atkins & de paula: elements of physical chemistry: 5e

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Atkins & de Paula: Elements of Physical Chemistry: 5e. Chapter 10: Chemical Kinetics: The Rates of Reactions. End of chapter 10 assignments. Discussion questions: 2, 3, 4, 5, 7 Exercises: 1, 2, 4, 5, 7, 9, 12, 13, 19, 20 Use Excel if data needs to be graphed. Homework assignments. - PowerPoint PPT Presentation

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• Atkins & de Paula: Elements of Physical Chemistry: 5eChapter 10: Chemical Kinetics: The Rates of Reactions

• End of chapter 10 assignmentsDiscussion questions:2, 3, 4, 5, 7

Exercises:1, 2, 4, 5, 7, 9, 12, 13, 19, 20

Use Excel if data needs to be graphed

• Homework assignmentsDid you:Read the chapter?Work through the example problems?Connect to the publishers website & access the Living Graphs?Examine the Checklist of Key Ideas?Work assigned end-of-chapter exercises?Review terms and concepts that you should recall from previous courses

• Empirical chemical kineticsIn order to investigate the rate and mechanism of a reaction:Determine the overall stoichiometry of the rxn and any side rxnsDetermine how the concentrations of reactants and products change over timeSpectrophotometry, conductivity, pH, GC/MS, NMR, polarimetry, etc

• SpectrophotometryBeer-Lambert law

log = [J] l

Io = incident lightI = transmitted lightl = length of light path = molar absorption coefficient[J] = molar concentration of JI = Io 10[J]l

• Molar extinction coefficient?Molar absorption coefficient () was known as the molar extinction coefficient Use of the term molar extinction coefficient has been discouraged since the 1960s

• Preferred terminology of Molar absorption coefficient () Synonyms: Molar extinction coefficient, molar absorptivity "The recommended term for the absorbance for a molar concentration of a substance with a path length of 1.0 cm determined at a specific wavelength. Its value is obtained from the equation = A / cl -- R.C. Denney, Dictionary of Spectroscopy, 2nd ed. (Wiley, 1982), p.119-20.

• Preferred terminology of Molar absorption coefficient () Strictly speaking, in compliance with SI units the path length should be specified in meters, but it is current general practice for centimeters to be used for this purpose. -- R.C. Denney, Dictionary of Spectroscopy, 2nd ed. (Wiley, 1982), p.119-20.

• Preferred terminology of Molar absorption coefficient () Under defined conditions of solvent, pH, and temperature the molar absorption coefficient for a particular compound is a constant at the specified wavelength." -- R.C. Denney, Dictionary of Spectroscopy, 2nd ed. (Wiley, 1982), p.119-20.

• SpectrophotometryBeers law: [J] =

Thus, absorbance is directly proportional to the molar concentration A = [J] l (notice A is dimensionless)Absorbance a/k/a optical densityWhat is max? Do we always use max? Is specific to a compound? To a ?

• Table 10.1 Kinetic techniques for fast reactions

TechniqueRange of time-scales/s

Femtochemistry1015

Flash photolysis1012

Fluorescence decay1010106

Ultrasonic absorption1010104

EPR*109104

Electric field jump1071

Temperature jump106 1

Phosphorescence10610

NMR*1051

Pressure jump105

Stopped flow103

* EPR is electron paramagnetic resonance (or electron spin resonance); NMR is nuclear magnetic resonance; see Chapter 21.

• SpectrophotometryFig 10.1 (231)The intensity of the absorbed light increases exponentially with path length

• SpectrophotometryFig 10.2 (231)Two concentrations of two absorbing species can be determined from their at two different s within their joint absorption region

• SpectrophotometryFig 10.3 (232)An isosbestic point is formed when two unrelated absorbing species are present in the rxn solutionThe curves repre-sent different stages of the rxn

• Applications of SpectrophotometryWe can use spectrophotometers to follow the progress of a reaction in real time

• Applications of spectrophotometryFig 10.4 (232)Flow technique

Fig 10.5 (232)Stopped-flow technique

• Applications of spectrophotometryFlash photolysisQuenching methodsRapid coolingAdding a large volume of solventRapid neutralizationApplicable to relatively slow rxns

• Reaction rate

Reaction rate is the change in the concentration of a reactant or a product with time (M/s).D[A] = change in concentration of A over time period DtD[B] = change in concentration of B over time period DtBecause [A] decreases with time, D[A] is negative. Review from Gen Chem

• Reaction Rates and StoichiometryTwo moles of A disappear for each mole of B that is formed.Review from Gen Chem

• Reaction Rates and StoichiometryTwo moles of A disappear for each mole of B that is formed.Another generic chemical reactionReview from Gen Chem

• Definition of reaction rate

Rate =

More precisely, Rate =

Partial pressures can be used instead of molar concentrationsNotice Atkins/de Paula use the absolute valuet is infinitesimally small

