Chem 115 POGIL Wrksheet - Week 12 Mlecular Shapes Why? Cntrary t the impressin that Lewis structures may give, many mlecules have threedimensinal gemetries. These mlecular shapes are very imprtant t understanding hw mlecules interact with each ther, bth chemically and physically. Althugh the Lewis structures themselves d nt cnvey shape infrmatin, they can be used as the starting pint fr applying a cnceptually simple but pwerful apprach t predicting mlecular gemetries. This methd is called the Valence Shell Electrn Repulsin Thery, r VSEPR fr shrt. Knwing the shape f a mlecule enables us t predict whether r nt it has an electrical plarity, which is an imprtant prperty determining hw the species interacts with ther mlecules. Learning Objective Understand the basis f the VSEPR thery. Knw the expected gemetries fr ne thrugh six electrn dmains abut a central atm Understand hw bnd pairs and lne pairs abut a central atm interact t prduce the mlecular shape Knw hw bnd plarity and mlecular shape cmbine t make a mlecule plar r nnplar. Success Criteria Be able t use a Lewis structure and VSEPR thery t predict the shape f mlecules Be able t sketch the shapes f simple mlecules Be able t name electrn dmain and mlecular shape gemetries f simple mlecules Be able t predict whether a particular mlecule is plar r nnplar Prerequisite Have read sectins 9.1-9.3.
Infrmatin (Basic Dmain Shapes frm VSEPR Thery) One f the mst successful appraches t predicting the shapes f mlecules is based almst slely n cnsideratins f hw best t minimize electrn-pair repulsins abut a central atm. This apprach, which was riginated by Nyhlm and Gillespie in the 1950's, has becme knwn 1 as the Valence Shell Electrn Pair Repulsin Thery, r VSEPR. thery. The fundamental premise f this thery can be stated as fllws: Electrns in bnded atms ccupy spatially riented rbitals in such a way as t minimize electrn-electrn repulsins arising mainly frm electrstatic (culmbic) frces. The apprach is remarkably accurate in predicting the basic shapes f mlecules f nntransitin elements, althugh sme details f bnd angle and bnd length are nt well explained by electrn repulsin alne. At this pint we will nt be cncerned with the identity f the spatially riented rbitals. Hwever, assuming that such rbitals are available, we can determine fr varius numbers f pairs f electrns abut a central atm the mst favrable electrn pair gemetry t minimize electrn-electrn repulsins. T illustrate the apprach, let us cnsider a number f mlecules in which all f the valence electrns abut the central atm are engaged in bnd frmatin with uter-lying (pendant) atms. Cnsider BeCl, fr which the Lewis dt structure is 2 There are tw pairs f electrns arund the central Be atm. If they are riented 180 frm each ther their repulsins will be minimized. Therefre, the best electrn pair gemetry fr tw pairs is a linear arrangement. Bth pairs are invlved in frming single bnds in BeCl 2, s the resulting mlecular gemetry r shape f the mlecule is als linear. Cnsider BCl 3, fr which the Lewis dt structure is This has three pairs arund the central B atm. Electrn-pair repulsins are minimized by placing these three pairs at 120 apart in a plane, called a trignal planar arrangement. All three 1 Mre recently, Gillespie has prpsed renaming this Electrn Dmain Thery r ED thery, but mst chemists persist in calling it VSEPR thery. See R. J. Gillespie. J. Chem. Educ. 1992, 69, 116.
