Chapter 3 An Introduction to Organic Reactions: Acids and Bases Chapter 3 An Introduction to Organic Reactions: Acids and Bases Organic Reactions and their Mechanisms A reaction mechanism is a detailed description of the bonding changes as a reaction proceeds. The reaction mechanism also includes the many important principles of organic chemistry. A plausible reaction mechanism must be consistent with the principles of organic chemistry. Four General Categories of Organic Reactions Organic reactions tend to fall into four categories: substitutions, additions, eliminations, rearrangements. Substitutions In a substitution reaction, one atom or group replaces another in a structure. This type of reaction is commonly observed in saturated hydrocarbons and aromatics. + Na+ -OH R-X H2O R-OH + Na+ X- an alkyl halide Ar-H an aromatic + Br2 Fe Ar-Br + HBr The mechanisms of the above two substitution reactions are completely different. Additions Addition reactions are found in organic compounds with multiple bonds: alkenes, alkynes, carbonyl-containing compounds. In this reaction, thecomponent of the multiple bond is lost as new bonds are formed to the carbon (or other atomic) centers . H H C H C + Br2 H H H H C C Br Br Bromine adds to the alkene (ethene). H Eliminations These reactions are the reverse of addition reactions. In an elimination reaction, a molecule loses atoms or groups from adjoining carbon (or other atomic) centers, forming a multiple bond. H H H C C H Br H H C H + KOH H + K+ Br- + H2O C H The above reaction is a dehydrohalogenation, loss of HBr, of an alkyl halide to form an alkene. Rearrangements In rearrangement reactions, there is a reorganization of the atoms or groups in a structure. H+ In the presence of acid, the alkene on the left rearranges to the alkene on the right. Reaction Mechanisms and Chemical Intermediates Reaction mechanisms are detailed descriptions of changes at the molecular level as reactants become products. Often the reactions involve a sequence of steps with one or more chemical species called intermediates that are formed and consumed. Chemical intermediates typically are not stable structures that can be put in a bottle. Many exist for very short times (10-6 - 10-9 seconds). We will explore how structural and electronic influences affect the stability of chemical intermediates and, thereby, control the path that reactions follow. Bond Making and Bond Breaking Processes: Heterolysis and Homolysis A covalent bond may break by either of two different processes: heterolysis or homolysis. Heterolysis (Gr: hetero- "different" + lysis-"cleavage") A:B + A + B Double-barbed arrow is used to show movement of an electron pair. ions Homolysis (Gr: homo-"the same" + lysis) A:B A. + B . radicals Single-barbed arrow is used to show movement of a single electron. Cleavage of Covalent Bonds • Homolysis • Heterolysis 9 • Heterolytic reactions almost always occur at polar bonds • The reaction is often assisted by formation of a new bond to another molecule 10 Acid-Base Reactions The Brønsted-Lowry Definitions In 1923 the Danish chemist Johannes Brønsted (1879-1947) and the English chemist Thomas Lowry (1874-1936) independently proposed that acids and bases be defined in terms of their ability to give up or accept a proton. base acid (accepts H+) (gives up H+) + :Cl : : : H-Cl : : + : : : H-O: H + H-O-H H conjugate acid conjugate base of HCl of H2O • Example • Aqueous hydrogen chloride and aqueous sodium hydroxide are mixed • The actual reaction is between hydronium and hydroxide ions 12 Conjugate Pairs The species formed when an acid loses a proton is the conjugate base. The species formed when a base accepts a proton is the conjugate acid. Conjugate pairs are pairs of chemical species that only differ in H+ such as H2O/H3O+ HCl/Cl- Diprotic Acids Diprotic acids have two acidic protons that may be released. An example is sulfuric acid where the two H+ are sequentially released. (1) H2SO4 + H2O H3O+ + HSO4- (2) HSO4- + H2O H3O+ + SO42- Step 1 occurs completely while step 2 proceeds to only about 10% in water. The Leveling Effect of Water The "leveling effect of water" refers to the limitations imposed on acid and base strengths in water because of the acid-base reactions of water. The strongest acids and bases that can exist in water are H3O+ and HO-. When stronger acids or bases are added to water, they immediately react with water to produce these species. H-A + H2O fast H3O+ + A- fast HO- very strong acid B:- + H2O + H-B very strong base chemical species in water A practical consequence of the leveling effect of water is that most organic reactions that involve very strong bases or acids are carried out in nonaqueous solvents such as ethers or hydrocarbons. Acids and Bases The Lewis Definitions of Acids and Bases In 1923, the same year the Brønsted-Lowry definitions were introduced, G.N. Lewis (1875-1946) broadened the definitions of acids and bases: An acid is a chemical species that can accept an electron pair. A base is a chemical species that can donate an electron pair. Lewis acid + Lewis base reactions H+ + :F: + :Br-Br: NH4+ : : : : F F-B-F F Br - + Br-Fe:Br-Br: Br : : : : :NH3 : : F F-B F Br Br-Fe Br + Note: Any electron deficient atom can act as a Lewis acid by accepting an electron pair. This idea is important in organic reaction mechanisms. Quiz Chapter 3 Section 2 In the reaction below, identify the acid, base, conjugate acid and conjugate base. CH3 C C H + NaNH2 acid base CH3 C CNa + NH3 conjugat e base conjugat e acid Solut ion Use t he Brønst ed-Low ry definit ions. Look for t he species t hat giv e up and accept t he prot on.. • Lewis Definition of Acids and Bases • Lewis Acid: electron pair acceptor • Lewis