OXIDATION NUMBER (OXIDATION STATE)31 covalence. the efeds po the number of bonds allched to the atom in stion.Ir ence,more precisely called ionic valence,is the absolute charge on a monoatomic ion. Erample.The valence of Mg+is 2.The covalency of carbon in carbon monoxide. written as c=o:is 2,but in carbon dioxide,0=C=0:,it is 4.The ionic valence of both Ca and O in Cao is 2.The word"valence"standing alone is rather ambiguous and the more precise terms such as ionic valence.covalence,valence orbitals valence electron oxidation number,and formal charge are preferred. 2.10 OXIDATION NUMBER (OXIDATION STATE) A whole number assigned to an atom in a molecule representative of its formal ownership of the valence electrons around it.It is calculated by first assuming that all the electrons involved in bonding to the atom in question in the Lewis structure are assigned to either that atom or to its partner,if its partner is more electroneg ative.The number of valence electrons maining on the atom is then determined if the atom is bonded tot e sam lement asnaC-C bond re the bonding electrons are divided equally,and this number is then subtracted from the number of valence electrons associated with the atom in its elemental form.The difference between the two numbers is the oxidation number of the atom in question. Example.In the structures shown in Fig.2.10,the bonding electrons are removed with the more electronegative atoms as shown and the oxidation numbers for carbon (which can r ge from +4 to-4)and sulfur are displayed below the structure.The nber for oxygen in all these compounds is-2 and for the hydroger Figure 2.10.The oxidation numbers of carbon and sulfur in various compounds.The atoms numbers
covalence, corresponds to the number of bonds attached to the atom in question. In the case of ions, the valence, more precisely called ionic valence, is the absolute charge on a monoatomic ion. Example. The valence of Mg is 2. The covalency of carbon in carbon monoxide, written as is 2, but in carbon dioxide, , it is 4. The ionic valence of both Ca and O in CaO is 2. The word “valence” standing alone is rather ambiguous and the more precise terms such as ionic valence, covalence, valence orbitals, valence electrons, oxidation number, and formal charge are preferred. 2.10 OXIDATION NUMBER (OXIDATION STATE) A whole number assigned to an atom in a molecule representative of its formal ownership of the valence electrons around it. It is calculated by first assuming that all the electrons involved in bonding to the atom in question in the Lewis structure are assigned to either that atom or to its partner, if its partner is more electronegative. The number of valence electrons remaining on the atom is then determined if the atom is bonded to the same element, as in a C–C bond where the bonding electrons are divided equally, and this number is then subtracted from the number of valence electrons associated with the atom in its elemental form. The difference between the two numbers is the oxidation number of the atom in question. Example. In the structures shown in Fig. 2.10, the bonding electrons are removed with the more electronegative atoms as shown and the oxidation numbers for carbon (which can range from 4 to 4) and sulfur are displayed below the structure. The oxidation number for oxygen in all these compounds is 2 and for the hydrogen C O O C O OXIDATION NUMBER (OXIDATION STATE) 31 C O O C O S O O O O C C H H H H H C H H H C O H H H C O +2 +4 +6 H −2 H −4 O 0 H +2 ( ) ( ( ) ) ( ( ) ( ) ( ) ) ) ) ) ) ) ( ( ) ( ) Figure 2.10. The oxidation numbers of carbon and sulfur in various compounds. The atoms inside the curves between atoms are in each case the more electronegative atoms, and the bonding electrons are, therefore, associated with those atoms in determining the oxidation numbers. c02.qxd 5/17/2005 5:13 PM Page 31
32 BONDS BETWEEN ADJACENT ATOMS atoms it is +1.For monoatomic ions,the oxidation number is the same as the charge on the ion.For a neutral compound (all the compounds shown in Fig.2.10 are neu- tral,i.e.,they have no net charge),the sum of the oxidation numbers of all atoms must equal zero. 2.11 FORMAL CHARGE This is the positive or negative charge of an atom in a molecule indicating that the atom has a fewer or greater number of valence electrons associated with it than it would have as an isolated atom in its elemental form.To determine the magnitude and sign of the formal charge,the atom is assigned all its lone pair electrons plus half of those electrons involved in the bonds with neighboring atoms;this number is then subtracted from the number of valence electrons in the isolated atom Erample.In the neutral,(Fig.2.11),the nitrogen atom is sur- rounded by four electron-paired bonds.The isolated nitrogen atom has five valence electrons and hence the formal charge is 5-8/2=+1.The formal