pairs are invlved in bnd frmatin, s the mlecular shape is trignal planar, as a result f the electrn pair gemetry. Cnsider methane, CH 4, fr which the Lewis dt structure is Cntrary t what this mdel seems t suggest, a square planar arrangement f the fur pairs abut carbn is nt the best fr minimizing electrn repulsins. By assuming the threedimensinal tetrahedral arrangement, the pairs will be in psitins 109.5 apart. Thus methane is tetrahedral. Given the prevalence f an ctet abut a central atm, this electrn pair gemetry ccurs in many cmpunds. It is a highly symmetrical arrangement in which all fur psitins are equivalent. When representing this three-dimensin structure in a tw-dimensinal sketch, we ften emply drawings such as the fllwing:: The slid lines are psitins in the plane f the page. The slid wedge is a psitin cming ut f the plane f the page, and the dtted line is a psitin ging back belw the plane f the page. It is imprtant t realize that regardless f the drawing, any psitin is surrunded by three thers, all making an angle f 109.5 t each ther. N psitin is acrss frm any ther, as culd be the case in a square planar arrangement. Cnsider PCl 5. This is a case f hypervalence, with five pairs f electrns abut the central atm. The best electrn pair gemetry is a trignal bipyramid. 2 A trignal bipyramid has tw kinds f psitins, which are nt equivalent t each ther. The tw axial psitins make a 180 angle t each ther and a 90 t the plane f the three equatrial psitins. The equatrial psitins frm a 120 angle between each ther. equivalent. 2 This is the nly basic gemetry we will cnsider in which all psitins are nt
Cnsider SF 6, a hypervalent mlecule with six pairs abut the central sulfur atm. The best electrn pair gemetry is achieved by placing all pairs at 90 t ne anther, as with the axes f a Cartesian crdinate system. This arrangement is ctahedral. Unlike the trignal bipyramid, all psitins in the ctahedrn are equivalent. Electrn pairs invlved in multiple bnd frmatin ccupy the same regin f space. Therefre, all pairs in a duble r triple bnd functin in the same way as a single pair in determining gemetry. Fr this reasn, we shuld lk at the number f electrn dmains abut the central atm, rather than the number f electrn pairs, particularly when multiple bnds are invlved. Fr example, frmaldehyde, H2CO, has the fllwing Lewis structure, with three electrn dmains arund the central atm Althugh there are fur pairs abut the central carbn atm, they are gruped int nly three dmains, tw fr single C H bnds and a third fr the C=O bnd. The best arrangement t minimize repulsins is trignal planar. All bnd angles will nt be perfectly 120. The larger xygen atm frces the tw hydrgen atms tgether slightly, s that the H-C-H angle is smewhat less than 120. Similarly, HCN is a linear mlecule because the fur pairs arund the central carbn atm are arranged in tw dmains:
H C N: The shapes f mlecules that are resnance hybrids can be deduced frm any ne f the hypthetical resnance frms. Fr example, any ne f the three principal resnance frms f the nitrate in shws fur pairs arund the central nitrgen atm arranged in three dmains: Recall that in resnance frms like these, there are n real duble bnds, and all the N O bnds are equivalent (bnd rder f 1a). Therefre, the structure f the nitrate in is truly trignal planar, with 120 O N O angles. Key Questins 1. Give the names fr the shapes f the dmain gemetries fr tw thrugh six regins f electrn density abut a central atm. 2. Draw Lewis structures fr the fllwing mlecules, and predict the the shapes n the basis f VSEPR cnsideratins: SnH, CO, AsF, Cl CO. 4 2 5 2 Infrmatin (Shapes f Mlecules with Lne Pairs) In many mlecules sme pairs f valence electrns arund the central atm may be nn-bnding lne pairs. In these cases, the electrn dmain arrangements will be the same fr the ttal number f electrn pairs, but the mlecular shape will be different. Keep in mind that the shape f a mlecule refers t the gemetrical arrangement f its atms, nt the dmain gemetry f its electrn pairs. Hwever, the resulting shape fr mlecules with lne pairs n the central atm will be based n the electrn dmain gemetries we have just seen. Bnd angles in these mlecules will ften deviate frm the ideal angles f the electrn dmain gemetries. This is the result f differences in the strengths f repulsins between electrns invlved in bnd frmatin and thse that are nt. In general, the strengths f electrn pair repulsins decline in the rder lne pair - lne pair > lne pair - bnd pair > bnd pair - bnd pair When adding lne pairs in electrn dmain gemetries in which all psitins are equivalent the arrangement that clearly minimizes lne pair - lne pair repulsin results. We will nt g thrugh every pssible shape here, but the case f NH 3 serves t illustrate the effects f lne pair - bnd pair repulsins n the resulting shape. The Lewis dt structure is shwn belw:
With fur dmains abut the central N atm, the electrn dmain gemetry is tetrahedral. But the shape f the mlecule cannt be described as tetrahedral, because there are nly three bnds. The cmbinatin f three bnd pairs and ne lne pair (3 b.p. + 1 l.p.) results in a tripd-like arrangement f the atms, called a trignal pyramid. The lne-pair - bnd-pair repulsins, being strnger than bnd-pair repulsins, cause all H N H angles t clse dwn frm the ideal 109.5 f the tetrahedrn, becming ~107 in ammnia. Cases invlving five dmains abut a central atm require sme care in placing any lne pairs. Such hypervalent structures are all based n a trignal bipyramidal (tbp) gemetry f the electrn dmains. But as we previusly nted, there are tw kinds f psitins fr tbp: axial and equatrial. Fr mst cases in which the central atm is a main-grup element, the axial psitins are smewhat lnger than the equatrial psitins. A lne pair is assciated with nly ne nucleus, whereas a bnd pair is assciated with tw. Therefre, in structures based n a tbp dmain gemetry, any lne pair will be clser t the ne nucleus with which it is assciated if it is in ne f the shrter equatrial psitins. Therefre, when building shapes based n a tbp dmain gemetry, always place the lne pairs in the equatrial psitins. SF 4 illustrates the effect n shape f placing a lne pair in an equatrial psitin f a tbp dmain gemetry. Withut careful cnsideratin, SF 4 might seem t be a tetrahedral mlecule, but as the Lewis dt structure shws it is a hypervalent case with five electrn dmains..