Base: electron pair donor • Curved arrows show movement of electrons to form and break bonds 17 Opposite Charges Attract and React • BF3 and NH3 react based on their relative electron densities • BF3 has substantial positive charge on the boron • NH3 has substantial negative charge localized at the lone pair 18 Carbon Bond Heterolysis Processes: Carbocations and Carbanions When a bond to carbon is broken heterolytically, the carbon may carry either a positive (carbocation) or negative (carbanion) charge.. Modes of Heterolytic Bond Cleavage Heterolysis of Bonds to Carbons: Carbanions and Carbocations • Reaction can occur to give a carbocation or carbanion depending on the nature of Z • Carbocations have only 6 valence electrons and a positive charge 20 Formal Charges Carbocations have only six electrons in the valence or bonding level and are electron-deficient. The charge on carbon can be determined by a simple calculation. Step One: Determine how many of the valence electrons "belong" to carbon. For each pair of bonding electrons, one "belongs" to carbon. All nonbonding electrons in the valence level "belong" to carbon. C+ a carbocation In a carbocation, only 3 of the 6 bonding electrons "belong" to the carbon. There are no nonbonding electrons. Step Two: Compare the number of "owned" electrons in the valence level of the bonded state with the number in the atomic state. Atomic carbon has 4 electrons in the valence level. Since in the carbocation, only 3 electrons belong to carbon, there is a deficiency of one electron (a formal charge imbalance at carbon). Therefore, there is a formal charge of +1 on carbon. Carbanions Carbanions have 6 bonding and two nonbonding electrons in the valence level, and have a formal charge of -1. C: a carbanion Three of the bonding electrons and the two nonbonding electrons belong to carbon. Calculation of Formal Charge Since atomic carbon has 4 electrons in the valence level while 5 of the 8 valence electrons in the carbanion belong to carbon, there is a surplus of one electron in the bonded state. The formal charge is -1. • Carbanions have 8 valence electrons and a negative charge • Organic chemistry terms for Lewis acids and bases • Electrophiles (“electron-loving” reagents ): seek electrons to obtain a stable valence shell of electrons – Are electron-deficient themselves e.g. carbocations • Nucleophiles (“nucleus-loving” reagents): seek a proton or some other positively charged center – Are electron-rich themselves e.g. carbanions 23 The Reactivity of Chemical Intermediates Carbocations as Electrophiles Since carbocations are electron-deficient in the valence level, they are strong Lewis acids. Carbocations react rapidly with Lewis bases, species that are capable of donating electrons. Carbocations are called electrophiles. C+ + :B - CB C B a carbocation (an electrophile) An Example C+ + O H H Lewis Base H -H+ H C O H H H H H C O H H an alcohol Carbanions as Nucleophiles Carbanions are Lewis bases. They donate an electron pair to Lewis acids such as H+ and other electropositive atoms and groups. Carbanions are called nucleophiles. - C + carbanion (a nucleophile) - C + H-A C H +A Lewis acid C L carbanion Lewis acid (a nucleophile) C C + L- The Curved Arrow Formalism The above bonding changes are illustrated with a formalism called curved arrows where the arrow shows the direction of electron flow from nucleophile to electrophile. The curved arrow begins at an electron pair (bonding or nonbonding) and moves towards an electron-deficient atom or group (Lewis acid). direction of electron flow nucleophile electrophile Examples C C nucleophile + H Cl - electrophile nucleophile : : :O H H O CH3C O : + = : = O CH3C O H + electrophile C C H + Cl H + :O H H The Use of Curved Arrows in Illustrating Reactions • Curved arrows show the flow of electrons in a reaction • An arrow starts at a site of higher electron density (a covalent bond or unshared electron pair) and points to a site of electron deficiency • Example: Mechanism of reaction of HCl and water 27 Quiz Chapter 3 Section 4 : : : In the reaction below, use the curved arrow formalism to show movement of an electron pair. + + C6H5CH2-OCH3 C6H5CH2 + CH3OH H electrophile nucleophile Lewis acid Lewis base Identify the electrophile and nucleophile in the reaction. Identify the Lewis acid and Lewis base in the reaction. Acid and Base Strengths: Ka and pKa Organic acids (carboxylic acids) typically are weaker acids than the mineral acids (HCl, H2SO4). While the latter dissociate completely in water, carboxylic acids, such as acetic acid, dissociate only to a small degree . + H2O O CH3CO- = = O CH3CO-H + H3O+ In a 0.1 M solution of acetic acid in water at 25oC, only about 10% of the acetic acid molecules are dissociated to the acetate and hydronium ions. Acidity Constant, Ka An equilibrium is established for the dissociation of acetic acid in water with an equilibrium constant, Keq, that is expressed as Keq = [H3O+] [CH3CO2-] [CH3COOH] [H2O] However, for dilute solutions, the concentration of water (~55.5 M) does not change significantly during the reaction (the activity of water a = 1) , and a new equilibrium constant is defined: the acidity constant, Ka. Ka = Keq[H2O] = [H3O+] [CH3CO2-] [CH3COOH] Values of Ka are tabulated. For acetic acid, at 25oC, Ka = 1.76 x 10-5. The units of Ka are mol/L, but they are usually omitted. Magnitude of Ka and Acid Strength For the general case, HA + H2O Ka = [H3O+] [A- ] [HA] H3O+ + AThe larger the magnitude of Ka, the more the equilibrium is shifted to the products side, and the greater the acid strength of HA. Strengths of Acids and Bases • Ka and pKa • Acetic acid is a relatively weak acid and a 0.1M solution is only able to