6CHAPTER2ACH,-CH,-OH.O26HHCH-CH2-0H0105°CH2CHaFigure2-1.ThewatermoleculehastetrahedralRlHgeometry.RINTERACTIONWITHWATERINFLUENCESFigure2-3.Additional polar groups participate inTHESTRUCTUREOFBIOMOLECULEShydrogen bonding.Shown arehydrogen bondsformedCovalent&NoncovalentBondsStabilizebetweenanalcoholandwater,betweentwomoleculesBiologic Moleculesofethanol,andbetweenthepeptidecarbonyl oxygenandthepeptidenitrogenhydrogenofanadjacentThe covalent bond is the strongest force that holdsamino acid.molecules together (Table 2-1).Noncovalent forces,while of lesser magnitude, make significant contribu-tions to the structure,stability,and functional compe-phosphatidyl serine or phosphatidyl ethanolamine con-tence of macromolecules in living cells. These forces,tact water while their hydrophobic fatty acyl side chainswhich can be either attractive or repulsive, involve in-cluster together, excluding water. This pattern maxi-teractions both within thebiomolecule and between itmizes the opportunities for the formation of energeti-and the water that forms the principal component ofcally favorable charge-dipole, dipole-dipole, and hydro-thesurroundingenvironment.gen bonding interactions betweenpolargroups onthebiomolecule and water.It also minimizes energeticallyunfavorablecontact between waterandhydrophobicBiomoleculesFoldtoPositionPolar&groups.ChargedGroupsonTheirSurfacesMost biomolecules are amphipathic, that is, they pos-HydrophobicInteractionssess regions rich in charged or polar functional groupsas well as regions with hydrophobic character. ProteinsHydrophobic interaction refers to the tendency of non-tend to fold with the R-groups of amino acids with hy-polar compounds to self-associate in an aqueous envi-drophobic side chains in the interior. Amino acids withronment. This self-association is driven neither by mu-charged or polar amino acid side chains (eg, arginine,tual attraction nor by what are sometimes incorrectlyglutamate, serine)generally are present on the surfacereferred to as“hydrophobic bonds."Self-associationin contactwith water.Asimilarpatternprevails inaarises from the need to minimize energetically unfavor-phospholipid bilayer, where the charged head groups ofable interactions between nonpolar groups and water.Table2-1.Bondenergiesforatomsofbiologicsignificance.BondEnergyBondEnergyType(kcal/mol)Type(kcal/mol)Q0-0349600H51Ss99C--HC-N70C=s108Figure2-2.Left:Association of two dipolarwaterSH81O-H110molecules by a hydrogen bond (dotted line).Right:82C=C147C-CHydrogen-bondedclusteroffourwatermoleculesC-o84C=N147Note that water can serve simultaneously both as a hy-94N--HC=0164drogendonorandasahydrogenacceptor
6 / CHAPTER 2 2e H H 105° 2e O H H H H O O H O H H H H O H O H O H H H Figure 2–2. Left: Association of two dipolar water molecules by a hydrogen bond (dotted line). Right: Hydrogen-bonded cluster of four water molecules. Note that water can serve simultaneously both as a hydrogen donor and as a hydrogen acceptor. Figure 2–1. The water molecule has tetrahedral geometry. H H CH3 CH2 O H O CH3 CH O H O H CH2 CH3 O H R R N II III C R RI 2 Figure 2–3. Additional polar groups participate in hydrogen bonding. Shown are hydrogen bonds formed between an alcohol and water, between two molecules of ethanol, and between the peptide carbonyl oxygen and the peptide nitrogen hydrogen of an adjacent amino acid. Table 2–1. Bond energies for atoms of biologic significance. Bond Energy Bond Energy Type (kcal/mol) Type (kcal/mol) O—O 34 O==O 96 S—S 51 C—H 99 C—N 70 C==S 108 S—H 81 O—H 110 C—C 82 C==C 147 C—O 84 C==N 147 N—H 94 C==O 164 INTERACTION WITH WATER INFLUENCES THE STRUCTURE OF BIOMOLECULES Covalent & Noncovalent Bonds Stabilize Biologic Molecules The covalent bond is the strongest force that holds molecules together (Table 2–1). Noncovalent forces, while of lesser magnitude, make significant contributions to the structure, stability, and functional competence of macromolecules in living cells. These forces, which can be either attractive or repulsive, involve interactions both within the biomolecule and between it and the water that forms the principal component of the surrounding environment. Biomolecules Fold to Position Polar & Charged Groups on Their Surfaces Most biomolecules are amphipathic; that is, they possess regions rich in charged or polar functional groups as well as regions with hydrophobic character. Proteins tend to fold with the R-groups of amino acids with hydrophobic side chains in the interior. Amino acids with charged or polar