Page 20TABLE2Physical Properties ofWaterand IceValueProperty18.0153Molecular weightPhase transition properties0.000°℃Melting pointat 101.3k Pa (1 atm)100.000°℃Boiling point at 101.3 k Pa (I atm)373.99°℃Critical temperature22.064MPa (218.6atm)Critical pressureTriple point0.01°C and 611.73 Pa (4.589 mm Hg)6.012 kJ (1.436 kcal)/molEnthalpy of fusion at o°℃Enthalpyof vaporization at100°C40.657kJ (9.711 kcal)/molEnthalpy of sublimination at o°C50.91kJ (12.16kcal)/molTemperature0℃20℃0°C (ice)-20°C (ice)OtherpropertiesDensity (g/em30.998210.999840.91680.91931.002×10-31.793×10-3Viscosity (pa'sec)-一72.75×10-375.64×10-3Surfacetensionagainstair(N/m)2.33880.61130.61130.103Vapor pressure (kPa)1.95444.18184.21762.1009Heat capacity (J/g·K)0.59840.56102.2402.433Thermal conductivity (liquid) (W/m·K)1.4×10-71.3×10-711.7×10-711.8 ×10-7Thermal diffusitity (m2/s)~90~9880.2087.90Permittivity (dielectricconstant)Source.Mainly Ref 69solids. Of greater interest is the fact that the thermal conductivity of ice at O°C is approximately four times that of water at thesame temperature, indicating that ice will conduct heat energy at a much greater rate than will immobilized water (e.g., in tissue)The thermal diffusivities of water and ice are of even greater interest since these values indicate the rate at which the solid andliquid forms of HOH will undergo changes in temperature. Ice has a thermal diffiusivity approximately nine times greater than thatof water, indicating that ice, in a given environment, will undergo a temperature change at a much greater rate than will water.These sizable differences in thermal conductivity and thermal diffusivity values of water and ice provide a sound basis forexplaining why tissues freeze more rapidly than they thaw, when equal but reversed temperature differentials are employed.2.3The Water MoleculeWater's unusual properties suggest the existence of strong attractive forces among water molecules, and uncommon structuresfor water and ice.Thesefeatures are best explained by considering the natureoffirst a singlewatermoleculeand then smallgroups of molecules. To form a molecule of water, two hydrogen atoms approach the two sp bonding orbitals of oxygen andform two covalent sigma () bonds (40% partial ionic character), each of which has a dissociation energy of4.6x102 kJ/mol(110 kcal/mol).The localized molecular orbitals remain symmetrically oriented about the original orbital axes, thus retaining anapproximate
Pag e 20 TABLE 2 Physical Properties of W ater and Ice Property Value Molecular weig ht 18.0153 Phase transition properties Melting point at 101.3 k Pa (1 atm) 0.000°C Boiling point at 101.3 k Pa (1 atm) 100.000°C Critical temperature 373.99°C Critical pressure 22.064 MPa (218.6 atm) Triple point 0.01°C and 611.73 Pa (4.589 mm Hg ) Enthalpy of fusion at 0°C 6.012 kJ (1.436 kcal)/mol Enthalpy of vaporization at 100°C 40.657 kJ (9.711 kcal)/mol Enthalpy of sublimination at 0°C 50.91 kJ (12.16 kcal)/mol Temperature Other properties 20°C 0°C 0°C (ice) -20°C (ice) Density (g /cm3 0.99821 0.99984 0.9168 0.9193 Viscosity (pa·sec) 1.002×10-3 1.793×10-3 — — Surface tension ag ainst air (N/m) 72.75×10-3 75.64×10-3 — — Vapor pressure (kPa) 2.3388 0.6113 0.6113 0.103 Heat capacity (J/g ·K) 4.1818 4.2176 2.1009 1.9544 Thermal conductivity (liquid) (W /m·K) 0.5984 0.5610 2.240 2.433 Thermal diffusitity (m2 /s) 1.4×10-7 1.3×10-7 11.7×10-7 11.8 ×10-7 Permittivity (dielectric constant) 80.20 87.90 ~90 ~98 Source: Mainly Ref. 69. solids. Of greater interest is the fact that the thermal conductivity of ice at 0°C is approximately four times that of water at the same temperature, indicating that ice will conduct heat energy at a much greater rate than will immobilized water (e.g., in tissue). The thermal diffusivities of water and ice are of even greater interest since these values indicate the rate at which the solid and liquid forms of HOH will undergo changes in temperature. Ice has a thermal diffusivity approximately nine times greater than that of water, indicating that ice, in a given environment, will undergo a temperature change at a much greater rate than will water. These sizable differences in thermal conductivity and thermal diffusivity values of water and ice provide a sound basis for explaining why tissues freeze more rapidly than they thaw, when equal but reversed temperature differentials are employed. 2.3 The Water Molecule Water's unusual properties suggest the existence of strong attractive forces among water molecules, and uncommon structures for water and ice. These features are best explained by considering the nature of first a single water molecule and then small groups of molecules. To form a molecule of water, two hydrogen atoms approach the two sp3 bonding orbitals of oxygen and form two covalent sigma (s) bonds (40% partial ionic character), each of which has a dissociation energy of 4.6×102 kJ/mol (110 kcal/mol). The localized molecular orbitals remain symmetrically oriented about the original orbital axes, thus retaining an approximate
