

Question 4

1. Zero order in GSH, because the rate does not change when [GSH] increases
2. First order in GSH, because doubling [GSH] doubles the rate
3. Second order in GSH, because tripling [GSH] triples the rate
4. Second order in GSH, because doubling [GSH] quadruples the rate (correct answer)

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.

Question 5

1. Catalyst X likely lowers the activation energy more, increasing the rate constant (correct answer)
2. Catalyst X likely increases $\Delta G^\circ$ of the reaction, driving faster product formation
3. Catalyst Y likely lowers activation energy more, but only affects equilibrium, not rate
4. Catalyst X must increase reactant concentration over time, which raises the initial rate

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.

Question 6

1. Zero order in B, because changing [B] does not affect the rate when [A] is fixed
2. First order in B, because doubling [B] doubles the rate
3. Second order in B, because doubling [B] quadruples the rate (correct answer)
4. Third order in B, because doubling [B] increases the rate eightfold

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.

Question 7

1. $k$ decreases because higher temperature reduces the fraction of molecules above the activation energy
2. $k$ increases because a larger fraction of collisions have energy $\ge E_a$ (correct answer)
3. $k$ is unchanged because temperature affects rate only through reactant concentrations
4. $k$ changes only if a catalyst is added, not with temperature

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.

Question 8

1. First order, because decomposition is typically unimolecular
2. Zero order, because the initial rate is unchanged when [D] doubles (correct answer)
3. Second order, because doubling [D] should double the rate but does not due to error
4. Cannot be determined without time-course data

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.

Question 9

1. $\text{rate}=k[A][B]$
2. $\text{rate}=k[A]^2[B]$ (correct answer)
3. $\text{rate}=k[A]^2[B]^2$
4. $\text{rate}=k[A]^4[B]$

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.

Question 10

1. The rate doubles because only one reactant concentration matters
2. The rate quadruples because the rate is proportional to the product $[A][B]$ (correct answer)
3. The rate increases 8-fold because doubling concentrations doubles collision energy
4. The rate is unchanged because association reactions are diffusion-limited

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.

Question 11

1. 0, because one reactant shows zero-order behavior
2. 1, because the reaction is first order in A and zero order in B (correct answer)
3. 2, because there are two reactants in the balanced equation
4. 3, because doubling A doubles rate and doubling B should also double rate

Explanation: This question assesses understanding of chemical kinetics and reaction orders. Overall order is the sum of individual orders in the rate law. Data show order 1 in A (doubling doubles rate) and 0 in B (doubling no change), so overall order 1. Option B is correct because it sums to 1. Option C is incorrect as stoichiometry does not dictate order. When determining overall order, add exponents. This helps predict rate changes with concentrations.

Question 12

1. Zero order because the rate would be constant if [P] changes
2. First order because doubling [P] doubles the initial rate (correct answer)
3. Second order because doubling [P] quadruples the initial rate
4. Third order because the rate increases faster than linearly

Explanation: This question tests the ability to determine reaction order from concentration-rate data. Reaction order describes how the rate depends on reactant concentration, determined by examining how rate changes with concentration changes. In the data, when [P] doubles from 0.50 to 1.00 mM, the rate doubles from 0.010 to 0.020 mM·min⁻¹, and when [P] doubles again from 1.00 to 2.00 mM, the rate doubles from 0.020 to 0.040 mM·min⁻¹. Option B is correct because this consistent proportional relationship (doubling concentration doubles rate) indicates first-order kinetics. Option C is incorrect because second order would show the rate quadrupling when concentration doubles. To determine reaction order, calculate the ratio of rate changes to concentration changes across multiple data points.

Question 13

1. Zero order in Cl because Cl is a disinfectant and often in excess
2. First order in Cl because doubling [Cl] quadruples the rate
3. Second order in Cl because doubling [Cl] increases the rate by a factor of 4 (correct answer)
4. Half order in Cl because radical pathways are fractional order

Explanation: This question assesses determining reaction order from initial rate data with multiple reactants. To find the order with respect to Cl, compare runs where only [Cl] changes while [N] remains constant. Comparing runs 1 and 3: when [Cl] doubles from 1.0 to 2.0 mM while [N] stays at 1.0 mM, the rate increases from 0.30 to 1.20 mM·s⁻¹, a 4-fold increase. Option C is correct because when doubling concentration causes a 4-fold rate increase, this indicates second-order kinetics with respect to that reactant. Option B is incorrect because it misinterprets the relationship - first order would only double the rate when concentration doubles. When analyzing kinetic data, the rate change factor equals the concentration change factor raised to the power of the reaction order.

Question 14

1. First order in A because A is a reactant in the balanced equation
2. Zero order in A because doubling [A] does not change the initial rate (correct answer)
3. Second order in A because A and B react together
4. Cannot be determined because [B] changes in one run

Explanation: This question tests understanding of determining individual reaction orders in multi-reactant systems. To find the order with respect to A, compare runs where only [A] changes while [B] is constant. Comparing runs 1 and 2: when [A] doubles from 1.0 to 2.0 mM while [B] remains at 1.0 mM, the initial rate stays constant at 0.10 mM·s⁻¹. Option B is correct because when changing a reactant's concentration does not affect the rate, the reaction is zero order with respect to that reactant. Option A is incorrect because being a reactant in the balanced equation doesn't determine kinetic order - reaction orders must be determined experimentally. The data also shows the reaction is first order in B, as doubling [B] doubles the rate when [A] is constant.

