Chemical Kinetics: Rate Laws and Mechanisms

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Questions and Answers

Consider a reaction with the rate law: rate = $k[A]^2[B]$. If the concentration of A is doubled and the concentration of B is halved, what is the effect on the reaction rate?

  • The reaction rate is quadrupled.
  • The reaction rate remains unchanged.
  • The reaction rate is doubled. (correct)
  • The reaction rate is halved.

The experimentally determined rate law for the reaction $2NO(g) + O_2(g) ightarrow 2NO_2(g)$ is rate = $k[NO]^2[O_2]$. If the volume of the reaction vessel is suddenly halved, what will be the effect on the reaction rate?

  • The reaction rate is increased by a factor of eight. (correct)
  • The reaction rate is quadrupled.
  • The reaction rate remains unchanged.
  • The reaction rate is doubled.

For a reaction with multiple steps, how does the rate-determining step influence the overall reaction rate and the observed rate law?

  • The rate-determining step has no impact on the overall reaction rate or the rate law.
  • The rate-determining step speeds up the reaction but is not reflected in the rate law.
  • The rate-determining step only affects the equilibrium constant of the reaction.
  • The rate-determining step determines the overall reaction rate and is reflected in the observed rate law. (correct)

A proposed mechanism for a reaction is: Step 1: $A + B ightleftharpoons C$ (fast equilibrium) Step 2: $C + A ightarrow D$ (slow) What is the rate law predicted by this mechanism?

<p>rate = $k[A]^2[B]$ (B)</p> Signup and view all the answers

For a certain first-order reaction, the half-life is 45 minutes. What percentage of reactant remains after 135 minutes?

<p>12.5% (C)</p> Signup and view all the answers

Consider a reaction where increasing the temperature from 25C to 35C results in a rate constant that is approximately tripled. Estimate the activation energy ($E_a$) for this reaction.

<p>Approximately 83 kJ/mol (C)</p> Signup and view all the answers

Which of the following statements is correct concerning the relationship between the pre-exponential factor (A) in the Arrhenius equation and the reaction rate?

<p>A reflects the frequency of effective collisions between reactant molecules and their orientation; higher A values generally indicate faster reaction rates. (B)</p> Signup and view all the answers

For a reaction $A + B ightarrow C$, the rate law is observed to be rate = $k[A][B]^2$. If the initial concentration of A is much greater than that of B, how would you best describe the observed reaction order with respect to B?

<p>The reaction is pseudo-second order with respect to B. (C)</p> Signup and view all the answers

If a catalyst is added to a reaction, which of the following happens to the forward and reverse activation energies?

<p>Both the forward and reverse activation energies decrease. (C)</p> Signup and view all the answers

Consider a reaction with the following mechanism: $A ightleftharpoons B$ (fast equilibrium) $B + C ightarrow D$ (slow) $D ightarrow E + C$ (fast) Which species is a catalyst in this reaction?

<p>Species C (D)</p> Signup and view all the answers

How does the addition of an inert gas at constant volume affect the rate of a gas-phase reaction?

<p>It has no effect on the reaction rate. (A)</p> Signup and view all the answers

Given the rate law rate = $k[A]^m[B]^n$, what experimental method is most appropriate to determine the values of m and n?

<p>Vary the initial concentrations of A and B and measure the initial reaction rates. (C)</p> Signup and view all the answers

For a zero-order reaction, what plot will yield a straight line, and how is the rate constant determined from this plot?

<p>Plot of [A] vs. time; the rate constant is the negative of the slope. (C)</p> Signup and view all the answers

If a reaction proceeds via the following two-step mechanism: Step 1: $A + B ightleftharpoons I$ (fast equilibrium) Step 2: $I + B ightarrow C$ (slow) Which of the following rate laws is consistent with this mechanism?

<p>rate = $k[A][B]^2$ (A)</p> Signup and view all the answers

A reaction has an activation energy of 75 kJ/mol. By what factor will the rate constant increase when the temperature is raised from 20C to 60C?

<p>Approximately 10 (D)</p> Signup and view all the answers

A proposed mechanism for a reaction is given below: Step 1: $Cl_2(g) ightleftharpoons 2Cl(g)$ (fast equilibrium) Step 2: $Cl(g) + CHCl_3(g) ightarrow HCl(g) + CCl_3(g)$ (slow) Step 3: $CCl_3(g) + Cl(g) ightarrow CCl_4(g)$ (fast) What is the overall reaction and the rate law predicted by this mechanism?

