“I came to my professor, Cleve, and I said, ‘I have a new theory of electrical conductivity as a cause of chemical reactions.’ He said, ‘That is very interesting,’ and then he said ‘Goodbye’. He explained to me later, when he had to pronounce the reason for my receiving the Nobel Prize for that work, that he knew very well that there are so many different theories formed, and that they are all almost certain to be wrong, for after a short time they disappear; and therefore, by using the statistical manner of forming his ideas, he concluded that my theory also would not exist very long.

Remarks by ArrheniusThe April issue of the ACS Chicago Section’s Chemical Bulletin carries excerpts from a talk by Svente Arrhenius on May 11, 1912, when he received the section’s first Willard Gibbs Award.The full address appears in J. Am. Chem. Soc., 36, 353 (1912). A few lines follow:

““I was not very content with that opinion, and then I thought, I was not very content with that opinion, and then I thought, in foreign countries there are such prominent scientist they might in foreign countries there are such prominent scientist they might look at it differently; it might appeal to them. Then I wrote to look at it differently; it might appeal to them. Then I wrote to Clausius, and said, ‘What do you think of that?’ I wrote to Clausius, and said, ‘What do you think of that?’ I wrote to Ostwald – he worked on the same line. I wrote to Thomsen. Ostwald – he worked on the same line. I wrote to Thomsen. I received friendly answers … they were very glad to make my I received friendly answers … they were very glad to make my acquaintance, and so on, but it was not very much more. The acquaintance, and so on, but it was not very much more. The only exception was Ostwald, and he describes how it was that only exception was Ostwald, and he describes how it was that he got on the same day this dissertation, a toothache, and a nice he got on the same day this dissertation, a toothache, and a nice daughter, and that was too much for one day, and the worst was daughter, and that was too much for one day, and the worst was the dissertation.”the dissertation.”

Wag (9) a humorous person; joker (Am. College Dictionary,Wag (9) a humorous person; joker (Am. College Dictionary,Random House, NY, 1961)Random House, NY, 1961)

In the "standard" Arrhenius form of the rate constant, A,In the "standard" Arrhenius form of the rate constant, A,and Eand EAA are constants independent of temperature. are constants independent of temperature.

Arrhenius first Arrhenius first guessedguessed the form of the kinetic rate constant the form of the kinetic rate constant in the late 1800’s:in the late 1800’s:

A is called the “pre-exponential” factor and EA is called the “pre-exponential” factor and EAA the activation the activationenergy.energy.

Using this form and taking the natural log of kUsing this form and taking the natural log of kraterate gives gives

ln[kln[kraterate] = ln(A) - E] = ln(A) - EAA/RT/RT

Temperature Dependence of kTemperature Dependence of kraterate

kkraterateAeAe -E-EAA // RTRT

Taking the derivative with respect to T:Taking the derivative with respect to T:

dd {ln[k {ln[kraterate]} ]} /dT/dT = = dd {ln(A) - E {ln(A) - EAA/RT} /RT} /dT/dT

dd {ln[k {ln[kraterate]} ]} /dT/dT = = dd {- E {- EAA/RT} /RT} /dT/dT

dd {ln[k {ln[kraterate]} ]} /dT/dT = E = EAA/RT/RT22

This expression predicts that a plot of ln[kThis expression predicts that a plot of ln[kraterate] vs 1/T will be a] vs 1/T will be aa straight line with a slope of -Ea straight line with a slope of -EAA/R/R

dd {ln[k {ln[kraterate]} = [-E]} = [-EAA/R] /R] d(1/T)d(1/T)

(Because d(1/T) = (-1/T(Because d(1/T) = (-1/T22) dT)) dT)

(Because A is assumed(Because A is assumedConstant in this model.)Constant in this model.)

could be obtained from a reaction cross section of the form could be obtained from a reaction cross section of the form

Where Where AB AB is the sum of the radii of molecules A and Bis the sum of the radii of molecules A and B

<u<urelrel> = (8kT/> = (8kT/))1/21/2

If we set A=If we set A=ABAB22<u<urelrel>>

then kthen kraterate=Ae=Ae-E-EAA/RT/RT

But notice A here scales like TBut notice A here scales like T1/21/2. It is. It is NOT independent of T as ArrheniusNOT independent of T as Arrheniusassumed!assumed!

We saw using gas kinetic theory collision rate argumentsWe saw using gas kinetic theory collision rate arguments(binary collision model) that a form for k(binary collision model) that a form for kraterate like like