amino acid side chains (eg, arginine, glutamate, serine) generally are present on the surface in contact with water. A similar pattern prevails in a phospholipid bilayer, where the charged head groups of phosphatidyl serine or phosphatidyl ethanolamine contact water while their hydrophobic fatty acyl side chains cluster together, excluding water. This pattern maximizes the opportunities for the formation of energetically favorable charge-dipole, dipole-dipole, and hydrogen bonding interactions between polar groups on the biomolecule and water. It also minimizes energetically unfavorable contact between water and hydrophobic groups. Hydrophobic Interactions Hydrophobic interaction refers to the tendency of nonpolar compounds to self-associate in an aqueous environment. This self-association is driven neither by mutual attraction nor by what are sometimes incorrectly referred to as “hydrophobic bonds.” Self-association arises from the need to minimize energetically unfavorable interactions between nonpolar groups and water. ch02.qxd 2/13/2003 1:41 PM Page 6
17WATER&pHWhile the hydrogens of nonpolar groups such as thethe backbone to water while burying the relatively hy-methylene groups of hydrocarbons do not form hydro-drophobic nucleotide bases inside. The extended back-bone maximizes the distance between negativelygen bonds, they do affect the structure of the water thatsurrounds them. Water molecules adjacent to a hy-charged backbonephosphates, minimizing unfavorabledrophobic group are restricted in the number of orien-electrostatic interactions.tations (degrees of freedom) that permit them to par-ticipate in the maximum number of energeticallyWATERISANEXCELLENTNUCLEOPHILEfavorablehydrogenbonds.Maximal formation of mul-Metabolic reactions often involve the attack by lonetiple hydrogen bonds can be maintained only by in-pairs of electrons on electron-rich molecules termedcreasing the order of theadjacent water molecules, withnucleophiles on electron-poor atoms called elec-acorrespondingdecreaseinentropy.trophiles. Nucleophiles and electrophiles do not neces-It follows from the second law of thermodynamicssarily possess a formal negative or positive charge.that the optimal free energy of a hydrocarbon-waterWater,whosetwolonepairs ofsp electronsbeara par-mixture is a function of both maximal enthalpy (fromtial negative charge, is an excellent nucleophile.Otherhydrogen bonding)and minimum entropy (maximumnucleophiles of biologic importance include the oxygendegreesoffreedom).Thus,nonpolarmoleculestendtoatoms ofphosphates,alcohols,and carboxylicacids;theform droplets with minimal exposed surface area,resulfur of thiols; the nitrogen of amines; and the imid-ducing the number of water molecules affected.For theazole ring of histidine. Common electrophiles includesame reason, in the aqueous environment of the livingthe carbonyl carbons in amides, esters, aldehydes, andcell the hydrophobic portions of biopolymers tend toketones and thephosphorus atoms of phosphoesters.beburied inside the structure of the molecule,or withinNucleophilic attack by water generally results in thea lipid bilayer,minimizing contact with water.cleavage of the amide, glycoside, or ester bonds thathold biopolymers together.This process is termed hy-ElectrostaticInteractionsdrolysis. Conversely, when monomer units are joinedtogether to form biopolymers such as proteins orglyco-Interactions between charged groups shape biomolecugen, water is a product, as shown below for theforma-lar structure.Electrostatic interactions between oppotion of a peptide bond between two amino acids.sitely charged groups within or between biomoleculesare termed salt bridges. Salt bridges are comparable instrength to hydrogen bonds but act over larger dis-O*H,Ntances. They thus often facilitate the binding of chargedOH+HNEmolecules and ionstoproteins andnucleic acids.AlanineVanderWaals Forces=OVan der Waals forces arise from attractions betweenValinetransient dipoles generated by the rapid movement ofelectrons on all neutral atoms. Significantly weakerthan hydrogen bonds but potentially extremely numer.0ous,vanderWaalsforcesdecreaseas thesixthpowerofthe distance separating atoms.Thus, they act over veryshort distances, typically 2-4 A.