Question 15

1. A decrease in activation energy $E_a$ because temperature lowers the barrier height
2. An increase in the fraction of molecules with energy \ge $E_a$, increasing successful collisions (correct answer)
3. An increase in reactant concentration due to thermal expansion of the solvent
4. A decrease in collision frequency because molecules move more randomly at higher temperature

Explanation: This question evaluates understanding of temperature effects on reaction rates through the Arrhenius equation. Temperature affects reaction rates primarily by changing the fraction of molecules with sufficient energy to overcome the activation energy barrier. At higher temperatures, the Maxwell-Boltzmann distribution shifts to higher energies, meaning more molecules possess energy ≥ Ea. Option B is correct because this increased fraction of energetic molecules leads to more successful collisions and thus higher reaction rates. Option A is incorrect because temperature doesn't change the activation energy itself - Ea is an intrinsic property of the reaction. The Arrhenius equation k = Ae^(-Ea/RT) shows that rate constants increase exponentially with temperature due to this Boltzmann factor.

Question 16

1. It decreases by a factor of 2
2. It is unchanged
3. It increases by a factor of 2 (correct answer)
4. It increases by a factor of 4

Explanation: This question tests application of rate laws to predict rate changes. Given the rate law rate = k[A]²[B], we need to determine how the rate changes when [A] is doubled and [B] is halved. The new rate = k(2[A])²(½[B]) = k(4[A]²)(½[B]) = 2k[A]²[B] = 2 × original rate. Option C is correct because the combined effect of doubling [A] (which quadruples the A contribution) and halving [B] (which halves the B contribution) results in a net doubling of the rate. Option D is incorrect because it would require an 8-fold increase from [A] alone, which isn't possible with second-order dependence. When multiple concentration changes occur simultaneously, multiply their individual effects according to their reaction orders.

Question 17

1. The rate increases 2-fold because only one reactant concentration matters
2. The rate increases 4-fold because both reactant concentrations double (correct answer)
3. The rate is unchanged because $k$ does not depend on concentration
4. The rate decreases because higher pressure lowers activation energy

Explanation: This question assesses understanding of how pressure affects gas-phase reaction rates. For the rate law rate = k[X][Y], the rate depends on the product of the two concentrations. When the volume is halved at constant temperature, both gas concentrations double according to the ideal gas law (P = nRT/V). The new rate = k(2[X])(2[Y]) = 4k[X][Y] = 4 × original rate. Option B is correct because both reactant concentrations doubling leads to a 4-fold rate increase for this second-order overall reaction. Option A is incorrect because it ignores the effect on one reactant. In gas-phase reactions, pressure changes affect rates by changing concentrations, not by altering the rate constant k.

Question 18

1. Zero order in R because doubling [R] does not change the rate (correct answer)
2. First order in R because R appears in the reaction stoichiometry
3. Second order in R because the rate is proportional to $[R]^2$
4. Negative order in R because increasing [R] inhibits dye formation

Explanation: This question evaluates understanding of zero-order kinetics in multi-reactant systems. To determine the order with respect to R, compare runs where only [R] changes while [S] is constant. Comparing runs 2 and 3: when [R] doubles from 1.0 to 2.0 mM while [S] remains at 2.0 mM, the rate stays constant at 0.32 mM·s⁻¹. Option A is correct because when changing a reactant's concentration has no effect on the rate, the reaction is zero order with respect to that reactant. Option B is incorrect because appearing in the stoichiometry doesn't determine kinetic order. The data shows the reaction is second order in S (quadrupling when [S] doubles) but zero order in R, giving rate = k[S]²[R]⁰ = k[S]².

Question 19

1. It decreases by a factor of 2
2. It is unchanged
3. It increases by a factor of 2 (correct answer)
4. It increases by a factor of 8

Explanation: This question evaluates applying complex rate laws to predict rate changes. Given rate = k[A][B]², we calculate: original rate = k(1.0)(1.0)² = k, and new rate = k(0.50)(2.0)² = k(0.50)(4.0) = 2k. The rate increases by a factor of 2. Option C is correct because halving [A] reduces the rate by half, while doubling [B] increases it by a factor of 4 (due to second-order dependence), giving a net 2-fold increase. Option D is incorrect as it would require third-order dependence on B. When multiple concentrations change, calculate each effect separately based on its order, then multiply the factors together.

Question 20

1. First order overall because each reactant is first order and $1+0=1$
2. Second order overall because the reaction is first order in A and first order in B (correct answer)
3. Third order overall because doubling either reactant doubles the rate
4. Zero order overall because the rate changes only modestly with concentration

Explanation: This question assesses understanding of overall reaction order determination. From the data: doubling [A] (runs 1→2) doubles the rate, indicating first order in A; doubling [B] (runs 1→3) doubles the rate, indicating first order in B. The rate law is therefore rate = k[A]¹[B]¹, and the overall order is the sum of individual orders: 1 + 1 = 2. Option B is correct because the reaction is first order in both A and B, making it second order overall. Option A is incorrect due to a mathematical error - it incorrectly adds 1 + 0 instead of 1 + 1. Overall reaction order is always the sum of all individual reaction orders in the rate law.