Page21tetrahedral structure. A schematic orbital model of a water molecule is shown in Figure 1A and the appropriate van der Waalsradi are shown in Figure 1BThebondangleoftheisolatedwatermolecule(vaporstate)is104.5°andthisvalueisneartheperfecttetrahedralangleof109°28. The O-H internuclear distance is 0.96 A and the van der Waals radii for oxygen and hydrogen are, respectively, 1.40and 1.2 A.At this point, it is important to emphasize that the picture so far presented is oversimplified. Pure water contains not onlyordinaryHOHmoleculesbut alsomany other constituents in traceamounts.In additiontothecommon isotopesi6O and'Halsopresentare17,18O,2H+HI?O中4+His④(a)33A-12AAO0.968(b)FIGURE1Schematicmodelofa singleHOHmolecule:(a)sp3configuration,and (b)vanderWaalsradiforaHOHmolecule inthevaporstate
Pag e 21 tetrahedral structure. A schematic orbital model of a water molecule is shown in Figure 1A and the appropriate van der Waals radii are shown in Figure 1B. The bond angle of the isolated water molecule (vapor state) is 104.5° and this value is near the perfect tetrahedral angle of 109°28'. The O-H internuclear distance is 0.96 Å and the van der Waals radii for oxygen and hydrogen are, respectively, 1.40 and 1.2 Å. At this point, it is important to emphasize that the picture so far presented is oversimplified. Pure water contains not only ordinary HOH molecules but also many other constituents in trace amounts. In addition to the common isotopes 16O and 1H, also present are 17O, 18O, 2H FIGURE 1 Schematic model of a sing le HOH molecule: (a) sp 3 config uration, and (b) van der W aals radii for a HOH molecule in the vapor state
Page22(deuterium) and "H (tritium), giving rise to 18 isotopic variants of molecular HOH. Water also contains ionic particles such ashydrogen ions (existing as HO+), hydroxyl ions, and their isotopic variants. Water therefore consists of more than 33 chemicalvariantsofHOH,butthevariantsoccurinonlyminuteamounts.2.4AssociationofWaterMoleculesTheV-likeformofanHOHmoleculeandthepolarizednatureoftheO-Hbond result inan unsymmetrical chargedistributionandavapor-statedipolemomentof1.84Dforpurewater.Polarityofthismagnitudeproducesintermolecularattractiveforcesand water molecules therefore associate with considerable tenacity. Water's unusually large intermolecular attractive forcecannot,however,befully accountedforonthebasis ofitslargedipolemoment.This isnot surprising,sincedipolemomentsgiveno indication ofthe degree to which charges are exposed or of the geometry of the molecule, and these aspects, of course, havean important bearingon the intensityofmolecular association.Water's large intermolecular attractive forces can be explained quite adequately in terms of its ability to engage in multiplehydrogenbondingonathree-dimensionalbasis.Comparedtocovalentbonds(averagebondenergyofabout335kJ/mol)hydrogen bonds are weak (typically 2-40 kJ/mol) and have greater and more variable lengths. The hydrogen bond betweenoxygen and hydrogen has a dissociation energy of about 13-25 kJ/mol.Since electrostatic forces make a major contribution to the energy of the hydrogen bond (perhaps the largest contribution), andsince an electrostatic model of water is simple and leads to an essentially correct geometric picture of HOH molecules as theyare known to exist in ice, further discussion of the geometrical pattems formed by association of water molecules will emphasizeelectrostatic effects.This simplified approach, while entirely satisfactoryfor present purposes, must be modified ifotherbehavioralcharacteristicsofwateraretobeexplainedsatisfactorilyThe highly electronegative oxygen ofthewater molecule can be visualized as partiallydrawing away the single electrons from thetwocovalentlybondedhydrogenatoms,therebyleavingeachhydrogenatomwithapartialpositivechargeand aminimalelectron shield; that is, each hydrogen atom assumes some characteristics of a bare proton. Since the hydrogenoxygenbondingorbitalsarelocatedontwooftheaxesofan imaginarytetrahedron(Fig.la),thesetwoaxescanbethoughtofasrepresenting lines of positive force (hydrogen-bond donor sites).Oxygen's two lone-pair orbitals can be pictured as residingalong the remaining two axes of the imaginary tetrahedron, and these then represent lines of negative force (hydrogen-bondacceptor sites).By virtue of thesefour lines offorce, each water molecule is able to hydrogen-bond with a maximum of fourothers.Theresultingtetrahedral arrangement isdepictedinFigure2Because each water molecule has an equal number of