*HaNVHOMultipleForces StabilizeBiomolecules-0The DNA double helix illustrates the contribution ofmultipleforcestothestructureof biomolecules.WhileWhile hydrolysis is a thermodynamically favored re-each individual DNA strand is held together by cova-lent bonds,the two strands of the helix are held to-action,the amide and phosphoester bonds of polypep-gether exclusively by noncovalent interactions. Thesetides and oligonucleotides are stable in the aqueous en-noncovalent interactions include hydrogen bonds bevironment of thecell. This seemingly paradoxictween nucleotide bases (Watson-Crick base pairing)behavior reflects the fact that the thermodynamics gov-and van der Waals interactions between the stackederning the equilibrium of a reaction do not determinepurine and pyrimidine bases. The helix presents thethe rate at which it will take place. In the cell, proteincharged phosphate groups and polar ribose sugars ofcatalysts called enzymes are used to accelerate the rate
WATER & pH / 7 While the hydrogens of nonpolar groups such as the methylene groups of hydrocarbons do not form hydrogen bonds, they do affect the structure of the water that surrounds them. Water molecules adjacent to a hydrophobic group are restricted in the number of orientations (degrees of freedom) that permit them to participate in the maximum number of energetically favorable hydrogen bonds. Maximal formation of multiple hydrogen bonds can be maintained only by increasing the order of the adjacent water molecules, with a corresponding decrease in entropy. It follows from the second law of thermodynamics that the optimal free energy of a hydrocarbon-water mixture is a function of both maximal enthalpy (from hydrogen bonding) and minimum entropy (maximum degrees of freedom). Thus, nonpolar molecules tend to form droplets with minimal exposed surface area, reducing the number of water molecules affected. For the same reason, in the aqueous environment of the living cell the hydrophobic portions of biopolymers tend to be buried inside the structure of the molecule, or within a lipid bilayer, minimizing contact with water. Electrostatic Interactions Interactions between charged groups shape biomolecular structure. Electrostatic interactions between oppositely charged groups within or between biomolecules are termed salt bridges. Salt bridges are comparable in strength to hydrogen bonds but act over larger distances. They thus often facilitate the binding of charged molecules and ions to proteins and nucleic acids. Van der Waals Forces Van der Waals forces arise from attractions between transient dipoles generated by the rapid movement of electrons on all neutral atoms. Significantly weaker than hydrogen bonds but potentially extremely numerous, van der Waals forces decrease as the sixth power of the distance separating atoms. Thus, they act over very short distances, typically 2–4 Å. Multiple Forces Stabilize Biomolecules The DNA double helix illustrates the contribution of multiple forces to the structure of biomolecules. While each individual DNA strand is held together by covalent bonds, the two strands of the helix are held together exclusively by noncovalent interactions. These noncovalent interactions include hydrogen bonds between nucleotide bases (Watson-Crick base pairing) and van der Waals interactions between the stacked purine and pyrimidine bases. The helix presents the charged phosphate groups and polar ribose sugars of the backbone to water while burying the relatively hydrophobic nucleotide bases inside. The extended backbone maximizes the distance between negatively charged backbone phosphates, minimizing unfavorable electrostatic interactions. WATER IS AN EXCELLENT NUCLEOPHILE Metabolic reactions often involve the attack by lone pairs of electrons on electron-rich molecules termed nucleophiles on electron-poor atoms called electrophiles. Nucleophiles and electrophiles do not necessarily possess a formal negative or positive charge. Water, whose two lone pairs of sp3 electrons bear a partial negative charge, is an excellent nucleophile. Other nucleophiles of biologic importance include the oxygen atoms of phosphates, alcohols, and carboxylic acids; the sulfur of thiols; the nitrogen of amines; and the imidazole ring of histidine. Common electrophiles include the carbonyl carbons in amides, esters, aldehydes, and ketones and the phosphorus atoms of phosphoesters. Nucleophilic attack by water generally results in the cleavage of the amide, glycoside, or ester bonds that hold biopolymers together. This process is termed hydrolysis. Conversely, when monomer units are joined together to form biopolymers such as proteins or glycogen, water is a product, as shown below for the formation of a peptide bond between two amino acids. While hydrolysis is a thermodynamically favored reaction, the amide and phosphoester bonds of polypeptides and oligonucleotides are stable in the aqueous environment of the cell. This seemingly paradoxic behavior reflects the fact that the thermodynamics governing the equilibrium of a reaction do not determine the rate at which it will take place. In the cell, protein catalysts called enzymes are used to accelerate the rate O + H3N O NH H2O OH + H + H3N NH O– O– O O Alanine Valine ch02.qxd 2/13/2003 1:41 PM Page 7