charge on the boron atom is 3-82=-1.leaving a net charge of zero on the complex.The for mal charge on ions is calculated in the same way.In the negatively charged hydox- ide ion loHl.the oxvgen atom is surrounded with three lone pairs of electrons plus the pair it shares with the n.Thus the formal charge on oxyge n ie 6 .6+2J2)=-1.Fo N0J,(fg.2.11a the fo al ch gen is /2=+1 The form he two singl altoms is 6- 5+22 c on on the doubly bo ded oxygen (4 42)=0 eaving a net formal charge of 20-1)+(+1)+0= -1 on the ion.Formal charges should not be confused with oxidation numbers,which for the N atom in H,N-BF is 5-8=-3,and for the B atom is 3-0=+3.For the N in NH;and the C in CH. both with formal charges of zero,the oxidation numbers are-3 and-4,respectively. (a) Figure 2.11.Formal charges on atoms in (a)[NO and (b)H-BF 2.12 NONPOLAR COVALENT BOND A bond between atoms involving equal or almost equal sharing of the bonding elec- trons.As a rule of thumb or rough approximation,and quite arbitrarily,the difference
atoms it is 1. For monoatomic ions, the oxidation number is the same as the charge on the ion. For a neutral compound (all the compounds shown in Fig. 2.10 are neutral, i.e., they have no net charge), the sum of the oxidation numbers of all atoms must equal zero. 2.11 FORMAL CHARGE This is the positive or negative charge of an atom in a molecule indicating that the atom has a fewer or greater number of valence electrons associated with it than it would have as an isolated atom in its elemental form. To determine the magnitude and sign of the formal charge, the atom is assigned all its lone pair electrons plus half of those electrons involved in the bonds with neighboring atoms; this number is then subtracted from the number of valence electrons in the isolated atom. Example. In the neutral complex H3N – BF3 (Fig. 2.11b), the nitrogen atom is surrounded by four electron-paired bonds. The isolated nitrogen atom has five valence electrons and hence the formal charge is 5 8/2 1. The formal charge on the boron atom is 3 8/2 1, leaving a net charge of zero on the complex. The formal charge on ions is calculated in the same way. In the negatively charged hydoxide ion [OH], the oxygen atom is surrounded with three lone pairs of electrons plus the pair it shares with the hydrogen. Thus, the formal charge on oxygen is 6 (6 2/2) 1. For nitrogen in [NO3] , (Fig. 2.11a), the formal charge on nitrogen is 5 8/2 1. The formal charge on each of the two singly bonded oxygen atoms is 6 (6 2/2) 1, and on the doubly bonded oxygen it is 6 (4 4/2) 0, leaving a net formal charge of 2(1) (1) 0 1 on the ion. Formal charges should not be confused with oxidation numbers, which for the N atom in H3N BF3 is 5 8 3, and for the B atom is 3 0 3. For the N in NH3 and the C in CH4, both with formal charges of zero, the oxidation numbers are 3 and 4, respectively. 2.12 NONPOLAR COVALENT BOND A bond between atoms involving equal or almost equal sharing of the bonding electrons. As a rule of thumb or rough approximation, and quite arbitrarily, the difference 32 BONDS BETWEEN ADJACENT ATOMS N H H H B F F F O N O O (a) (b) + − − − + − Figure 2.11. Formal charges on atoms in (a) [NO3]−1 and (b) H3N − − BF3. c02.qxd 5/17/2005 5:13 PM Page 32
DIPOLE MOMENTS OF POLYATOMIC MOLECULES 33 sified as nonpolar. 2.13 DIPOLE MOMENT A vectorial property of individual bonds or entire molecules that characterizes their polarity.A diatomic molecule in which the electrons are not shared equally gives rise to a dipole moment vector with a negative end and a positive end along the bond con- necting the two atoms.Therefore.such a molecule acts as a dipole and tends to become aligned in an electrical field.The (electric)dipole moment u (see also Sect.4.31)is btained by multiplying the charge m (pole)(in electrostatic units or esu) by the distance(ce meters)betwe h atom (in esu-cm) are usu ly expres: are shown in C-CI distance is larger than the C-F distance even though fluorine is more elec- tronegative than chlorine.The direction of the dipole of a bond is frequently indicated by a crossed arrow over the bond in question with the crossed tail at the positive end and the head of the arrow over the negative end,as shown in the examples. =0d 4=0.22 1-141 Figure 2.13.Dipole moments for the C-H.C-N.C-F.and C-Cl bonds 2.14 DIPOLE MOMENTS OF POLYATOMIC MOLECULES; VECTORIAL ADDITION OF DIPOLE MOMENTS The dipole moment of a molecule may be calculated from the vectorial sum of the individual bo ond dipole n ents.Each bond betwee h ciateddirecteddipole of the moment tha appro the n t of the mo ue The resu t of the ve orial addition of al