hydrogen-bond donor and receptor sites, arranged to permit three-dimensional hydrogen bonding, it is found that the attractive forces among water molecules are unusually large, even whencompared to those existing among other small molecules that also engage in hydrogen bonding (e.g.,NHs, HF).Ammonia, withitstetrahedralarrangementofthreehydrogensandonereceptorsite,and hydrogenfluoride,with itstetrahedralarrangementofone hydrogen and three receptor sites,do not have equal numbers of donor and receptor sites and therefore can form only twodimensional hydrogen-bonded networks involving less hydrogen bonds per molecule than water.Conceptualizingtheassociationofafewwatermolecules becomesconsiderablymorecomplicatedwhenoneconsiders isotopicvariantsandhydroniumandhydroxylions.The
Pag e 22 (deuterium) and 3H (tritium), giving rise to 18 isotopic variants of molecular HOH. Water also contains ionic particles such as hydrogen ions (existing as H3O+ ), hydroxyl ions, and their isotopic variants. Water therefore consists of more than 33 chemical variants of HOH, but the variants occur in only minute amounts. 2.4 Association of Water Molecules The V-like form of an HOH molecule and the polarized nature of the O-H bond result in an unsymmetrical charge distribution and a vapor-state dipole moment of 1.84D for pure water. Polarity of this magnitude produces intermolecular attractive forces, and water molecules therefore associate with considerable tenacity. Water's unusually large intermolecular attractive force cannot, however, be fully accounted for on the basis of its large dipole moment. This is not surprising, since dipole moments give no indication of the degree to which charges are exposed or of the geometry of the molecule, and these aspects, of course, have an important bearing on the intensity of molecular association. Water's large intermolecular attractive forces can be explained quite adequately in terms of its ability to engage in multiple hydrogen bonding on a three-dimensional basis. Compared to covalent bonds (average bond energy of about 335 kJ/mol), hydrogen bonds are weak (typically 2–40 kJ/mol) and have greater and more variable lengths. The hydrogen bond between oxygen and hydrogen has a dissociation energy of about 13–25 kJ/mol. Since electrostatic forces make a major contribution to the energy of the hydrogen bond (perhaps the largest contribution), and since an electrostatic model of water is simple and leads to an essentially correct geometric picture of HOH molecules as they are known to exist in ice, further discussion of the geometrical patterns formed by association of water molecules will emphasize electrostatic effects. This simplified approach, while entirely satisfactory for present purposes, must be modified if other behavioral characteristics of water are to be explained satisfactorily. The highly electronegative oxygen of the water molecule can be visualized as partially drawing away the single electrons from the two covalently bonded hydrogen atoms, thereby leaving each hydrogen atom with a partial positive charge and a minimal electron shield; that is, each hydrogen atom assumes some characteristics of a bare proton. Since the hydrogen—oxygen bonding orbitals are located on two of the axes of an imaginary tetrahedron (Fig. 1a), these two axes can be thought of as representing lines of positive force (hydrogen-bond donor sites). Oxygen's two lone-pair orbitals can be pictured as residing along the remaining two axes of the imaginary tetrahedron, and these then represent lines of negative force (hydrogen-bond acceptor sites). By virtue of these four lines of force, each water molecule is able to hydrogen-bond with a maximum of four others. The resulting tetrahedral arrangement is depicted in Figure 2. Because each water molecule has an equal number of hydrogen-bond donor and receptor sites, arranged to permit threedimensional hydrogen bonding, it is found that the attractive forces among water molecules are unusually large, even when compared to those existing among other small molecules that also engage in hydrogen bonding (e.g., NH3, HF). Ammonia, with its tetrahedral arrangement of three hydrogens and one receptor site, and hydrogen fluoride, with its tetrahedral arrangement of one hydrogen and three receptor sites, do not have equal numbers of donor and receptor sites and therefore can form only twodimensional hydrogen-bonded networks involving less hydrogen bonds per molecule than water. Conceptualizing the association of a few water molecules becomes considerably more complicated when one considers isotopic variants and hydronium and hydroxyl ions. The