81CHAPTER2of hydrolytic reactions when needed.Proteases catalyzeH,O,+. The proton is nevertheless routinely repre-the hydrolysis of proteins into their component aminosented as Ht, even though it is in fact highly hydrated.acids, while nucleases catalyze the hydrolysis of theSince hydronium and hydroxide ions continuouslyphosphoester bonds in DNA and RNA.Careful controlrecombine to form water molecules, an individual hy-of theactivitiesof theseenzymes isrequired to ensuredrogen or oxygen cannot be stated to be present as anthat they act only on appropriatetarget molecules.ion or as part of a water molecule.At one instant it isan ion.An instant later it ispart of a molecule.Individ-ManyMetabolicReactions Involveual ions or molecules are therefore not considered. WeGroupTransferrefer instead to the probability that at any instant intime a hydrogen will be present as an ion or as part of aIn group transfer reactions, a group G is transferredwatermolecule,Since1g of water contains3.46×1022from a donorD to an acceptor A, formingan acceptormolecules, the ionization of water can be described sta-group complex A-G:tistically.To state that the probability that a hydrogenexists as an ion is 0.01 means that a hydrogen atom hasD-G+A=A-G+Done chance in 100 of being an ion and 99 chances outof 100 of being part of a water molecule.The actualThe hydrolysis and phosphorolysis of glycogen repre-probability of a hydrogen atom in pure water existing assent group transfer reactions in whichglucosyl groupsa hydrogen ion is approximately1.8×10-.The proba-are transferred to water or to orthophosphate. Thebility of its being part of a molecule thus is almostequilibrium constant for the hydrolysis of covalentunity. Stated another way, for every hydrogen ion andbonds strongly favors theformation of splitproductshydroxyl ion in pure water there are 1.8 billion or 1.8 xThe biosynthesis of macromolecules also involves groupio2 water molecules. Hydrogen ions and hydroxyl ionstransfer reactions in which the thermodynamically un-nevertheless contribute significantly to the properties offavored synthesis of covalent bonds is coupled to fa-water.vored reactions so that the overall change in free energyFordissociation of water,favors biopolymer synthesis.Given the nucleophiliccharacter of water and its high concentration in cells,K= IH*)[IOH]why are biopolymers such as proteins and DNA relatively stable?And how can synthesis of biopolymers[H,0]occur in an apparently aqueous environment?Centralto both questions are the properties of enzymes.In thewhere brackets represent molar concentrations (strictlyabsence of enzymic catalysis, even thermodynamicallyspeaking, molar activities) and K is the dissociationhighly favored reactions do not necessarily take placeconstant.Since one mole (mol)of water weighs 18g,rapidly. Precise and differential control of enzyme ac-one liter (L) (1000g)of water contains1000×18=tivityand thesequestration of enzymes in specific or-55.56 mol.Pure water thus is 55.56molar.Since theganelles determine under what physiologic conditions aprobability that a hydrogen in pure water will exist as agiven biopolymer will be synthesized or degraded.hydrogen ion is 1.8×10-,the molar concentration ofNewly synthesized polymers are not immediately hy-H+ions (or of OH-ions) in pure water is the productdrolyzed,in partbecausethe active sitesof biosyntheticoftheprobability,1.8x10-,times themolarconcen-enzymessequestersubstratesinanenvironmentfromtration of water,55.56 mol/L.The result is 1.0× 10-which water can be excluded.mol/L.We can now calculate Kfor water:Water Molecules Exhibita Slight butImportantTendencytoDissociateK = [H 1H-]_[10~′ [1~-]The ability ofwater to ionize, while slight, is of central[H,0] [55.56]importancefor life.Since water can act bothas an acid= 0.018×10-14=1.8×10-16mol/Land as a base, its ionization may be represented as anintermolecular proton transfer thatforms a hydroniumThemolar concentrationofwater,55.56mol/L,ision (H,O+) and a hydroxide ion (OH):too great to be significantly affected by dissociation. ItH2O + H,OH,O++ OH-therefore is considered to be essentially constant.ThisconstantmaythenbeincorporatedintothedissociatiorconstantKtoprovideauseful new constantKtermedThe transferred proton is actually associated with athe ion product for water. The relationship berweenclusterofwatermolecules.Protonsexist in solutionnotKw and K is shown below:only as HO+, but also as multimers such as H,O,* and