RR22 = 0 = 0 E < EE < EAA

RR22 = = ABAB

22 (1 - E (1 - EA A / E)/ E) E E E EAA

kkraterate = = ABAB22 < u < urelrel > e > e-E-EAA/RT/RT

If we write A=(const) TIf we write A=(const) T1/21/2, then k, then krate rate becomesbecomes

kkraterate=(const) [T=(const) [T1/21/2]e]e-E-EAA/RT/RT

ln[kln[kraterate] = ln(const)+ln[T] = ln(const)+ln[T1/21/2] - E] - EAA/RT/RT

ln[kln[kraterate] = ln(const)+(1/2)ln[T] - E] = ln(const)+(1/2)ln[T] - EAA/RT/RT

dd {ln[k {ln[kraterate]} ]} /dT/dT = [(1/(2T)] + E = [(1/(2T)] + EAA/RT/RT22

dd {ln[k {ln[kraterate]} ]} /dT/dT = [(1/2)RT + E = [(1/2)RT + EAA]/RT]/RT22

dd {ln[k {ln[kraterate]} ]} /dT/dT = [ = [AA]/RT]/RT22

Define Define [(1/2)RT + E[(1/2)RT + EAA] = ] = AA

A plot of ln kA plot of ln kraterate vs 1/T has a slope vs 1/T has a slope

--A A /R (no longer independent of T!)/R (no longer independent of T!)

dd {ln[k {ln[kraterate]} = -[]} = -[AA]/R ]/R d(1/T)d(1/T)

A A = = [(1/2)RT + E[(1/2)RT + EAA] ] provides a more strict definition ofprovides a more strict definition of the activation energy for a reaction since it includes the Tthe activation energy for a reaction since it includes the T dependence of relative speed. Note that this activation dependence of relative speed. Note that this activation energy is T dependent.energy is T dependent.

Since the slope is not a constant, the plot of lnkSince the slope is not a constant, the plot of lnkrate rate

vs 1/T is not a straight line.vs 1/T is not a straight line.

Kinetics and EquilibriaKinetics and EquilibriaBy definition, By definition, kinetic processeskinetic processes are not are not equilibrium processesequilibrium processes..In fact, we may think of kinetic processes as the mechanismIn fact, we may think of kinetic processes as the mechanismthat nature uses to reach the equlibrium state.that nature uses to reach the equlibrium state.

has 2 rate constants, we can write, has 2 rate constants, we can write, assuming these are ELEMENTARY reaction steps:assuming these are ELEMENTARY reaction steps:

kkff[A][A]ee[B][B]ee=k=krr[C][C]ee[D][D]ee (Equilibrium condition) (Equilibrium condition)Where [A]Where [A]e e etc. are the equilibrium concentrationsetc. are the equilibrium concentrationsof [A] etc. of [A] etc. kkff/k/krr = = [C][C]ee[D][D]ee / / [A][A]ee[B][B]e e = K= Kequilibriumequilibrium

If we realize A + B C + DIf we realize A + B C + Dk f⏐ → ⏐ ⏐ k r

← ⏐ ⏐ ⏐ Binary Collision rateBinary Collision ratein reverse direction.in reverse direction.

Binary Collision rateBinary Collision ratein forward direction.in forward direction.

Using the Arrhenius form for the rate constants kUsing the Arrhenius form for the rate constants kff and k and krr

But later we will learn (or you already know from high school):But later we will learn (or you already know from high school):

ln[Kln[Keqeq]= -]= -GG00/RT/RTGG00== HH0 0 - T - T SS0 0

Where Where HH0 0 is the enthalpy change for the reaction and is the enthalpy change for the reaction and SS00 is the is theentropy change for the reaction. entropy change for the reaction. GG0 0 is called the Free Energy is called the Free Energy

kkff AAff ee EE AfAf // RTRT kkrr AArr ee EEArAr // RTRT

But we also knowBut we also know Keq −G o

RT (−Ho

RT )• (So

R )

KKeqeq = k = kff/k/krr = = (A(Aff/A/Arr) exp [-(E) exp [-(EAfAf-E-EArAr)/RT])/RT]

Equating these two forms for the equilibrium constant allows usEquating these two forms for the equilibrium constant allows us to connect thermodynamics and kinetics!to connect thermodynamics and kinetics!

““Identify” AIdentify” Aff / A / Arr with {e with {e ((SS/R)/R)} (T “independent” assuming ∆Sº} (T “independent” assuming ∆Sº indep of T).indep of T).EEAfAf - E - EArAr “identify” with ∆Hº “identify” with ∆Hº

A + BA + B

Act StateAct State

EEAfAf EEArAr

C + DC + D

+∆H+∆Hoo = E = EAfAf - E - EArAr

(∆H(∆Hoo = Enthalpy = Enthalpy change forchange forA+B A+B C+D)C+D)

(A(Aff/A/Arr) exp [-(E) exp [-(EAfAf-E-EArAr)/RT] =)/RT] = {e {e ((SS/R)/R)} } { e { e (-(-HH/RT)/RT)}}

Thermodynamic form of KThermodynamic form of Keqeq Kinetic form of KKinetic form of Keqeq

Acid-Base EquilibriaAcid-Base EquilibriaSeveral ways to define acid, base:Several ways to define acid, base:

Evidence exists for presence of HEvidence exists for presence of H33OO++ in solution. Small size of H in solution. Small size of H++ allows it to be incorporated into the structure of the solvent.allows it to be incorporated into the structure of the solvent.