protonate water to the extent of about 1% • The equilibrium equation for this reaction is: 32 • Dilute acids have a constant concentration of water (about 55.5 M) and so the concentration of water can be factored out to obtain the acidity constant (Ka) – Ka for acetic acid is 1.76 X 10-5 • Any weak acid (HA) dissolved in water fits the general Ka expression – The stronger the acid, the larger the Ka 33 Acidity and pKa Because Ka values range over many powers of 10, a logarithmic scale is used where pKa = -Log Ka in analogy with pH = -Log [H3O+] For acetic acid at 25oC, pKa = -Log Ka = -Log (1.76 x 10-5) = -(-4.75) = 4.75 Note the inverse relationship between the magnitude of Ka and the magnitude of pKa because of the negative sign in the definition of pKa. The smaller the magnitude of Ka, the larger the magnitude of pKa. • Acidity is usually expressed in terms of pKa – pKa is the negative log of Ka – The pKa for acetic acid is 4.75 • The larger the pKa, the weaker the acid 35 A Quantitative Measure of Acid Strength: Examples of Ka and pKa Values acid Ka pKa H-F 6.8 x 10--4 3.17 strongest acid C6H5COOH H-CN 6.5 x 10-5 4.9 x 10-10 4.19 9.3 weakest acid "Acidity" in Organic Chemistry In organic chemistry, the term "acidity" is broadly used and is a fundamental property of all organic materials. Many reactions depend on the relative acidities of organic compounds which direct proton transfers, and the course of reactions. The range of acidities of organic compounds is enormous, with the Ka values covering many powers of 10. Conjugate Pair Relationships The acidity of a compound and the basicity of its conjugate base are related by Ka x Kb = Kw = 1.0 x 10-14 or pKa + pKb = 14 for conjugate pairs This relationship means the stronger the acid strength of HA, the weaker the base strength of A-. Also, if the value of Ka for HA is known, the value of Kb for A- may be calculated. Some Selected Acids and their Conjugate Bases The defining equilibrium for acid strength (Ka or pKa) is HA + H2O H3O+ + A- either from direct measurement or from indirect methods. Clearly, the magnitude of Ka for the very weak "acids" in the table on the next slide cannot be directly measured in water. acid H2SO4 HCl approximate pKa strongest acid C6H5SO3H -10 -7 conjugate base weakest base C6H5SO3- -6.5 H3O+ HNO3 HSO4Cl- -1.74 H2O -1.4 NO3- CF3COOH 0.18 CF3CO2- CH3COOH 4.75 CH3CO2- NH4+ H2O CH3CH2OH HC CH H2 NH3 CH2=CH2 CH3CH3 weakest acid 9.2 NH3 15.7 HO- 16 CH3CH2O- 25 HC C:- 35 38 HNH2- 44 >50 strongest base H2C=CHCH3CH2- 40 Self-Ionization of Water Even in pure water, there are still finite concentrations of H3O+ and HO- because of the self-ionization of water: H-O: + :O-H H H acid : : : : : + H O-H + H-O: H base In pure water, at 25oC, [H3O+] = [HO-] = 1.0 x 10-7 M. Since the concentration of water in pure water is 55.5 M,, Ka = [H3O+] [HO-] [H2O] (10-7) (10-7) = (55.5) and the pKa of water is 15.7. = 1.8 x 10-16 The Acidity of the Hydronium Ion, H3O+ The acidity of H3O+ is calculated from the defining equilibrium: H3O+ Ka = + H3O+ H2O [H3O+] [H2O] [H3O+] = [H2O] + H2O = 55.5 M and the pKa of H3O+ = -Log (55.5) = -(1.74) = -1.74 Acidity Order: pKa H3O+ >> H2O -1.74 15.7 Predicting Base Strengths According to the Brønsted-Lowry definitions of acids and bases, B: H + A: H-A + B: acid conjugate acid base and the conjugate pairs are: conjugate base H-A / A: and B: / B:H An important relationship between acids and their conjugate bases is: Ka x Kb = Kw = 1.0 x 10-14 pKa + pKb = 14 where Ka is the acidity constant of an acid, and Kb is the basicity constant of its conjugate base defined as Kb A:H + HO A: + H2O Because of this intrinsic relationship between acids and their conjugate bases, the relative order of acid strengths (pKa values) automatically provides a relative order of the strengths of the conjugate bases. Predicting Base Strengths acids pKa CH3NH3+ C6H5NH3+ methylaminium ion anilinium ion 10.6 4.6 acid strengths conjugate bases CH3NH2 methylamine C6H5NH2 aniline predicted base strengths Predicting the Strengths of Bases • The stronger the acid, the weaker its conjugate base will be • An acid with a low pKa will have a weak conjugate base • Chloride is a very weak base because its conjugate acid HCl is a very strong acid 45 • Methylamine is a stronger base than ammonia • The conjugate acid of methylamine is weaker than the conjugate acid of ammonia 46 Quiz Chapter 3 Section 5 : = : = = Based on the information provided, which organic compound below is the stronger acid? O O CH3SNH2 CH3CNH2 O acetamide methanesulfonamide pKa ~15 ~10 Which anion is the stronger base? O CH3SNH O : : = = : : = O CH3CNH Predicting the Outcome of Acid-Base Reactions • Acid-base reaction always favor the formation of the weaker acid/weaker base pair • The weaker acid/weaker base are always on the same side of the equation • Example • Acetic acid reacts with sodium hydroxide to greatly favor products 48 Another Example: Amines in Aqueous HCl Solution Amines (RNH2) dissolve in hydrochloric acid solution because of a highly favorable equilibrium: stronger base H + R-N-H ClH pKa ~ ~ 9-10 stronger acid weaker acid : : R-NH2 + H-O-H Cl+ H pKa = -1.74 + H2O weaker base products are more stable than reactants This equilibrium highly favors the products on the right, which means that water-insoluble amines may be dissolved in hydrochloric acid solution. Quiz Chapter 3 Sections 5 and 6 Based on the information provided below, determine if each reaction below will proceed as written. O N H pKa CH3COOH NH4+ Cl- O phthalimide 8.3 O O N K+ + NH4+ Cl- NO N H + WA SB SA O O - + N K + CH3COOH SB O NH3 + KCl O O WB acetic acid 4.7 ammonium chloride 9.2 SA YES N H + CH3COO- K+ WA O WB • Water Solubility as a