in the electronegativities of the bonded atoms should be less than 0.5 (Pauling scale) for the covalent bond to be classified as nonpolar. Example. The C–H and the C–P bonds; the electronegativity difference in these bonds in each case is 0.4. 2.13 DIPOLE MOMENT A vectorial property of individual bonds or entire molecules that characterizes their polarity. A diatomic molecule in which the electrons are not shared equally gives rise to a dipole moment vector with a negative end and a positive end along the bond connecting the two atoms. Therefore, such a molecule acts as a dipole and tends to become aligned in an electrical field. The (electric) dipole moment µ (see also Sect. 4.31) is obtained by multiplying the charge at either atom (pole) q (in electrostatic units or esu) by the distance d (in centimeters) between the atoms (poles): q × d µ (in esu-cm). Dipole moments are usually expressed in Debye units (named after Peter Debye, 1884–1966), abbreviated D, equal to 1018 esu-cm. Example. Typical dipole moments (in Debye units) of some C–Z bonds are shown in Fig. 2.13. The dipole moment of the C–Cl bond is greater than that of C–F because the C–Cl distance is larger than the C–F distance even though fluorine is more electronegative than chlorine. The direction of the dipole of a bond is frequently indicated by a crossed arrow over the bond in question with the crossed tail at the positive end and the head of the arrow over the negative end, as shown in the examples. 2.14 DIPOLE MOMENTS OF POLYATOMIC MOLECULES; VECTORIAL ADDITION OF DIPOLE MOMENTS The dipole moment of a molecule may be calculated from the vectorial sum of the individual bond dipole moments. Each bond between atoms in a molecule has an associated directed dipole moment that is approximately independent of the nature of the groups in the rest of the molecule. The resultant of the vectorial addition of all bond moments yields the overall dipole moment of the molecule. DIPOLE MOMENTS OF POLYATOMIC MOLECULES 33 C H C N C F C Cl µ = 0.4 µ = 0.22 µ =1.41 µ =1.46 Figure 2.13. Dipole moments for the C–H, C–N, C–F, and C–Cl bonds. c02.qxd 5/17/2005 5:13 PM Page 33
34 BONDS BETWEEN ADJACENT ATOMS Erample.Chlorobenzene has a measured dipole moment of 1.70 D:see Fig.2.14 (the point O represents the center of the hexagon).The dipole moment of 1,2- dichlorobenzene can be approximated from the dipole moment of chlorobenzene by vector addition,as shown in Fig.2.14b.The component vector Ob is equal to 1.70 cos 30=1.47.and the resultant dipole moment (OB.Fig.2.146)is the sum of the two com rs.2.94 D.How r,the ntal alue for the dipolem ent of 1 2 experimental value into the rearrange vector sum equation and calculates the individual component vectors,one gets 0CI=0B/2cos30°=2.25/2cos30°=1.30D These vector components are considerably less that the single vector (1.70 D)in monochlorobenzene,indicating that the dipole vectors in dichlorobenzene interact with each other,resulting in a vector sum less than that calculated on the basis of no interaction. μ=1.70 4=1.70 29 u=1.47 (a) ( Figure 2.14.Vectorial addition of bond moments. 2.15 POLAR COVALENT BOND;PARTIALLY IONIC BOND This is a covalent bond with appreciable ionic character,that is,a bond between atoms in which the shared electrons reside much closer to the atom of greater elec tronegativity.The distinction between a nonpolar and a polar covalent bond is arbi- trary:if the difference in electronegativities of the bonded atoms is greater than 0.5 (Pauling scale),the bond has an appreciable ionic character and may be considered a polar covalent bond. tude of the bond's dipole moment,which in tum is depend tronegativities of the two atoms comprising the bond.Thus,if we assume,for purposes of calculation,that in the molecule H-F,the entire charge of one electron
Example. Chlorobenzene has a measured dipole moment of 1.70 D; see Fig. 2.14a (the point O represents the center of the hexagon). The dipole moment of 1,2- dichlorobenzene can be approximated from the dipole moment of chlorobenzene by vector addition, as shown in Fig. 2.14b. The component vector Ob is equal to 1.70 cos 30°1.47, and the resultant dipole moment (OB, Fig. 2.14b) is the sum of the two component vectors, 2.94 D. However, the experimental value for the dipole moment of 1,2- dichlorobenzene is 2.25 D. If one substitutes this experimental value into the rearranged vector sum equation and calculates the individual component vectors, one gets OCl OB/2 cos 30° 2.25/2 cos 30° 1.30 D These vector components are considerably less that the single vector (1.70 D) in monochlorobenzene, indicating that the dipole vectors in dichlorobenzene interact with each other, resulting in a vector sum less than that calculated on the basis of no interaction. 2.15 POLAR COVALENT BOND; PARTIALLY IONIC BOND This is a covalent bond with appreciable ionic character, that is, a bond between atoms in which the shared electrons reside much closer to the atom of greater electronegativity. The distinction between a nonpolar and a polar covalent bond is arbitrary; if the difference in electronegativities of the bonded atoms is greater than 0.5 (Pauling scale), the bond has an appreciable ionic character and may be considered a polar covalent bond. Example. The percent ionic character of a bond can be approximated by the magnitude of the bond’s dipole moment, which in turn is dependent on the relative electronegativities of the two atoms comprising the bond. Thus, if we assume, for purposes of calculation, that in the molecule H–F, the entire charge of one electron 34 BONDS BETWEEN ADJACENT ATOMS (a) (b) µ = 1.70 30˚ µ = 2.94 30˚ µ = 1.70 b µ = 1.47 Cl Cl Cl Ο B Ο Figure 2.14. Vectorial addition of bond moments. c02.qxd 5/17/2005 5:13 PM Page 34