8 / CHAPTER 2 of hydrolytic reactions when needed. Proteases catalyze the hydrolysis of proteins into their component amino acids, while nucleases catalyze the hydrolysis of the phosphoester bonds in DNA and RNA. Careful control of the activities of these enzymes is required to ensure that they act only on appropriate target molecules. Many Metabolic Reactions Involve Group Transfer In group transfer reactions, a group G is transferred from a donor D to an acceptor A, forming an acceptor group complex A–G: The hydrolysis and phosphorolysis of glycogen represent group transfer reactions in which glucosyl groups are transferred to water or to orthophosphate. The equilibrium constant for the hydrolysis of covalent bonds strongly favors the formation of split products. The biosynthesis of macromolecules also involves group transfer reactions in which the thermodynamically unfavored synthesis of covalent bonds is coupled to favored reactions so that the overall change in free energy favors biopolymer synthesis. Given the nucleophilic character of water and its high concentration in cells, why are biopolymers such as proteins and DNA relatively stable? And how can synthesis of biopolymers occur in an apparently aqueous environment? Central to both questions are the properties of enzymes. In the absence of enzymic catalysis, even thermodynamically highly favored reactions do not necessarily take place rapidly. Precise and differential control of enzyme activity and the sequestration of enzymes in specific organelles determine under what physiologic conditions a given biopolymer will be synthesized or degraded. Newly synthesized polymers are not immediately hydrolyzed, in part because the active sites of biosynthetic enzymes sequester substrates in an environment from which water can be excluded. Water Molecules Exhibit a Slight but Important Tendency to Dissociate The ability of water to ionize, while slight, is of central importance for life. Since water can act both as an acid and as a base, its ionization may be represented as an intermolecular proton transfer that forms a hydronium ion (H3O+) and a hydroxide ion (OH− ): The transferred proton is actually associated with a cluster of water molecules. Protons exist in solution not only as H3O+, but also as multimers such as H5O2 + and H O H O H O OH 2 23 + + + − DG A AG D − = + −+ H7O3 +. The proton is nevertheless routinely represented as H+, even though it is in fact highly hydrated. Since hydronium and hydroxide ions continuously recombine to form water molecules, an individual hydrogen or oxygen cannot be stated to be present as an ion or as part of a water molecule. At one instant it is an ion. An instant later it is part of a molecule. Individual ions or molecules are therefore not considered. We refer instead to the probability that at any instant in time a hydrogen will be present as an ion or as part of a water molecule. Since 1 g of water contains 3.46 × 1022 molecules, the ionization of water can be described statistically. To state that the probability that a hydrogen exists as an ion is 0.01 means that a hydrogen atom has one chance in 100 of being an ion and 99 chances out of 100 of being part of a water molecule. The actual probability of a hydrogen atom in pure water existing as a hydrogen ion is approximately 1.8 × 10−9 . The probability of its being part of a molecule thus is almost unity. Stated another way, for every hydrogen ion and hydroxyl ion in pure water there are 1.8 billion or 1.8 × 109 water molecules. Hydrogen ions and hydroxyl ions nevertheless contribute significantly to the properties of water. For dissociation of water, where brackets represent molar concentrations (strictly speaking, molar activities) and K is the dissociation constant. Since one mole (mol) of water weighs 18 g, one liter (L) (1000 g) of water contains 1000 × 18 = 55.56 mol. Pure water thus is 55.56 molar. Since the probability that a hydrogen in pure water will exist as a hydrogen ion is 1.8 × 10−9 , the molar concentration of H+ ions (or of OH− ions) in pure water is the product of the probability, 1.8 × 10−9 , times the molar concentration of water, 55.56 mol/L. The result is 1.0 × 10−7 mol/L. We can now calculate K for water: The molar concentration of water, 55.56 mol/L, is too great to be significantly affected by dissociation. It therefore is considered to be essentially constant. This constant may then be incorporated into the dissociation constant K to provide a useful new constant Kw termed the ion product for water. The relationship between Kw and K is shown below: K = = = × =× + [ ][ ] [ ] [ ][ ] [.] . ./ H OH H O mol L − −− − − 2 7 7 14 16 10 10 55 56 0 018 10 1 8 10 K = + [ ][ ] H OH H O − ] [ 2 ch02.qxd 2/13/2003 1:41 PM Page 8
WATER&pH19termediates,whosephosphorylgroup contains two disK{H*[OH- 1.8×10-16 mo/ sociable protons, the first of which is strongly acidic.[H,O]The following examples illustrate how to calculatethepH of acidic and basic solutions.Kw = (K)[H2O] = [H* [OH-]Example l:What is the pH of a solution whose hy=(1.8×10-16 mol/L) (55.56 mol/ L)drogenionconcentrationis3.2×10-mol/L?=1.00 ×10-14 (mol /L)2pH=-log [H*]Note that the dimensions of K are moles per liter and=-log (3.2×10=4)those of Kare molesper liter.As its name suggests=-log (3.2)log (10-4)the ion product Kis numerically equal to the product=0.5+4.0ofthemolarconcentrationsofH+andOH-:=3.5Kw = [H*][OH-]Example2:What is the pH ofa solution whose hyAt 25 °C, K, = (10-7)2, or 10-14 (mol/L)2. Ar tempera-droxideion concentrationis 4.0×10-mol/L?Wefirstturesbelow25°C,Kwis somewhat less than10-14;anddefine a quantity pOH that is equal to-log [OH] andat temperaturesabove25C it is somewhatgreater thanthat may be derived from the definition of K:10-14 Within the stated limitations of the effect of tem-perature,K,equals10- (mol/L)for all aqueous so-Kw =[H*[OH"] =10-14lutions,even solutions of acids orbases.We shall useKtocalculatethepH ofacidicandbasicsolutions.Therefore:log [H*]+ log [OH"]= log 10-14PHISTHENEGATIVELOGOFTHEHYDROGENIONCONCENTRATIONorThe term pH was introduced in 1909 by Sorensenwho defined pH as the negative log of the hydrogen ionpH+pOH=14concentration:To solve the problem by this approach:pH= -log [H*][OH"]= 4.0×10-4This definition, while not rigorous, suffices for manypOH=-log [OH]biochemical purposes.Tocalculate thepH ofa solution:=-log (4.0x10-4)1.Calculatehydrogen ion concentration[H+]2. Calculate the base 10 logarithm of [H+].=-log (4.0)log (10-)3.pH is the negative of the value found in step2=0.60+4.0For example,forpurewaterat 25°C,=3.4pH= -log [H+]=-log 10-7 =-(-7)= 7.0Now:Low pH values correspond tohigh concentrations ofpH=14pOH=143.4H+ and high pH values correspond to low concentra-=10.6tions of Ht.Example3:What arethe pH values of (a)2.0×10-2Acids are proton donors and bases are proton acmol/LKOHandof (b)2.0×10-mol/LKOH?Theceptors.Strong acids(eg,HClorH,SO)completelydissociate into anions and cations even in strongly acidicOH-arises from two sources,KOH and water.Sincesolutions (lowpH).Weak acids dissociate only partiallypH isdetermined bythetotal [H+](and pOHbytheinacidic solutions.Similarly,strongbases (eg,KOHortotal [OH]), both sources must be considered. In theNaOH)-—but not weak bases (eg, Ca[OH]2)—arefirst case(a),the contribution of water tothe totalcompletely dissociated at high pH. Many biochemicals[OH] is negligible.The same cannot be said for theare weak acids. Exceptions include phosphorylated in-second case (b):
WATER & pH / 9 Note that the dimensions of K are moles per liter and those of Kw are moles2 per liter2 . As its name suggests, the ion product Kw is numerically equal to the product of the molar concentrations of H+ and OH− : At 25 °C, Kw = (10−7 ) 2 , or 10−14 (mol/L)2 . At temperatures below 25 °C, Kw is somewhat less than 10−14; and at temperatures above 25 °C it is somewhat greater than 10−14. Within the stated limitations of the effect of temperature, Kw equals 10-14 (mol/L)2 for all aqueous solutions, even solutions of acids or bases. We shall use Kw to calculate the pH of acidic and basic solutions. pH IS THE NEGATIVE LOG OF THE HYDROGEN ION CONCENTRATION The term pH was introduced in 1909 by Sörensen, who defined pH as the negative log of the hydrogen ion concentration: This definition, while not rigorous, suffices for many biochemical purposes. To calculate the pH of a solution: 1. Calculate hydrogen ion concentration [H+]. 2. Calculate the base 10 logarithm of [H+]. 