Result of Salt Formation • Organic compounds which are water insoluble can sometimes be made soluble by turning them into salts • Water insoluble carboxylic acids can become soluble in aqueous sodium hydroxide • Water insoluble amines can become soluble in aqueous hydrogen chloride 51 Acid Strength: Structure and Reactivity Relationships There are several important relationships between acid strength (Ka) and structure of compounds. Ka + H-A H2O H3O+ + A- (1) Bond Strength The acidity of H-A decreases as the bond strength increases. An example is the order of acidity of the hydrogen halides (H-X). pKa 3.2 H-F H-Cl -7 H-Br -9 H-I -10 increasing acid strength increasing H-X bond strength Order of Base Strength F- > Cl - > Br- > I- The Relationship Between Structure and Acidity • Acidity increases going down a row of the periodic table • Bond strength to hydrogen decreases going down the row and therefore acidity increases 53 • Acidity increases from left to right in a row of the periodic table • Increasingly electronegative atoms polarize the bond to hydrogen and also stabilize the conjugate base better 54 Influences of Electronegativity on Acidity Increasing electronegativity of the central atom enhances acidity in two ways: (1) The polarity of the covalent A-H bond increases with increasing electronegativity of atom A, resulting in a more electropositive H. As positive charge density on H increases, its reactivity towards a base increases. reactivity towards B:- H2N-H HO-H slower faster (2) As the electronegativity of A increases, the stability of the anion, A-, increases, resulting in a larger Ka for the equilibrium: A-H + H2O H3O+ + A- • Overview of Acidity Trends 56 The Effect of Orbital Hybridization The acidity of hydrocarbons varies considerably according to the type of hybrid orbital projected by the carbon atom. hydrocarbon HH C H C HH H ethane pKa H >50 H C C H H C C H H ethene 44 ethyne 25 increasing acidity hybrid orbital projected by C sp3 sp2 sp The acidity of the hydrocarbon increases with the amount of scharacter in the hybrid orbital projected by the carbon atom. Hybrid Orbital Electronegativities Electrons in the 2s atomic orbital are more stable than electrons in a 2p atomic orbital. S-type orbitals are centered on the nucleus which enhances interaction between the positively charged nucleus and the orbital electrons. P-type orbitals are projected out from the nucleus so there is less stabilization of the orbital electrons by the positive nuclear charge. The shape and directionality of a hybrid orbital reflects the mix of atomic orbitals. The greater the degree of s-character, the shorter the hybrid orbital (less directionality), and the greater the stabilization of the orbital electrons by the positive nucleus. This influence can be called hybrid orbital electronegativity. H C sp3 C sp2 H C sp increasing hybrid orbital electronegativity H The Effect of Hybridization on Acidity • Hydrogens connected to orbitals with more s character will be more acidic • s orbitals are smaller and closer to the nucleus than p orbitals • Anions in hybrid orbitals with more s character will be held more closely to the nucleus and be more stabilized 59 Inductive Effects Alkanes are nonpolar compounds. For example, the C-C bond in ethane has no net polarization of charge . H H H C C H H H Because of symmetry, there is no polarization of charge within ethane. ethane (nonpolar) If an electronegative group is introduced into ethane, the sigma bond electrons are attracted (polarized) towards the electronegative group, as shown in ethyl fluoride. H F H C C H H H ethyl fluoride The highly electronegative fluorine atom polarizes the sigma electrons in the C-F bond. Charge Polarization through Sigma Bonds H H H C C F H H The strongest polarization occurs in the C-F bond resulting in a net positive charge on the -carbon. In turn, the positive charge on the carbon polarizes electrons in the C-C bond leading to a small positive charge on the -carbon. The polarization of charge through sigma bonds due to electronegativity differences is called the inductive effect. Inductive effects weaken as the distance from the substituent increases. C C C X Inductive Effects • Electronic effects that are transmitted through space and through the bonds of a molecule • In ethyl fluoride the electronegative fluorine is drawing electron density away from the carbons – Fluorine is an electron withdrawing group (EWG) – The effect gets weaker with increasing distance 62 Energy Changes The physical world is described in terms of matter and energy. Matter is the physical stuff around us. It occupies space, has mass, and can be measured by various methods. Energy is not always observable. Types of Energy Energy is the capacity to do work. The two general categories are kinetic and potential energy. Kinetic energy is the capacity to do work by a moving object: Kinetic Energy = (1/2) mv2 where m is the mass of the object and v is its velocity. The moving object may be as small as an electron. Potential energy is stored energy such as the energy of chemical bonds. Kinetic and potential energy are interchangeable. An Example: two balls attached to the ends of a spring We can define the relaxed position of the spring as zero kinetic energy and zero potential energy. relaxed position KE = 0 PE = 0 As the spring is stretched, work is being done on it, and energy is expanding spring transferred into the spring. The expanding KE = + PE = + spring has kinetic energy (moving mass) which is being converted into potential energy. When the spring is at rest in a stretched position, the KE is again zero, but the potential energy is at some finite value. When the stretched spring is released, a