(4) Molecular Structure

8/3/2019 (4) Molecular Structure

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By: Budiman Anwar


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An ionic bond is a chemical bond formed bythe electrostatic attraction betweenpositiveand negative ions. The bond forms between twoatoms when one or more electrons aretransferredfromthe valence shellofone atomtothe valence

shelloftheother. The atomthatloses electronsbecomes a cation (positive ion), and theatomthat gains electrons becomes an anion(negative ion). Any given ion tends toattract as many neighboring ions ofoppositecharge as possible. When large numbersof ions gathertogether,they form an ionic solid.The solid normallyhas a regular, crystallinestructurethat allows forthemaximum attractionof ions, given theirparticular sizes.


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1. Sublimation of sodium. Metallic sodium is vaporized to a gas ofsodium atoms. (Sublimation is the transformation of a solid to a gas.)The enthalpy change forthis process, measured experimentally, is 108kJ per mole of sodium.

2. Dissociation ofchlorine. Chlorine molecules are dissociated to atoms.

The enthalpy change for this equals the ClOCl bond dissociationenergy, which is 240 kJ per mole of bonds, or 120 kJ per mole of Clatoms.

3. Ionization of sodium. Sodium atoms are ionized to Na ions. Theenthalpy change is essentiallythe ionization energyof atomic sodium,

whichequals 496 kJ per moleof Na.4. Formation ofchloride ion. The electrons from the ionization of sodium

atoms are transferred to chlorine atoms. The enthalpychange for thisis the electron affinity of atomic chlorine, which equals 349 kJ permoleofCl atoms.


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5. Formation of NaCl(s) from ions. The ions Na and Cl formed in Steps 3and 4 combine to give solid sodium chloride. Because this process isjust the reverse of the one corresponding to the lattice energy

(breaking the solid into ions), the enthalpychange is the negative ofthe lattice energy. If we let U be the lattice energy, the enthalpychange for Step 5 is U.


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Typically, ionic substances are high-melting solids. Sodium chloride,NaCl, ordinar y salt, melts at 801rC, and magnesium oxide, MgO, aceramic, melts at 2800rC.Small, spherical cations and anions interact by strong bonds thatessentially depend on the electrical force of attraction described byCoulombs law.


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We looked at ionic substances, which are typicallyhighmelting solids. Many substances, however, aremoleculargases, liquids, or lowmelting solids consistingof molecules. A molecule is a group of atoms, frequently

nonmetal atoms, stronglylinked bychemical bonds. Oftenthe forces that hold atoms together in a molecular substancecannot be understood on the basis of the attraction ofoppositely charged ions (the ionic model). An obviousexample is the molecule H2, in which the two H atoms are

held together tightly and no ions are present. In 1916 GilbertNewton Lewis proposed that the strong attractive forcebetween two atoms in a molecule results from a covalentbond, a chemical bond formed by the sharing of a pair ofelectrons between atoms.


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Consider the formation of a covalent bond between two H atoms to givethe H2 molecule. As the atoms approach one another, their 1s orbitals beginto overlap. Each electron can then occupythe space around both atoms. In

other words, the two electrons can be shared bythe atoms. The electronsare attracted simultaneously bythe positive charges of the two hydrogennuclei. This attraction that bonds the electrons to both nuclei is the forceholding the atoms together. Although ions do not exist in H2, the force thatholds the atoms together can still be regarded as arising from the attractionofoppositelycharged particles: nuclei and electrons.


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The Lewis theoryofcovalent bonding may be regarded as an elementaryform of valence bond theory. It is nonetheless useful for describingcovalent molecules with simple covalent bonds, and works successfully indescribing the majorityof, for example, organic compounds.Although main group elements tend to adopt inert gas configurations,

which may be represented byeight valence electrons (an octet), or twoin the case of helium, a number of elements are energetically stablewith incomplete octets. The most commonly cited example is boron,which is stable with six valence electrons as in BF3, or Be with four as inBeCl2. Larger elements are capable of hypervalency, where it isenergeticallyfavorable for more than eight valence electrons to be held

in an expanded octet. Examples of this are PF5 (ten valence electrons)and XeF4 (twelvevalence electrons)


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Aluminum chloride, AlCl3, offers an interesting study in bonding. Atroom temperature, the substance is a white, crystalline solid and an ioniccompound, as might be expected for a binarycompound of a metal and a

nonmetal. However, the substance has a relatively low melting point(192rC) for an ionic compound. Apparently this is due to the fact thatinstead ofmelting to a liquid of ions, as happens with most ionic solids,the compound forms Al2Cl6 molecules, with Lewis formula

Each atom has an octet of electrons around it. Note that two of the Clatoms are in bridge positions, with each Cl atom having two covalent bonds.When this liquid is heated, itvaporizes as Al2Cl6 molecules. As thevapor isfurther heated, these molecules break up into AlCl3 molecules. Thesemolecules have an electron structure similartothat ofBF3.


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Write the Lewis formula that best describes the charge distribution inthe sulfuric acid molecule, H2SO4, according to the rules of formalcharge.