3. pH is the negative of the value found in step 2. For example, for pure water at 25°C, Low pH values correspond to high concentrations of H+ and high pH values correspond to low concentrations of H+. Acids are proton donors and bases are proton acceptors. Strong acids (eg, HCl or H2SO4) completely dissociate into anions and cations even in strongly acidic solutions (low pH). Weak acids dissociate only partially in acidic solutions. Similarly, strong bases (eg, KOH or NaOH)—but not weak bases (eg, Ca[OH]2)—are completely dissociated at high pH. Many biochemicals are weak acids. Exceptions include phosphorylated inpH H === + − − −− − log [ ] ( log 10 7) = 7.0 7 pH H = + −log [ ] K w = H OH + [ ][ ] − K K K = =× = = = × = × + + [ ][ ] [ ] . / ( )[ ] [ ][ ] ( . / )( . / ) . ( /) H OH H O mol L H O H OH mol L mol L mol L w − − − − − 2 16 2 16 14 2 1 8 10 1 8 10 55 56 1 00 10 termediates, whose phosphoryl group contains two dissociable protons, the first of which is strongly acidic. The following examples illustrate how to calculate the pH of acidic and basic solutions. Example 1: What is the pH of a solution whose hydrogen ion concentration is 3.2 × 10−4 mol/L? Example 2: What is the pH of a solution whose hydroxide ion concentration is 4.0 × 10−4 mol/L? We first define a quantity pOH that is equal to −log [OH− ] and that may be derived from the definition of Kw: Therefore: or To solve the problem by this approach: Now: Example 3: What are the pH values of (a) 2.0 × 10−2 mol/L KOH and of (b) 2.0 × 10−6 mol/L KOH? The OH− arises from two sources, KOH and water. Since pH is determined by the total [H+] (and pOH by the total [OH− ]), both sources must be considered. In the first case (a), the contribution of water to the total [OH− ] is negligible. The same cannot be said for the second case (b): pH pOH = = = 14 14 3 4 10 6 − − . . [ ]. log [ ] log ( . ) log ( . ) log ) OH pOH OH − − − − − − − − −( −. + . = . = × = = × = = 4 0 10 4 0 10 4 0 10 0 60 4 0 3 4 4 4 4 pH pOH + = 14 log [ ] log [ ] log H OH + − + = 10−14 K w = = H OH + [ ][ ] − −1 10 4 pH H = = × = = + = + − − − − − − − log [ ] log ( . ) log ( . ) log ( ) . . . 3 2 10 3 2 10 05 40 3 5 4 4 ch02.qxd 2/13/2003 1:41 PM Page 9
10/CHAPTER2below are the expressions for the dissociation constantConcentration (mol/L)(K,)for two representativeweak acids,R-COOH and(b)(a)R-NH,t.2.0×10-22.0×10-6MolarityofKOHR-COOHR-COO'+H2.0×10-22.0×10~6[OH'] fromKOH1.0 ×10-71.0×10-7[OH] fromwaterk, - [RC0O'H"2.1×10~62.00001×10-2Total [OH][R—COOH]R-NH3* R-NH2+H*OnceadecisionhasbeenreachedaboutthesignificanceKg - [RNH,1Hof the contributionbywater,pH maybecalculated asabove.[RNH,*]The above examples assumethatthe strong baseKOH is completely dissociated in solution and that theSince the numeric values of Kfor weak acids are negaconcentrationof OHionswasthusequal tothatofthetiveexponential numbers,weexpressK,aspK,whereKOH.This assumption is valid for dilute solutions ofstrong bases or acids but not for weak bases or acidspKa = - log KSince weak electrolytes dissociate only slightly in solu-tion, we must use the dissociation constant to calcu-Note that pK is related to K, as pH is to [H+]. Thelate the concentration of [Ht] (or [OH']) produced bystronger the acid, the lower its pK, value.a given molarity of a weak acid (or base) before calcu-pK, is used to express the relative strengths of bothlating total [H+] (or total [OH-]) and subsequently pHacids and bases.For any weak acid, its conjugate is astrong base.Similarly,the conjugate of a strongbase isa weak acid. The relative strengths of bases are ex-FunctionalGroupsThat Are Weak Acidspressed in terms of the pK, oftheir conjugate acids.ForHaveGreatPhysiologicSignificancepolyproteic compounds containing more than one dis-Many biochemicals possess functional groups that aresociable proton, a numerical subscript is assigned toeach in order of relative acidity.For a dissociation ofweak acids orbases.Carboxyl groups, amino groups,the typeand the second phosphate dissociation of phosphatees-ters arepresent in proteins and nucleic acids,mostR—NH3*→R-NH2coenzymes,andmost intermediarymetabolites.Knowl-edgeof thedissociationof weakacids andbasesthusisbasic to understanding the influence of intracellular pHthe pK, is the pH at which the concentration of theon structure and biologic activity.Charge-based separa-acid RNH+ equals that of the base RNH2tions such as electrophoresis and ion exchange chro-From the above equations that relate K,to [H'] andmatography also are best understood in terms of thetotheconcentrations ofundissociatedacid andits con-dissociation