restoring force compresses the spring. As the spring compresses, stored potential energy is converted into kinetic energy. stretched spring KE = 0 PE = ++ compressing spring KE = + PE = + Energy Changes in Reactions • Kinetic energy is the energy an object has because of its motion • Potential energy is stored energy – The higher the potential energy of an object the less stable it is • Potential energy can be converted to kinetic energy (e.g. energy of motion) 65 Chemical Energy Chemical energy is potential energy. Large increments of potential energy are in the electronic structures of atoms and molecules, the chemical bonds, and intermolecular interactions. Relative Potential Energy and Relative Stabilities in Chemical Systems According to the potential energy diagram, A is less stable than B by the energy difference shown. A Relative Potential Energy While it is difficult to describe the absolute amount of energy in a chemical system, it is possible and useful to examine the relative amount of potential energy in different systems . higher PE less stable E B lower PE more stable • Potential Energy and Covalent Bonds • Potential energy in molecules is stored in the form of chemical bond energy • Enthalpy Ho is a measure of the change in bond energies in a reaction • Exothermic reactions – Ho is negative and heat is evolved – Potential energy in the bonds of reactants is more than that of products • Endothermic reactions – Ho is positive and heat is absorbed – Potential energy in the bonds of reactants is less than that of products 67 Standard State The relative potential energies of reactants and products are given as relative enthalpies or heat content, H. The change in enthalpy in going from reactants to products is H . When the change in enthapy during the reaction is given as Ho, the superscipt o means the reaction was carried out under standard conditions. Standard Conditions (25oC) a gas at 1 atm pressure a solute in a 1 M solution a liquid or solid as pure material Although reactions are usually not carried out under standard conditions, the calculation of the Ho does give useful information. • Example : Formation of H2 from H atoms • Formation of bonds from atoms is always exothermic • The hydrogen molecule is more stable than hydrogen atoms 69 The Equilibrium Constant and Free Energy Changes Gibbs Free Energy Late in the 19th century, Josiah Williard Gibbs (1839-1903) proposed a new function of chemical states that describes the spontaneity of a chemical reaction. Today, this state function is called the Gibbs Free Energy or simply the Free Energy, G. The change in free energy, G, for a chemical reaction indicates if it is spontaneous, if it proceeds without the input of work from the surroundings. • If G is negative, the reaction in the forward direction proceeds spontaneously. • If G is zero, the reaction is at equilibrium, there is no net driving force in the forward or reverse direction. • If G is positive, the forward reaction will not proceed without input of work from the surroundings. • Go encompasses both enthalpy changes (Ho) and entropy changes (So ) • Ho is associated with changes in bonding energy – If Ho is negative (exothermic) this makes a negative contribution to Go (products favored) • So is associated with the relative order of a system – More disorder means greater entropy – A positive So means a system which is going from more ordered to less ordered – A positive So makes a negative contribution to Go (products favored) • In many cases So is small and Go is approximately equal to Ho 71 Standard Free Energy Change, Go Because free energy is a state function, like enthalpy and entropy, it is possible to calculate the free energy of substances under standard conditions, Go. Standard Conditions of Substances state of matter standard state solid pure solid liquid pure liquid gas solution elements 1 atm 1 M concentration The standard free energy of formation of an element is defined as zero. Standard Free Energy of Formation, Gof The standard free energy of formation, Gof , of a compound is the standard free energy change associated with the formation of one mole of that substance from the constituent elements, with all reactants and products in their standard states. The values of Gof for many substances have been tabulated and can be used to calculate the standard free energy change for reactions. The standard free energy change for a chemical reaction is defined as the difference between the standard free energies of formation of the products and reactants: Go = n Gof (products) - m Gof (reactants) where n and m are the mole quantities of products and reactants. An Example: The Hydrogenation of Ethene to Ethane CH2=CH2(g) + H2(g) Gof (kJ/mol) 68.2 CH3CH3(g) 0 -32.6 These values are from tabulated data or by definition. Go = n Gof (products) - m Gof (reactants) Go = (-32.6 kJ/mol) - (68.2 kJ/mole + 0 kJ/mol) Go = -100.8 kJ/mol Since the standard free energy change is negative, this hydrogenation reaction will spontaneously occur. If Go is more negative than about -3 kcal/mol, the reaction is described as going to completion, meaning more than 99% of the reactants proceed to the products at equilibrium. The Acidity of Carboxylic Acids • Carboxylic acids are much more acidic than alcohols • Deprotonation is unfavorable (neither are negative) in both cases but much less favorable for ethanol 75 The Relationship Between the Equilibrium Constant and Go • Go is the standard free energy change in a reaction • This is the overall energy change of a reaction • It is directly related to the equilibrium constant of a reaction – R is the gas constant (8.314 J K-1 mol-1) and T is measured in kelvin (K) • If Go is negative, products