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Bond length (or bond distance) is the distance between the nuclei in abond. Bond lengths are determined experimentally using x-raydiffractionor the analysis ofmolecular spectra.

In manycases, bond lengths for covalent single bonds in compounds canbe predicted from covalent radii. Covalent radii are values assigned to

atoms in such a way that the sum of covalent radii of atoms A and Bpredicts an approximate AB bond length.

Thus, the radius ofthe Cl atom might be taken to be halfthe ClCl bondlength (198 pm). The covalent radius ofCl would be 12 198 pm 99 pm.To predict the bond length ofCCl, you add the covalent radii ofthe twoatoms, C and Cl. You get (77 +99) pm 176 pm, which compares favorably

withtheexperimentalvalue of 178 pm found in most compounds.


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The bond order, defined in terms of the Lewis formula, is thenumber of pairs ofelectrons in a bond. For example, in C : C the bondorder is 1 (single bond); in C : : C the bond order is 2 (double bond).Bond length depends on bond order. As the bond order increases, the

bond strength increases and the nuclei are pulled inward, decreasingthe bond length. Look at carboncarbon bonds. The average CC bondlength is 154 pm, whereas C=C is 134 pm long and C|C is 120 pm long.


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We define the AOB bond energy(denoted BE) as the averageenthalpy change for the breakingof an AB bond in a molecule in thegas phase.

For example, to calculate a value forthe CH bond energy, or BE(CH), you might look at theexperimentally determinedenthalpychange for the breaking of

all the C

H bonds in methane:


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Valence shell electron pair repulsion (VSEPR) theory is an elementaryapproach to explaining the shapes ofmolecules. The theorytreats eachatom in a molecule in isolation, and describes the geometry of thebonds and non-bonding electron pairs around it. The basic assumptionis that the electron pairs around an atom, both bonding and non-bonding, will adopt a geometrywhich will minimize repulsive forces bymaximizing the distances between pairs.

The precise geometryof electron pairs around a central atom dependsfirstly upon the number ofelectron pairs which are present. For certainnumbers ofelectron pairs (2, 3, 4, 6), it is possible to adopt a geometry

in which the pairs are equidistant. For atoms with 5 or 7 electron pairs,this is not possible, and t h e maximum separation involves somecompromise.


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The basic geometry is modified bythe variations in repulsion strengthsbetween the electron pairs. Because the charge in bonding pairs issomewhat offset by the presence of the bonded nuclei, the repulsion

increases in the order:bonding pair : bonding pair < non-bonding pair : bonding pair < non-bonding pair : non-bonding pair


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The VSEPR model is usually a satisfactory methodfor predicting molecular geometries. To understandbonding and electronic structure, however, you mustlook to quantum mechanics. We will consider twotheories stemming f rom quantum mechanics:VALENCE BOND THEORY and MOLECULARORBITAL THEORY. Both use the methods ofquantum mechanics but make different simplifying

assumptions.


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It is a fundamental requirement that the electrons in themolecular orbital are indistinguishable, and the simplest

orbital function compatible with this is the Heitler-Londonwavefunction:

=A(1)B(2)+A(2)B(1)


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In the simplest example, that of a hydrogen molecule, the atomic 1sorbitals are the sole contributors to the bond, and the wavefunction takesthe form:

The physical results of this mathematicalexpression are illustrated in Fig. rightsideand below. The resulting bond has

cylindrical symmetry about the bond axis,and is termed a (sigma) bond.


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In elements with accessible p orbitals, such as oxygen or nitrogen, morecomplex bonding may be obtained. The two atomic p orbitals which areparallel to the bonding axis (the pz orbitals, by convention) may be combined

so as to form W bond, but it is also possible for p orbital pairs which areperpendicular to the bonding axis (px on A and B orpy on A and B) to combineto give (pi) bonds. The strength ofthe -bond is significantlyless thanthat ofthe -bond, as the sidelong overlap ofthe p orbitals is less than thatofthe direct overlap


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The valence electron configuration of silicon, 3s23px13py

1 , for example,suggests a valency of two arising from the two singlyoccupied p orbitals. The

valency in fact increases through promotion, i.e. raising an electron into ahigher energy orbital. This process breaks up an electron pair to give twoadditional unpaired electrons, and so increases the valency bytwo. In thecase of silicon, promotion of an electron from the 3s to the 3p orbital resultsin a tetravalent configuration of 3s13px

13py13pz

1.

In all cases, the energy required for promotion of the electron must beoffset bythe energyrecouped in forming two additional chemical bondsforthis process to occur.


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The valence bond approach is broadlysuccessful in predicting the number ofavailable bonds, but is very unsatisfactory inits abilityto predict the shape ofmolecules.In a commonl y used example, the basic

theory predicts that the bonding in water,H2O, would consist of two -bonds formedfrom pairing of electrons in the hydrogen 1s1

orbitals and two oxygen p orbitals. As theatomic p orbitals are orthogonal, valence

bond theory predicts that the resulting -bonds are at 90 to one another. In fact, theinter-bond angle is closer to 104. Thedeviation of actual bond angles from theangles between pure atomic orbitals isaccounted for byhybridization.