behaviorof functional groups.jugate base, whenWeterm the protonated species (eg,HA orR-NH,+) the acid and the unprotonated species (eg,[R—COO"]=[R—COOH]A-orR-NH,)its conjugatebase.Similarly,wemayrefer to abase (eg,A-orRNH)and its conjugateor whenacid (eg,HA or R-NH,+).Representative weak acids(left), their conjugate bases (center), and the pK, values[R-NH,]=[R—NH,](right) include the following:R—CH2—COOHR—CH2—COO-pK,=4-5thenR-CH2—NH3R—CH2—NH2pKa=9-10Ka = [H*]HCO,H,CO3pK,=6.4Thus, when the associated (protonated) and dissociatedHPO,2H,PO4pKa =7.2(conjugatebase)speciesarepresentatequalconcentrations, the prevailing hydrogen ion concentration [H+]We express the relative strengths of weak acids andis numerically equal to the dissociation constant, K.Ifbases in terms of their dissociation constants. Shownthe logarithms of both sides of the above equation are
10 / CHAPTER 2 Concentration (mol/L) (a) (b) Molarity of KOH 2.0 × 10−2 2.0 × 10−6 [OH− ] from KOH 2.0 × 10−2 2.0 × 10−6 [OH− ] from water 1.0 × 10−7 1.0 × 10−7 Total [OH− ] 2.00001 × 10−2 2.1 × 10−6 Once a decision has been reached about the significance of the contribution by water, pH may be calculated as above. The above examples assume that the strong base KOH is completely dissociated in solution and that the concentration of OH− ions was thus equal to that of the KOH. This assumption is valid for dilute solutions of strong bases or acids but not for weak bases or acids. Since weak electrolytes dissociate only slightly in solution, we must use the dissociation constant to calculate the concentration of [H+] (or [OH− ]) produced by a given molarity of a weak acid (or base) before calculating total [H+] (or total [OH− ]) and subsequently pH. Functional Groups That Are Weak Acids Have Great Physiologic Significance Many biochemicals possess functional groups that are weak acids or bases. Carboxyl groups, amino groups, and the second phosphate dissociation of phosphate esters are present in proteins and nucleic acids, most coenzymes, and most intermediary metabolites. Knowledge of the dissociation of weak acids and bases thus is basic to understanding the influence of intracellular pH on structure and biologic activity. Charge-based separations such as electrophoresis and ion exchange chromatography also are best understood in terms of the dissociation behavior of functional groups. We term the protonated species (eg, HA or RNH3 +) the acid and the unprotonated species (eg, A− or RNH2) its conjugate base. Similarly, we may refer to a base (eg, A− or RNH2) and its conjugate acid (eg, HA or RNH3 +). Representative weak acids (left), their conjugate bases (center), and the pKa values (right) include the following: We express the relative strengths of weak acids and bases in terms of their dissociation constants. Shown R CH COOH COO NH NH H CO H PO a a a a —— — — — . . 2 3 2 2 3 2 4 4 5 9 10 6 4 7 2 R—CH p R—CH R—CH p HCO p HPO p 2 2 2 3 4 − − − −2 − − K K K K = = = = + below are the expressions for the dissociation constant (Ka ) for two representative weak acids, RCOOH and RNH3 +. Since the numeric values of Ka for weak acids are negative exponential numbers, we express Ka as pKa, where Note that pKa is related to Ka as pH is to [H+]. The stronger the acid, the lower its pKa value. pKa is used to express the relative strengths of both acids and bases. For any weak acid, its conjugate is a strong base. Similarly, the conjugate of a strong base is a weak acid. The relative strengths of bases are expressed in terms of the pKa of their conjugate acids. For polyproteic compounds containing more than one dissociable proton, a numerical subscript is assigned to each in order of relative acidity. For a dissociation of the type the pKa is the pH at which the concentration of the acid RNH3 + equals that of the base RNH2. From the above equations that relate Ka to [H+] and to the concentrations of undissociated acid and its conjugate base, when or when then Thus, when the associated (protonated) and dissociated (conjugate base) species are present at equal concentrations, the prevailing hydrogen ion concentration [H+] is numerically equal to the dissociation constant, Ka. If the logarithms of both sides of the above equation are Ka = H+ [ ] [ ][ ] R NH R NH — — 2 3 = + [ ][ R COO R COOH — — − = ] R NH — 3 + → R —NH2 pK K a = − log R COOH R COO H R COO H R COOH R NH R NH H R NH H R NH a a — — [ — ][ ] [ — ] — — [ — ][ ] [ — ] − − + = + = + + + + + + K K 3 2 2 3 ch02.qxd 2/13/2003 1:41 PM Page 10