are favored at equilibrium (Keq >1) • If Go is positive, reactants are favored at equilibrium (Keq<1) • If Go is zero, products and reactants are equally favored (Keq = 0) 76 Analysis of the Gibbs Equation Consider the equilibrium, A + B C + D where the Gibbs free energy change is given by G = Go + 2.303RTLog [C][D] [A][B] At the start of the reaction, when the reactants A and B are mixed, the concentrations of C and D are very low, so Q << 1. During these early stages of the reaction, the reaction quotient makes a favorable (2.3RTLogQ is negative) contribution to G. As long as G is negative in value, there is a chemical driving force pushing the reaction in a forward direction. At some point, the concentrations of products become greater than the concentrations of the reactants, and Q > 1. The term 2.3RTLogQ becomes positive, and no longer contributes favorably to the overall Gibbs free energy, G. When G = 0, equilibrium is reached and there is no net chemical driving force in either direction. At Equilibrium When G = 0, equilibrium is reached and G = 0 = Go + 2.303RTLog Q Therefore, Go = where Keq = From above, - 2.303RTLog Q = - 2.303RT Log Keq [C][D] , the equilibrium constant for the reaction. [A][B] Keq = 10 - Go/2.3RT Go/RT = e Keq = o/RT G - e The values of Keq in the table show that over a range of only 6 kcal/mol in free energy, reactions switch from highly favorable to highly unfavorable at ordinary temperatures. at 298 K Keq Go -3000 cal 161 -1000 5.4 1000 0.18 3000 0.0062 Quiz Chapter 3 Section 9 The Gibbs free energy change (G) for a reaction A + B C + D is given as G = G o + 2.3RTLog [C] [D] [A] [B] What is Go? This is the Gibbs standard free energy change for the reaction, which is the free energy change when all reactants and products are in their standard states. How can it be calculated? The Gibbs standard free energy change is the sum of the standard free energies of formation of the products less the sum of the standard free energies of formation of the reactants: G o = nG fo (products) - nG of (reactants) What is the significance of the sign of G? If it is negative, there is a net chemical driving force and the reaction will spontaneously proceed in the forward direction. If it is positive, the net chemical driving force is in the reverse direction and the reaction will not proceed in the forward direction without the input of energy from the surroundings. If it is zero, there is no net chemical driving force in either direction, the reaction is at equilibrium. Enthalpy and Entropy Gibbs defined his function of state in terms of enthalpy or heat (H) and entropy (S), two thermodynamic state functions. State functions define the properties of a thermodynamic state. In a change between two thermodynamic states, the change in value of the state function is given by the symbol . The standard free energy change (Go) is given as Go = Ho - TSo where Ho is the standard enthalpy change and is equal to the difference in the standard enthalpies of formation (Hof) between the products and the reactants. This state function is associated with changes in bonding between reactants and products. Changes in enthalpy during reactions are measured by calorimetry experiments. Standard Entropy Change, So The standard entropy change, So, is the difference in standard entropies between reactants and products. Entropy is a measure of the degree of order in a chemical system due to bond rotations, other molecular motions, and aggregation. The more random a system (disorder), the greater the entropy. The larger a structure, the more degrees of freedom it has, and the greater its entropy. The units of entropy are cal/degree. The standard entropies of materials (including elements), So, are for one mole of pure substance at 1 atm pressure usually at 25oC. These values are measured relative to the reference point which is the entropy of a perfectly ordered crystal at T = 0 K (absolute zero, where So is zero. Note the contribution of entropy to the Gibbs free energy. A positive value for the change in standard entropy (So ) during a reaction makes a favorable contribution to Go because of the negative sign in the Gibbs equation: Go = Ho - TSo The Hydrogenation of Ethene: Another Perspective CH2=CH2(g) + H2(g) CH3CH3(g) The following values are from the Handbook of Chemistry and Physics. Gof Hof So (kJ/mol) (kJ/mol) (J/K mol) C2H4(g) 68.1 52.2 219.2 H2(g) 0 0 130.5 C2H6(g) -32.8 -84.5 229.3 Calculation of Standard Enthalpy Change, Ho Ho = Ho n Hof (products) - m Hof (reactants) = (-84,500 J/mol) - (52,200 J/mol) = -136,700 J/mol Calculation of Standard Entropy Change, So n Sof (products) m Sof (reactants) So = So = (229.3 J/K mol) - (219.2 J/K mol + 130.5 J/K mol) So = (229.3 J/K mol) - (349.7 J/K mol) = -120.4 J/K mol - Calculation of Gibbs Free Energy Change, Go Go = Ho - TSo Using the values above, Go Go Go = (-136,700 J/mol) - (298) (- 120.4 J/K mol) = (-136,700 J/mol) - (-35,879 J/mol) = -100,821 J/mol = -100,821 J/mol, which is in agreement with earlier calculations. Slide 74 This calculation shows that the favorable Gibbs free energy change in the hydrogenation of ethene to ethane is driven by a very favorable Ho , changes in bonding. The So term actually makes an unfavorable contribution to the spontaneity of the reaction. Bonding changes in chemical reactions will often be used to evaluate Ho, and determine the feasibility of a reaction. A Second Example: The Hydrogenation of Ethyne to Ethane HC CH (g) + 2H 2(g) CH 3CH 3(g) Gof Hof So (kJ/mol) (kJ/mol) (J/K mol) 226.6 200.7 C2H2(g) 209 H2(g) 0 C2H6(g) -32.8 0 -84.5 130.5 229.3 from the Handbook of Chemistry and Physics Calculations Ho = (-84,500 J/mol) - (2 x 0 J/mol + 226,600 J/mol) Ho = (-84,500 J/mol) - (226,600 J/mol) = -311,100 J/mol So = (229.3 J/K mol) - (2 x 130.5 J/K mol + 200.7 J/K mol) So = (229.3 J/K mol) - (461.7 J/K mol) = -232.4 J/K mol Calculation of the Gibbs Free Energy Change Go = Ho - TSo = (-311,100 J/mole) - (298) (-232.4 J/K mol) Go = -311,100 J/mol + 69,255 J/mol) = -241,845 J/mol Go = -241.8 kJ/mole Again, the spontaneity of this hydrogenation reaction is due to the very favorable standard enthalpy change (-311.1 kJ/mol) that reflects differences in the bond strengths of the bonds lost and bonds made during the reaction. HC CH (g) + 2H 2(g) tw o relatively w eak tw o strong bonds are lost bonds are lost CH 3CH 3(g) four strong bonds are made • Explanation based on resonance effects • Both acetic acid and acetate are stabilized by resonance – Acetate is more stabilized by resonance than acetic acid – This decreases Go for the deprotonation 87 The Acidity of Carboxylic Acids Carboxylic acids are more acidic than alcohols. = O CH3COH CH3CH2OH acetic acid ethanol Ka = 1.78 x 10-5 pKa = 4.75 Ka = 1.0 x 10-16 pKa = 16 Go = 27.2 kJ/mol Go = 90.9 kJ/mol The Go values are calculated from the Ka values that describe the equilibrium: HA + H2O H3O+ + A- Free Energy Diagrams The Go values indicate that the ionization of acetic acid is much more energetically favorable than the ionization of ethanol. In both reactions, the ion product states are higher in free energy (both Go values are positive) than the reactant states. These features are shown in the Free Energy Diagrams below. change in free energy CH3CH2O- + H3O+ - + CH3CO2 + H3O o G = 90.9 kJ/mol o G = 27.2 kJ/mol CH3COOH + H2O The Go values set the levels of the product states. CH3CH2OH + H2O In the diagrams, the reactant states are set at the same level for easy comparison. The ionic state produced from ethanol is much higher in energy than the ionic state produced from acetic acid. This difference in stability may be explained by both resonance theory and the inductive effect. Explanations of the Relative Acidities of Ethanol and Acetic Acid Resonance It is generally accepted that a major factor contributing to the acidity of acetic acid and other carboxylic acids is resonance. Although resonance contributes to the stability of both the reactant and product states of acetic acid, the stabilizing influence of resonance is much more important in the product (ion) state.. : : O: : : + + H O 3 CH3C=O : : = :O: CH3C-O: Go : O: : + CH3C=OH minor contribution : : : :O: CH3C-OH = Relative Free Energy major contribution + H 2O Resonance reduces the energy of the carboxylate ion. • Explanation based on resonance effects • Neither ethanol nor its anion is stabilized by resonance – There is no decrease in Go for the deprotonation 91 • Explanation based on inductive effect • In acetic acid the highly polarized carbonyl group draws electron density away from the acidic hydrogen • Also the conjugate base of acetic acid is more stabilized by the carbonyl group 92 Inductive Effects of Other Groups • The electron withdrawing chloro group makes chloroacetic acid more acidic than acetic acid – The hydroxyl proton is more polarized and more acidic – The conjugate base is more stabilized 93 A Charge Dispersal Mechanism The greater acidity of chloroacetic acid is attributed to the electronegativity of the chlorine atom (compared with hydrogen). In addition to increasing the electropositive character of the protic hydrogen in the acid, the electronegative chlorine atom helps disperse the negative charge in the carboxylate anion. Cl CH2 O C O H + H2O O Cl CH2 C O H + H3O+ Charge dispersal stabilizes ions through either resonance or the inductive effect. Quiz Chapter 3 Section 10 Select the more acidic carboxylic acid in each pair below, and explain your choice. Cl CH3CHCOOH ClCH2CH2COOH The inductive effect decreases rapidly with distance. Cl CH3CHCOOH F CH3CHCOOH The inductive effect increases with electronegativity. The Effect of Solvent on Acidity • Acidity values in gas phase are generally very low – It is difficult to separate the product ions without solvent molecules to stabilize them – Acetic acid has pKa of 130 in the gas phase • A protic solvent is one in which hydrogen is attached to a highly electronegative atom such as oxygen or nitrogen e.g. water • Solvation of both acetic acid and acetate ion occurs in water although the acetate is more stabilized by this solvation – This solvation allows acetic acid to be much more acidic in water than in the gas phase 96 Effect of Solvent on Acidity Most acids are much weaker in the gas phase where there is no solvent to stabilize the ions produced in the product state. Stabilization of the ions through ion-dipole interactions (a charge dispersal mechanism) is worth hundreds of kilocalories per mole. When acetic acid ionizes in water, both the carboxylate anion and the hydronium ion are stabilized by solvation: H O H H H = O CH3-C-O-H + H2O O O H C CH3 O H O H O H H O H + H O H O H H O H H O O H H H H O H H O H H H Solvation is a combination of hydrogen bonding and charge-dipole interactions. Gas Phase Acidities The acidities of many compounds in the gas phase, in the absence of solvation, have been measured. H+ + AH-A The relative acidity order in the gas phase is surprisingly different from the acidity order in water (magnitude of Ka). Gas Phase Acidities OH NH2 > RS-H > > H-F > R C C H > CH3CH2-OH > H2O > CH4 most acidic Because the creation and separation of charge is a very high energy process (hundreds of kJ/mol), any factors that stabilize charge will reduce the energy requirement. In the absence of solvation, internal structural and electronic features determine the reactivity order. Polarizable atoms and groups enhance