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H ybridization is the process ofcombining pure atomic orbitals so as tocircumvent the rigid geometry which thepure orbitals require. In this way, valencebond theory becomes far more able toaccount for molecular shapes. The pureorbital functions have both negative andpositive signs. By directly combining the

atomic orbitals, these negative and positiveregions are added so as to enhance theamplitude of the resulting orbitals in somedirections, and to diminish their amplitudein others. The resulting combinations ofpureorbitals are termed hybrid orbitals.


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Describe the bonding on a given N atom in

dinitrogen difluoride, N2F2, using valencebond theory.


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Other hybridization schemes, particularly those involving dorbitals, are often invoked in elementarywork to be consistentwith other molecular geometries


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In MO theory, it is accepted that electrons should not be regarded asbelonging to particular bonds but should be treated as spreadingthroughout t h e entire molecule. This theory has been more fullydeveloped than VB theory and provides the language that is widely usedin modern discussions of bonding.


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Unlike atomic wavefunctions, the molecular wavefunction mustdescribe the relative motion of nuclei in addition to the motion of theelectrons. Primarily because oftheirrelative masses, the electrons move

some 103 times faster than the nucleus, and the Born-Oppenheimerapproximation simplifies the calculation of molecular orbitals byassuming that the nuclei are stationary relative to the motion of theelectron. This approximation allows the internuclear repulsion terms tobe treated completely separately from the electrostatic behavior of the

electrons.

The one-electron wavefunctions obtained by solving the Schrdingerequation H = E are called molecular orbitals (MO). A molecularorbital gives, through the value of ||2, the distribution of theelectron in the molecule. Amolecular orbital is like an atomic orbital,but spreads throughout the molecule.


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The Schrdinger equation can be solved analytically for H2+ (within the

BornOppenheimer approximation), but the wavefunctions are verycomplicated functions; moreover, the solution cannot be extended to

polyatomic systems. Molecular orbital theory therefore makes theapproximation that the molecular orbitals may be formed bythe LINEARCOMBINATION OF ATOMIC ORBITALS (LCAO). We adopt a simplerprocedure that, while more approximate, can be extended readilyto othermolecules.


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The wavefunctions for two electrons, (A) and (B), in theatomic orbitals on two atoms, A and B r espectively, arecombined to form a molecular orbital. The molecular

orbital wavefunction is given by:

where cm is a mixing coefficient, which is calculated for

each orbital so as to minimize the molecular energy ascalculated using the Schrdinger equation. It is a furtherrequirement that the mixing coefficients should benormalized, so that .

When the bond is formed between two identical nuclei therecan be no distinction between the nuclei, and so the mixingcoefficients (and therefore the orbital contributions), areequal.


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If an electron can be found in an atomicorbital belonging to atom A and also inan atomic orbital belonging to atom B,then the overall wavefunction i s asuperposition ofthe two atomic orbitals: = N(A B) where, for H2

+, A denotesH1s A, B denotes H1sB, and N i s a

normalization factor.

The technical term for the superpositionin eqn above is a linear combinationof atomic orbitals (LC AO). An

approximate molecular orbitalformed from a linear combination ofatomic orbitals is called an LCAO-MO.


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Bonding orbitals:According to the Born interpretation, theprobability density of the electron in H2

+ isproportional to the square modulus of its

wavefunction. The probability densitycorresponding to the (real) wavefunction + is

P(r) = N2

[(A)+(B)]2

= N2[(A)2 +(B)2 +2(A)(B)]


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An important feature of the probabilitydensity becomes apparent when weexamine the internuclear region, where both atomic orbitals have similaramplitudes. According to eqn above, the total probability densit y isproportionaltothe sum of1. (A)2, the probability density if the electron were confined to the atomic

orbital A. 2. (B)2, the probability density if the electron were confined to the atomic

orbital B.3. 2(A)(B), an extra contribution to the density.

This last contribution, the overlap density, iscrucial, because it represents an enhancement ofthe probability of finding the electron in theinternuclear region.The bonding orbital in H2, which we have just

described, is denoted W1s. The W (sigma) means thatthe molecular orbital has a cylindrical shape aboutthe bond axis. The subscript 1s tells us that themolecular orbital was obtained from 1s atomicorbitals.


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Antibonding OrbitalsThe linear combination corresponds to ahigher energythan that of+. Because it is

also a orbital we label it *. This orbitalhas an internuclear nodal plane where (A)and (B) cancel exactly. The probabilitydensity is P(r) = N 2[(A)2 + (B)2 2(A)(B)].

There is a reduction in probabilitydensitybetween the nuclei due to the 2(A)(B)term; in physical terms, there is destructiveinterference where the two atomic orbitalsoverlap. The * orbital is an example of anantibonding orbital, an orbital that, if

occupied, contributes to a reduction in thecohesion between two atoms and helps toraise the energyofthe molecule relative tothe separated atoms.


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(4) Molecular Structure

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