MORSE CURVE 35 (4.8x10-esu)is on the Fatom,we would have the completely ionic form,H+F The H-F distance determined experimentally is 0.917A =0.917x 10-8cm,leading for the completely ionized species to a dipole moment ofμ=q×d=[(4.8× 10-10)x(0.917x10-8)1/10-18=4.4 D.However,since the experimental value is 1.98 D.it may be concluded that the bond has (1.98/4.4)100=45%ionic character.When one desires to indicate the partial ionic character of a bond,the superscripts 8+and ne gative elem I guide for exampl A usefu ga ionic character (in parentheses)is 1.0(2%).1.(40%).2.0(60%).and 2.5(80%) 2.16 IONIC BOND The result of electrostatic attraction between oppositely charged ions.Such bonds be viewed as theoretically resultin from the complete transfer of an electron from an aton an elec result of any nqua sharing of theatom Erample.Sodium chloride.NaCl-,is an ionic compound.However.in the solid state,both ions are present in a lattice network in which each sodium ion is sur- rounded by six chloride ions and each chloride ion is surrounded by six sodium ions.There is no such species as a diatomic Na+Cl-molecule except in the vapor phase 2.17 SINGLE,DOUBLE,AND TRIPLE BONDS The covalent bonding between adjacent atoms involving two electrons(single bond) four electrons (double bond),and six electrons (triple bond).Conventionally,such bonding is indicated by one dash(single).two dashes (double),and three dashes (triple)between the bonded atoms. Example.HC-CH,.H.C=CH2.HC=CH. 2.18 MORSE CURVE This is a plot,named after Phillip M.Morse(1903-1985).showing the relationship between the potential energy E of a chemical bond between two atoms as a func- tion of the distance between them. Example.The Morse curve for the hydrogen molecule is shown in Fig.2.18. The minimum in the curve occurs at the equilibrium interatomic distance doA the two nuclei repe plarger thand the increases because of reduced o
(4.8 × 1010 esu) is on the F atom, we would have the completely ionic form, HF. The H-F distance determined experimentally is 0.917Å 0.917 × 108 cm, leading for the completely ionized species to a dipole moment of µ q × d [(4.8 × 1010) × (0.917 × 108 )]/1018 4.4 D. However, since the experimental value is 1.98 D, it may be concluded that the bond has (1.98/4.4)100 45% ionic character. When one desires to indicate the partial ionic character of a bond, the superscripts δ and δ are placed above the electropositive and electronegative element, for example, Hδ–Fδ. A useful guide for correlating electronegativity differences with percent ionic character (in parentheses) is 1.0 (20%), 1.5 (40%), 2.0 (60%), and 2.5 (80%). 2.16 IONIC BOND The result of electrostatic attraction between oppositely charged ions. Such bonds can be viewed as theoretically resulting from the complete transfer of an electron from an electropositive atom to an electronegative atom and not as a result of any unequal sharing of electrons between the atoms. Example. Sodium chloride, NaCl, is an ionic compound. However, in the solid state, both ions are present in a lattice network in which each sodium ion is surrounded by six chloride ions and each chloride ion is surrounded by six sodium ions. There is no such species as a diatomic NaCl molecule except in the vapor phase. 2.17 SINGLE, DOUBLE, AND TRIPLE BONDS The covalent bonding between adjacent atoms involving two electrons (single bond), four electrons (double bond), and six electrons (triple bond). Conventionally, such bonding is indicated by one dash (single), two dashes (double), and three dashes (triple) between the bonded atoms. Example. H3C–CH3, H2CCH2, HCCH. 2.18 MORSE CURVE This is a plot, named after Phillip M. Morse (1903–1985), showing the relationship between the potential energy Ep of a chemical bond between two atoms as a function of the distance between them. Example. The Morse curve for the hydrogen molecule is shown in Fig. 2.18. The minimum in the curve occurs at the equilibrium interatomic distance d0. At distances smaller than d0, the two nuclei repel each other and the potential energy Ep rises sharply; at distances larger than d0, the Ep increases because of reduced orbital MORSE CURVE 35 c02.qxd 5/17/2005 5:13 PM Page 35