<p>$CHCl_3(g) + Cl_2(g) ightarrow HCl(g) + CCl_4(g)$; rate = $k[Cl_2]^{1/2}[CHCl_3]$ (A)</p> Signup and view all the answers

A reaction has the following rate law: Rate = $k[A]^2[B]$. Which of the following mechanisms is consistent with this rate law?

<p>Step 1: $A + A ightarrow C$ (slow), Step 2: $C + B ightarrow D$ (fast) (D)</p> Signup and view all the answers

Consider the gas-phase reaction $A_2 + B ightarrow A + AB$. The experimental rate law is rate = $k[A_2]$. Which of the following mechanisms is consistent with this information?

<p>Step 1 (slow): $A_2 ightarrow 2A$, Step 2 (fast): $2A + B ightarrow A + AB$ (B)</p> Signup and view all the answers

The decomposition of a certain compound is found to be first order. If the concentration of the compound is reduced to half its initial value after 30 minutes, what length of time will it take for the concentration to be reduced to one-quarter of its initial value?

<p>60 minutes (D)</p> Signup and view all the answers

Consider a reaction that proceeds with the following mechanism: $A + B ightleftharpoons C \quad (fast, equilibrium constant = $K_1$) $C + D ightarrow E \quad (slow, rate constant = $k_2$) Assuming the concentrations of both B and D are significantly higher than that of A, what is the observed rate law?

<p>rate = $k[A]$, where $k=k_2K_1[B][D]$ (D)</p> Signup and view all the answers

Under what circumstances does a termolecular elementary step become more probable?

<p>Within highly confined spaces or on surfaces that concentrate reactants. (A)</p> Signup and view all the answers

How does the presence of a common ion affect the kinetics of a reaction in solution, and what underlying principle governs this effect?

<p>It may either increase or decrease the reaction rate depending on whether it stabilizes the activated complex or the reactants. (C)</p> Signup and view all the answers

For a multi-step reaction, altering reaction conditions shifts the rate-determining step. What is the MOST likely reason that the rate-determining step would shift?

<p>The frequency factor (A) differs substantially between the original and potential new rate-determining steps and has become dominant under the altered conditions. (D)</p> Signup and view all the answers

Which of the following is a key difference between collision theory and transition state theory in describing chemical kinetics?

<p>Collision theory assumes that all collisions lead to a reaction if sufficient energy is present, while transition state theory considers the formation of an activated complex. (B)</p> Signup and view all the answers

How does isotopic labeling experiments provide insights into reaction mechanisms, and what type of information can be obtained from such experiments?

<p>Isotopic labeling helps identify intermediates and trace the path of specific atoms during the reaction, revealing bond-breaking and bond-forming events. (C)</p> Signup and view all the answers

Flashcards

Rate Law

Expresses the relationship between reactant concentrations and reaction rate; determined experimentally.

Rate Constant (k)

The constant 'k' in the rate law; reflects the intrinsic speed of a reaction.

Overall Reaction Order

The sum of the individual reaction orders (m + n) in the rate law.

Reaction Mechanism

Details the series of elementary steps that constitute an overall reaction.

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Elementary Step

A single molecular event in a reaction mechanism.

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Molecularity

Indicates the number of molecules involved in an elementary step.

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Rate-Determining Step

The slowest step in a reaction mechanism; governs the overall reaction rate.

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Intermediate

Species formed in one step of a reaction mechanism and consumed in a subsequent step.

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Activation Energy (Ea)

The minimum energy required for a reaction to occur.

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Transition State

The highest-energy intermediate state during a reaction.

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Catalyst

Substances that lower the activation energy of a reaction, providing an alternative pathway; not consumed in the reaction.

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Arrhenius Equation

Quantifies the relationship between temperature and the rate constant: k = Ae^(-Ea/RT).

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Reaction Order

Defines how the concentration of reactants affects the rate.

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Zero-Order Reaction

The rate is independent of reactant concentration: rate = k.

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First-Order Reaction

Rate is directly proportional to reactant concentration: rate = k[A].

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Second-Order Reaction

Rate is proportional to the square of reactant concentration: rate = k[A]^2.