Page23hydronium ion, because of its positive charge, would be expected to exhibit a greater hydrogen-bond donating potential thannonionized water (dashed lines arehydrogenbonds)HSTRUCTURE1Structureandhydrogen-bondpossibilities fora hydroniumion. Dashed lines are hydrogenbonds.The hydroxyl ion, because of its negative charge, would be expected to exhibit a greater hydrogen-bond acceptor potential thanun-ionized water (XH represents a solute or a water molecule)XSTRUCTURE2Structureand hydrogen-bondpossibilities for a hydroxyion,Dashedlinesarehydrogenbonds andXHrepresentsa solute or a water moleculeWater's ability to engage in three-dimensional hydrogen bonding provides a logical explanation for many of its unusualproperties; its large values for heat capacity,melting point, boiling point, surface tension, and enthalpies ofvarious phasetransitionsallarerelatedtotheextraenergyneededtobreakintermolecularhydrogenbondsThe permittivity (dielectric constant) of water is also influenced by hydrogen bonding. Although water is a dipole, this fact alonedoes not account for the magnitude of its permittivity. Hydrogen-bonded clusters of molecules apparently give rise tomultimolecular di-
Pag e 23 hydronium ion, because of its positive charge, would be expected to exhibit a greater hydrogen-bond donating potential than nonionized water (dashed lines are hydrogen bonds). STRUCTURE 1 Structure and hydrog en-bond possibilities for a hydronium ion. Dashed lines are hydrog en bonds. The hydroxyl ion, because of its negative charge, would be expected to exhibit a greater hydrogen-bond acceptor potential than un-ionized water (XH represents a solute or a water molecule). STRUCTURE 2 Structure and hydrog en-bond possibilities for a hydroxyl ion. Dashed lines are hydrog en bonds and XH represents a solute or a water molecule. Water's ability to engage in three-dimensional hydrogen bonding provides a logical explanation for many of its unusual properties; its large values for heat capacity, melting point, boiling point, surface tension, and enthalpies of various phase transitions all are related to the extra energy needed to break intermolecular hydrogen bonds. The permittivity (dielectric constant) of water is also influenced by hydrogen bonding. Although water is a dipole, this fact alone does not account for the magnitude of its permittivity. Hydrogen-bonded clusters of molecules apparently give rise to multimolecular di-
Page24FIGURE2Hydrogenbondingofwatermolecules inatetrahedralconfiguration.Opencirclesareoxygenatomsand closed circles are hydrogen atoms.Hydrogenbonds are represented by dashed linespoles, which effectively increase the permittivity of water.Water's viscosity is discussed in a later section2.5StructureofIceThe structure of ice will be considered before the structure of water because the former is far better understood than the latter,and because ice's structure represents a logical extension of the information presented in the previous section.2.5.1PureIceWater,withitstetrahedrallydirectedforces,crystallizesinanopen(lowdensity)structurethathasbeenaccuratelyelucidatedTheO-0internuclearnearest-neighbordistancein iceis2.76AandtheO-O-0bond angle is about109,orveryclosetotheperfect tetrahedral angle of 109°28' (Fig. 3). The manner in which each HOH molecule can associate with four others(coordinationnumberoffour)iseasilyvisualized intheunitcellofFigure3byconsideringmoleculeWanditsfournearestneighbors 1, 2, 3, and W".Whenseveral unitcellsarecombinedandviewedfromthetop(downthecaxis)thehexagonalsymmetryoficebecomesapparent. This is shown in Figure 4a The tetrahedral
Pag e 24 FIGURE 2 Hydrog en bonding of water molecules in a tetrahedral config uration. Open circles are oxyg en atoms and closed circles are hydrog en atoms. Hydrog en bonds are represented by dashed lines. poles, which effectively increase the permittivity of water. Water's viscosity is discussed in a later section. 2.5 Structure of Ice The structure of ice will be considered before the structure of water because the former is far better understood than the latter, and because ice's structure represents a logical extension of the information presented in the previous section. 2.5.1 Pure Ice Water, with its tetrahedrally directed forces, crystallizes in an open (low density) structure that has been accurately elucidated. The O-O internuclear nearest-neighbor distance in ice is 2.76 Å and the O-O-O bond angle is about 109°, or very close to the perfect tetrahedral angle of 109°28' (Fig. 3). The manner in which each HOH molecule can associate with four others (coordination number of four) is easily visualized in the unit cell of Figure 3 by considering molecule W and its four nearest neighbors 1, 2, 3, and W'. When several unit cells are combined and viewed from the top (down the c axis) the hexagonal symmetry of ice becomes apparent. This is shown in Figure 4a. The tetrahedral