• Definition of reaction rateFig 10.6 (233)Concentration of reactant vs timeThe rxn rate changes as the rxn proceedsSlope is the instantaneous rate at that time

• Rate laws and rate constantsThe rate of a rxn is often (usually?) found proportional to the product of the molar concentrations raised to a simple power:Rate = [A]x [B]yThe units of the rate constant are determined by the form of the rate law (p.234)

• Rate laws and rate constantsThe rate law allows us to predict the concentrations of reactants and products at time t Proposed mechanisms must be consistent with the rate law

• Classification according to orderThe power to which a concentration is raised in the rate law is the order with respect to that speciesThe overall order of a reaction is the sum of the orders of all the reactantsThe order may be a fraction, zero, or indefiniteThe rate law is determined empirically and cannot be inferred from the stoichiometry of the chemical eqn

• Determination of the rate lawThe rate law is determined empirically Two common methods:The isolation method (as performed in Gen Chem lab; all reactants except one present in great excess, so their concentrations do not change much)The method of initial rates

• The method of initial rateslog rate0 = log k + a log[A]0This equation is of the form:y = intercept + slope x So, for a series of initial concentrations, a plot of the log rate0 vs log[A]0 should be a straight line, with the slope = a, the order of the rxn with respect to ALets look at an example

• Determination of the rate lawFig 10.7 (237)The slope of a graph of log(rate0) vs log[A]0 is equal to the order of the reaction

• The method of initial ratesYou should work through Example 10.1, pp.237f

• Integrated rate lawsFirst order rxns:

ln = kt

ln[A] = ln[A]0 kt OR [A] = [A]0 ektIn 1st order rxns, the [reactants] decays exponentially with time

• Integrated rate lawsFig 10.10 (239)The exponen-tial decay of reactant in a 1st order rxn. The larger the rate constant, the faster the decay

• Integrated rate lawsFig 10.11 (240)Part of Ex 10.2

You should work through Example 10.2

• Integrated rate lawsFig 10.12 (241)Variation with time of the [reactant] in a 2nd order rxn

• Integrated rate lawsFig 10.13 (241)The determination of the rate constant of a 2nd order rxnThe slope equals the rate constant

• Table 10.2 Kinetic data for first-order reactions

ReactionPhase/Ck/s1t1/2

2 N2O5 4 NO2 O2g 253.38 105 2.85 h

2 N2O5 4 NO2 O2Br2(l) 254.27 105 2.25 h

C2H6 2 CH3g7005.46 10421.2 min

Cyclopropane propeneg5006.17 10417.2 min

The rate constant is for the rate of formation or consumption of the species in bold type. The rate laws for the other species may be obtained from the reaction stoichiometry.

• Table 10.3 Kinetic data for second-order reactions

ReactionPhase/Ck/(dm3 mol1 s1)

2 NOBr 2 NO Br2g 100.80

2 NO2 2 NO O2g3000.54

H2 I2 2 HIg4002.42 102

D2 HCl DH DClg6000.141

2 I I2g 237 109

hexane 501.8 1010

CH3Cl CH3OCH3OH(l) 202.29 106

CH3Br CH3OCH3OH(l) 209.23 106

H OH H2Owater 251.5 1011

The rate constant is for the rate of formation or consumption of the species in bold type. The rate laws for the other species may be obtained from the reaction stoichiometry.

• Table 10.4 Integrated rate laws

OrderReaction typeRate lawIntegrated rate law

0A Prate k[P] kt for kt [A]0

1A Prate k[A][P] [A]0(1 ekt)

2A Prate k[A]2

A B Prate k[A][B]

_1168650209.unknown

_1168650513.unknown

• Half-lives and time constantsA half-life is a good indicator of the rate of a 1st order rxnThe half-life is the time it takes for [reactant] to drop to [reactant]0

• Half-lives and time constantsUseful for 1st order rxns[A] = [A]0 at t substitute into next eqn

ln = kt to get.

kt = ln = ln = ln 2

For 1st order rxn, t of a reactant is independent of its concentration

• Using a half-lifeFig 10.15 (242)Illustration 10.2

• Using a half-lifeFig 10.16 (243)Illustration 10.3

• The Arrhenius parameters In the 1800s Arrhenius noticed that the rates of many different rxns had a similar dependence on temperatureHe noticed that a plot of ln k vs 1/T gives a straight line with a slope characteristic of that rxnln k = intercept + slope 1/T

ln k = ln A

• The Arrhenius parameters

ln k = ln A

k = AeThe Arrhenius parameters:A is the pre-exponential factorEa is the activation energy, kJ/molWhen Ea is high, the rxn rate is sensitive to temperature, steep slopeWhen Ea is low, the rxn rate is less sensitive to temperature, less ste