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Concept 04 / 07Chemical Bonding and Molecular Structure

Covalent Bond Parameters: Bond Length, Angle, Enthalpy, Bond Order, Resonance and Dipole Moment

Bond length and covalent radii, bond angle, bond enthalpy and average bond enthalpies, bond order and its correlation with length and strength, resonance and resonance hybrids, polarity of bonds, dipole moment as a vector and using it to deduce molecular shape.

Figure 1
Bond length is the equilibrium distance between the nuclei of two bonded atoms, measured by X-ray diffraction or spectroscopy. It is roughly the sum of the covalent radii and decreases as bond order increases: C-C 154154 pm, C=C 134134 pm, C≡C 120120 pm. Bond angle is the angle between two bonds around a central atom; it reflects the arrangement of electron pairs (VSEPR) and hybridisation. H2O\mathrm{H_{2}O}: 104.5∘104.5^{\circ}; NH3\mathrm{NH_{3}}: 107∘107^{\circ}; CH4\mathrm{CH_{4}}: 109.5∘109.5^{\circ}. Bond enthalpy is the energy needed to break one mole of a particular bond in gaseous molecules (H-H 435.8435.8 kJ/mol). In polyatomic molecules the energy to break successive identical bonds differs, so average bond enthalpies are used (the four C-H bonds of methane average about 416416 kJ/mol). Higher bond order means greater bond enthalpy: N≡N (946946) > O=O (498498) > F-F (159159 kJ/mol, unusually weak because of lone-pair repulsion in the small F atoms). Bond order in the Lewis picture is the number of shared electron pairs between two atoms: H2\mathrm{H_{2}} 11, O2\mathrm{O_{2}} 22, N2\mathrm{N_{2}} 33. Isoelectronic species usually have the same bond order (N2\mathrm{N_{2}}, CO, NO+\mathrm{NO^{+}}, CN−\mathrm{CN^{-}} all 33). Higher bond order: shorter, stronger bond. Resonance. When a single Lewis structure cannot describe a molecule, the true structure is a resonance hybrid of several canonical forms that differ only in the placement of electrons (never of nuclei). Ozone has two equivalent forms, O=O-O and O-O=O; experimentally both O-O bonds are equal (128128 pm), intermediate between single (148148) and double (121121). The canonical forms do not exist separately and the molecule does not oscillate between them. Resonance lowers the energy (resonance energy) and averages bond orders: in CO32−\mathrm{CO_{3}^{2-}} each C-O bond order is 43\frac{4}{3}; in NO3−\mathrm{NO_{3}^{-}} also 43\frac{4}{3}; in benzene each C-C bond is 1.51.5. The average bond order =total bonds between the pairsnumber of such pairs= \frac{\text{total bonds between the pairs}}{\text{number of such pairs}}. Polarity and dipole moment. When two atoms of different electronegativity share electrons, the pair is displaced towards the more electronegative atom, giving partial charges δ+\delta^{+} and δ−\delta^{-}: a polar covalent bond. Its dipole moment is μ=q×d\mu = q \times d (charge times separation), measured in debye (1 D=3.336×10−301\ \mathrm{D} = 3.336 \times 10^{-30} C m). The dipole moment of a molecule is the vector sum of its bond moments (and lone-pair contributions), so it depends on shape, as the figure shows. Linear CO2\mathrm{CO_{2}} and planar BF3\mathrm{BF_{3}} and tetrahedral CCl4\mathrm{CCl_{4}} are non-polar despite polar bonds; bent H2O\mathrm{H_{2}O} (1.851.85 D) and pyramidal NH3\mathrm{NH_{3}} (1.471.47 D) are polar. Surprisingly, NF3\mathrm{NF_{3}} (0.230.23 D) has a much smaller moment than NH3\mathrm{NH_{3}}: in NH3\mathrm{NH_{3}} the lone-pair moment and the N-H bond moments point the same way, while in NF3\mathrm{NF_{3}} the N-F bond moments point away from the lone pair and largely cancel it. Percentage ionic character =μobservedμionic×100= \frac{\mu_{\text{observed}}}{\mu_{\text{ionic}}} \times 100, where μionic=e×d\mu_{\text{ionic}} = e \times d. Uses of dipole moment: deciding shape (a zero moment for ABn\mathrm{AB_{n}} implies a symmetric shape), distinguishing isomers (cis-1,2-dichloroethene is polar, trans is non-polar; p-dichlorobenzene has μ=0\mu = 0, o- and m- do not). Key Takeaways: - Higher bond order: shorter bond, higher bond enthalpy. - Resonance hybrid: real structure; canonical forms do not exist separately; bond orders average. - CO32−\mathrm{CO_{3}^{2-}}, NO3−\mathrm{NO_{3}^{-}}: bond order 43\frac{4}{3}; benzene 1.51.5; O3\mathrm{O_{3}} 1.51.5. - μ=q×d\mu = q \times d; molecular μ\mu is the vector sum of bond moments. - μ=0\mu = 0 for symmetric CO2\mathrm{CO_{2}}, BF3\mathrm{BF_{3}}, CH4\mathrm{CH_{4}}, CCl4\mathrm{CCl_{4}}, PCl5\mathrm{PCl_{5}}, SF6\mathrm{SF_{6}}. - μ(NH3)>μ(NF3)\mu(\mathrm{NH_{3}}) > \mu(\mathrm{NF_{3}}) because of lone-pair direction. - Pitfall: concluding a molecule is polar just because its bonds are polar. Brain-Teaser 1: The bond length of HCl is 127127 pm and its dipole moment is 1.031.03 D. Estimate its percentage ionic character. Solution: μionic=1.602×10−19×127×10−12=2.03×10−29\mu_{\text{ionic}} = 1.602 \times 10^{-19} \times 127 \times 10^{-12} = 2.03 \times 10^{-29} C m =2.03×10−293.336×10−30=6.10= \frac{2.03 \times 10^{-29}}{3.336 \times 10^{-30}} = 6.10 D. Percentage ionic =1.036.10×100≈17%= \frac{1.03}{6.10} \times 100 \approx 17\%. HCl is mostly covalent, though polar. Brain-Teaser 2: Find the C-O bond order in CO2\mathrm{CO_{2}}, CO and CO32−\mathrm{CO_{3}^{2-}}, and arrange the C-O bond lengths. Solution: CO2\mathrm{CO_{2}}: 22 (O=C=O); CO: 33; CO32−\mathrm{CO_{3}^{2-}}: 43\frac{4}{3} (one double and two single bonds shared over three positions). Bond length is inversely related to bond order: CO < CO2\mathrm{CO_{2}} < CO32−\mathrm{CO_{3}^{2-}}. Resonance-averaged orders let us compare molecules with different structures. Brain-Teaser 3: BF3\mathrm{BF_{3}} has zero dipole moment but NF3\mathrm{NF_{3}} does not. What do these facts say about their shapes? Solution: A non-zero moment rules out planar trigonal symmetry for NF3\mathrm{NF_{3}}: its lone pair makes it pyramidal, so the three N-F moments do not cancel. BF3\mathrm{BF_{3}} has no lone pair on boron; its three equal B-F moments at 120∘120^{\circ} cancel exactly, confirming a trigonal planar shape. Dipole moments are experimental evidence for VSEPR shapes.

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Covalent Bond Parameters: Bond Length, Angle, Enthalpy, Bond Order, Resonance and Dipole Moment — DPP

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