The strength of an acid/base is determined by degree of dissociationThe strength of an acid/base is determined by degree of dissociation

1) H1) H++ responsible for acid properties,responsible for acid properties,OHOH-- responsible for basic properties responsible for basic properties

Oversimplified:Oversimplified: HH++ ~ 10 ~ 10-13-13 cm in diameter because is a free proton cm in diameter because is a free proton

(unique in + charged species)(unique in + charged species)

HCl HCl H H++ + Cl + Cl--

CHCH33COOH COOH CH CH33COOCOO-- + H + H++

NaOH NaOH Na Na++ (aq) + OH (aq) + OH-- (aq) (aq)

HH33OO++ is called the hydronium ion-is particularly stable. is called the hydronium ion-is particularly stable.Less evidence for species like HLess evidence for species like H99OO44

++ (4H (4H22O+HO+H++))

Some non-OHSome non-OH-- species can neutralize acids: species can neutralize acids:HCl(aq)+NHHCl(aq)+NH3 3 NHNH44

++ +Cl+Cl--

2) Lowry-Bronsted Concept:2) Lowry-Bronsted Concept:Acids have a tendency to lose or donate a protonAcids have a tendency to lose or donate a protonwhile bases have a tendency to accept or add a protonwhile bases have a tendency to accept or add a proton

More accurate view:More accurate view:HCl +HHCl +H22O O H H33OO++ + Cl + Cl--

Acid is capable of Acid is capable of transferringtransferring a proton a protonBases neutralize acids.Bases neutralize acids.

HCl (aq) + HHCl (aq) + H22O O H H33OO++ (aq) + Cl (aq) + Cl-- (aq) (aq)acid base acid baseacid base acid base

Note: HNote: H22O is aO is abase here.base here.

Conjugate pairs: COConjugate pairs: CO332-2-, HCO, HCO33

-- and H and H22O, OHO, OH--

Strengths of Acids and Bases:Strengths of Acids and Bases:Equate to tendency to transfer a proton to HEquate to tendency to transfer a proton to H22OO

Need a Need a quantitative quantitative measure of acidity or Hmeasure of acidity or H++ donating power. donating power.

HCl, ClHCl, Cl-- differ only by H differ only by H++. Are called a . Are called a conjugateconjugateacid-base pair:acid-base pair:

COCO332-2- + H + H22O O HCO HCO33

-- + OH + OH--

base 1 acid 2 acid 1 base 2base 1 acid 2 acid 1 base 2

HCl + HHCl + H22O O H H33OO++ + Cl + Cl--

HSOHSO44-- + H + H22O O H H33OO++ + SO + SO44

2-2-

HA + HHA + H22O O H H33OO++ + A + A-- Define acid dissociation constant Define acid dissociation constant

Note: HNote: H22O is anO is anacid here.acid here.

K = [HK = [H33OO++][A][A--] / [HA]] / [HA]

HCl + HHCl + H22O O H H33OO++ + Cl+ Cl-- If HCl is a strong acid, If HCl is a strong acid, then Clthen Cl-- has only a weak tendency to acquire H has only a weak tendency to acquire H++

3) Lewis Concept (most general):3) Lewis Concept (most general): Acid is any substanceAcid is any substancethat can accept electrons and a base is any that can accept electrons and a base is any substance that can donate electrons.substance that can donate electrons.

If acid is strong, e.g., HCl, then conjugate base is weak (ClIf acid is strong, e.g., HCl, then conjugate base is weak (Cl--))Will prove this latter in a quantitative fashion.Will prove this latter in a quantitative fashion.

K = note HK = note H22O missing from K. Defined at equilibrium O missing from K. Defined at equilibrium for reaction:for reaction:

[H3O+][A−]

[HA]

BFBF3 3 + F + F -- BF BF44--

acid baseacid base

Note that large K is associated with strong acid since it means Note that large K is associated with strong acid since it means numerator is large compared to denominator. Large Knumerator is large compared to denominator. Large KHA is HA is a good proton donor to Ha good proton donor to H22O.O.

AgAg++ + 2 CN + 2 CN -- Ag(CN) Ag(CN)22--

acid baseacid base

HA + HHA + H22O O H H33OO++ + A + A--

Acid-Base Equilibria ConsiderationsAcid-Base Equilibria Considerations

KKaa is called the acid is called the acidionization constantionization constant

HSOHSO44-- + H + H22O O H H33OO++ + SO + SO44

2-2-

′ K =[H3O

+][SO42−]

[HSO4−][H2O]

[H[H22O] O] constant: 1 liter = 1000 gm. 1 mole = 18 gm constant: 1 liter = 1000 gm. 1 mole = 18 gm

= 55.5 moles/liter = 55.5 M (huge concentration)= 55.5 moles/liter = 55.5 M (huge concentration)1000

18

Acid ionization constantAcid ionization constant

′ K [H2O] = Ka =[H3O

+ ][SO42− ]

[HSO4−]

NHNH33 + H + H22O O NH NH44++ + OH + OH --

KKbb = Again [H = Again [H22O] taken as constantO] taken as constant[NH4

+][OH−][NH3]

(K’ is a (K’ is a truetrue equilibrium constant) equilibrium constant)

Write equilibriumequilibrium constant: constant:

QuickTime™ and aVideo decompressor

are needed to see this picture.

pH=pH=-log-log1010[H[H33OO++]]