acidity because they are able to disperse charge more effectively than atoms and groups of low polarizability. Acidity in Water: A Closer Look Water is a protic solvent, a solvent capable of hydrogen bonding to solutes. When acetic acid dissolves in water, water molecules associate with ("solvate") all solutes: acetic acid, acetate anion, hydronium ion. O CH3 C OH solvated acetic acid H + H2O O H H + CH3 O C O stronger solvation of ions The strong and ordered interaction between solvent and solute molecules decreases randomness and creates order, decreasing entropy. When acetic acid ionizes in water, the So is negative. Therefore, the change in entropy makes an unfavorable contribution to the Gibbs free energy for the ionization of acetic acid. Thermodynamic Parameters The change in Gibbs standard free energy for the reaction CH3COOH + H2O + H3O + CH3CO-2 o G = 27.2 kJ/mol contains both enthalpic and entropic contributions. A negative o change in standard entropy ( S ) makes an unfavorable energetic contribution ( -TS o ) to the Gibbs free energy. o G o o = H - TS The overall spontaneity of a chemical reaction (Go) depends on enthalpic changes arising from bonding, solvation factors, as well as entropic changes that measure the change in degree of order during the reaction. An Analysis of Acetic Acid and Chloroacetic Acid The greater acidity of chloroacetic acid is generally explained by the inductive effect of the electronegative chlorine. In the table below are the results of a detailed study showing the enthalpic and entropic contributions to the overall spontaneity of the ionization process for each acid. Acid pKa o G H S (kJ/mol) (kJ/mol) (J/K mol) (kJ/mol) (at 298 K) o o o - TS CH3COOH 4.75 +27.2 -0.4 -92.5 +27.6 ClCH2COOH 2.86 +16.3 -4.6 -70.3 +20.9 The enhanced acidity of chloroacetic acid results from a more favorable Ho (4.2 kJ/mol), and an even more favorable entropy contribution (-TSo is less positive by 6.7 kJ/mol). The thermodynamic parameters suggest that while the electronegative chlorine disperses negative charge and stabilizes the anion (more favorable Ho), the interaction between the chloroacetate ion and water is not as strong. The weaker solute-solvent interaction is associated with less ordering of the solvent, and a less negative standard entropy change (-70.3 vs -92.5). Organic Compounds as Bases • Any organic compound containing an atom with a lone pair (O,N) can act as a base 102 Organic Compounds as Bases All organic compounds with an unshared electron pair, or a-bond are potential bases. + H-Cl : methanol (base) : : : CH3-O: H + CH3-OH2 + Cl- (acid) When HCl gas is dissolved in methanol, it dissociates by protonation of the oxygen in the alcohol. This is a general reaction between alcohols and strong acids (HX, H2SO4) analogous to the ionization of strong acids in water. : R-O: H + H-A strong acid + ROH2 + :A- Ethers react in a similar way: + H-Cl : : : : CH3-O: R' + R O H + R' A (acid) Carbonyl compounds are involved in an equilibrium with strong acids that produces a low concentration of the conjugate acids: R + H-A R' weak base strong acid + H :O C R R' = = :O: C + :A- conjugate acid (a very strong acid) The table that follows compares the base strength of carbonyl compounds, alcohols, ethers and water. The latter three have about the same base strength and are comparably protonated by strong acids. Carbonyl compounds are considerably weaker bases (factor of 104 to 105). Some Representative pKB and pKBH+ Values pKB R-O : -7 17.5 + R-O H R -3.5 : : - H-O : hydroxide ion + H-O H H : 16 15.74 -2 -1.74 : : : H-O H water + RCH2O H H : : : : 21 R ether RCH2O H alcohol pKBH+ + R-C=O H R : R-C=O R ketone Conjugate Acid : : : Base -2 : H-O H water 16 • Electrons can also act as bases – Electrons are loosely held and available for reaction with strong acids 107 A Mechanism for an Organic Reaction • The Substitution Reaction of tert-Butyl Alcohol • All steps are acid-base reactions – Step 1 is a Brønsted acid-base reaction – Step 2 is a Lewis acid-base reaction in reverse with heterolytic cleavage of a bond – Step 3 is a Lewis acid-base reaction with chloride acting as a Lewis base and the carbocation acting as Lewis acid 108 109 Acids and Bases in Nonaqueous Solutions • Water has a leveling effect on strong acids and bases • Any base stronger than hydroxide will be converted to hydroxide in water • Sodium amide can be used as a strong base in solvents such as liquid NH3 111 Nonaqueous Solvents Reactions involving strong bases such as sodium amide are run in nonaqueous solvents such as ethers, hydrocarbons, or liquid ammonia (NH3, BP -33oC). RC terminal alkyne pKa = 25 + : CH + - Na : NH2 sodium amide liquid NH3 -33oC RC - + C : Na + :NH3 The solvent for a reaction must be compatible with the acid and base strengths of the reactants and products. pKa = 38 • Alkyl lithium reagents in hexane are very strong bases – The alkyl lithium is made from the alkyl bromide and lithium metal 113 Synthesis of Deuterium- and Tritium-Labeled Compounds • Deuterium (2H) and tritium (3H) are isotopes of hydrogen • They are used for labeling organic compounds to be able to track where these compounds go (e.g. in biological systems) • An alkyne can be labeled by deprotonating with a suitable base and then titrating with T2O 114 Introduction of Deuterium and Tritium Labels by Acid-Base Reactions Deuterium (2H) and tritium (3H) are used as isotopic "labels" in mechanistic and other studies. These labels may be introduced into organic structures by acid-base chemistry using deuterium oxide (D2O) or tritium oxide (T2O). D Li + D 2O very fast hexane phenyllithium (stronger base) + DO-Li+ deuteriobenzene (stronger acid) (weaker acid) (weaker base)