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Pseudo-Order Reaction

Occurs when one reactant is in large excess, simplifying the rate law to a lower order.

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Temperature Effect on Reaction Rate

Reaction where rates generally increase with increasing temperature.

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Half-Life

Time required for half the reactant to be consumed.

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First-Order Half Life

For a first-order reaction, this is constant and independent of initial concentration, t1/2 = 0.693 / k

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Initial Rates Method

Vary initial concentrations and measure initial rates.

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Integrated Rate Laws

Monitor concentration changes over time and fit data to integrated rate equations.

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Pre-exponential Factor (A)

A factor in the Arrhenius equation that relates to the frequency of collisions and orientation of molecules.

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Study Notes

  • Chemical kinetics studies reaction rates and factors influencing them.
  • It explores how reactions occur and their speed.

Rate Laws

  • Rate laws express the relationship between reactant concentrations and reaction rate.
  • They are experimentally determined.
  • A rate law typically takes the form: rate = k[A]^m[B]^n
    • k is the rate constant
    • [A] and [B] are reactant concentrations
    • m and n are reaction orders with respect to A and B
  • The overall reaction order is the sum of the individual orders (m + n).
  • Reaction orders are not related to the stoichiometric coefficients in the balanced equation.
  • The rate constant, k, reflects the reaction's intrinsic speed.
  • Its units depend on the overall reaction order.
  • Rate laws can only be determined experimentally.
  • Common methods involve measuring initial rates or concentration changes over time.

Reaction Mechanisms

  • A reaction mechanism details the series of elementary steps that constitute an overall reaction.
  • Elementary steps describe single molecular events.
  • The molecularity of an elementary step indicates the number of molecules involved.
  • Unimolecular steps involve one molecule.
  • Bimolecular steps involve two molecules.
  • Termolecular steps involve three molecules (rare).
  • The rate-determining step is the slowest step in the mechanism.
  • It governs the overall reaction rate.
  • Intermediates are species formed in one step and consumed in a subsequent step.
  • They do not appear in the overall balanced equation.
  • Mechanisms must be consistent with the experimentally determined rate law.
  • The elementary steps must sum to the overall balanced equation.

Activation Energy

  • Reactions require sufficient energy to overcome the activation energy barrier (Ea).
  • Activation energy is the minimum energy needed for a reaction to occur.
  • The transition state (or activated complex) is the highest-energy intermediate state during the reaction.
  • Catalysts lower the activation energy.
  • They provide an alternative reaction pathway.
  • Catalysts are not consumed in the reaction.

Temperature Effects

  • Reaction rates generally increase with increasing temperature.
  • Higher temperatures mean more molecules possess the required activation energy.
  • The Arrhenius equation quantifies the relationship between temperature and the rate constant: k = Ae^(-Ea/RT)
    • A is the pre-exponential factor (frequency factor)
    • Ea is the activation energy
    • R is the gas constant (8.314 J/mol·K)
    • T is the absolute temperature (in Kelvin)
  • The pre-exponential factor relates to the frequency of collisions and the orientation of molecules.

Reaction Order

  • Reaction order defines how the concentration of reactants affects the rate.
  • Zero-order reactions:
    • Rate is independent of reactant concentration: rate = k
    • A plot of [A] vs. time is linear with a slope of -k.
    • The half-life (t1/2) decreases as the initial concentration decreases: t1/2 = [A]0 / 2k
  • First-order reactions:
    • Rate is directly proportional to reactant concentration: rate = k[A]
    • A plot of ln[A] vs. time is linear with a slope of -k.
    • The half-life is constant and independent of initial concentration: t1/2 = 0.693 / k
  • Second-order reactions:
    • Rate is proportional to the square of reactant concentration: rate = k[A]^2 or rate = k[A][B]
    • A plot of 1/[A] vs. time is linear with a slope of k.
    • The half-life depends on initial concentration: t1/2 = 1 / k[A]0
  • Mixed-order reactions exhibit more complex rate laws.
  • They do not have simple dependencies on reactant concentrations.
  • Pseudo-order reactions:
    • Occur when one reactant is in large excess.
    • The rate law simplifies to a lower order.
  • Determining reaction order:
    • Initial rates method: Vary initial concentrations and measure initial rates.
    • Integrated rate laws: Monitor concentration changes over time and fit to integrated rate equations.

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