This is a case f 4 b.p. + 1 l.p. Placing the lne pair in an equatrial psitin results in the fllwing mlecular shape, with the rientatin f the mlecule flipped in the secnd sketch: When flipped, as shwn n the right, the shape resembles a playgrund see-saw with the tw equatrial-type psitins functining as the fulcrum and the tw axial-type psitins frming the plank. The fficial name f this is irregular tetrahedrn, althugh mathematicians call the 3 related slid plygn a disphenid. Nte that SF 4 has tw kinds f bnds with tw different lengths: the tw axial bnds f the tbp and the tw remaining equatrial bnds f the tbp. The lne-pair repulsins cause the angle between the tw axial-type bnds t be less than 180, and cause the angle between the tw equatrial-type bnds t be less than 120. The table in Appendix A summarizes the expected shapes fr all cmbinatins f bnd pairs (b.p.) and lne pairs (l.p.) fr tw thrugh six electrn dmains (ED). All f these shapes are illustrated in Tables 9.2 and 9.3 f yur text. Be sure that yu becme s familiar with all the pssibilities that yu d nt need t refer t Appendix A r a similar table t determine the shape f a mlecule by VSEPR thery. Anther useful way t rganize yur thinking abut mlecular gemetries is t cnsider what the pssible shapes are fr a certain number f pendant atms attached t a central atm. This helps rule ut impssible shapes at the start. The table in Appendix B rearranges the infrmatin in Appendix A n the basis f mlecular frmulas. Fr example, if a mlecule has a frmula MX 2, the fact that it is cmpsed f nly three atms means that they are either all aligned (linear) r they are nt (bent), regardless f the dmain gemetry that gave rise t the shape. N ther shapes are pssible. It makes n sense t say that a mlecule with a frmula MX 2 is trignal planar, tetrahedral, r trignal bipyramidal just because we can identify three, fur, r five dmains abut the central M atm. The first tw cases wuld be bent, and the last wuld be linear. Beynd this, we shuld expect a X M X angle slightly less than 120 if the shape is based n three dmains, and slightly less than 109.5 if based n fur dmains. 3See www.math.clumbia.edu/~zare/disphenid.html
Key Questins 3. Fr each f the fllwing mlecules r ins, sketch the shape and name it. Yu shuld start with a valid Lewis structure in each case, befre applying VSEPR cnsideratins. + SeCl 4, I 3, PSCl 3, IF 4, IF 4, PH 2, N 3, PH4 4. Describe the structure and bnding f the nitrite in, NO 2. Infrmatin (Mlecular Plarity and Diple Mments) The plarity f a mlecule is measured as its diple mment, defined as ì = äd + where ì is the diple mment, ä is the charge n each end f the mlecule (ä and ä ), separated acrss the mlecule by a distance d. The units f diple mment are the debye (D), defined as -3 3.34 x 10 C m. (C = culmb) In a diatmic mlecule the charges, which are generally much less than unit charges, reside n the tw atms and d is their internuclear separatin (bnd length). Fr a diatmic mlecule the mdel is smething like the fllwing: Fr heternuclear diatmic mlecules, the bnd has plarity, s the mlecule will have a diple mment. Thus, all heternuclear diatmic mlecules are plar. All hmnuclear diatmic mlecules have n diple mment. The fllwing data illustrate: Mlecule ì Mlecule ì H-H 0 D H-F 1.82 D F-F 0 D H-Cl 1.08 D Cl-Cl 0 D H-I 0.44 D Fr plyatmic mlecules, plarity depends n bth shape and cmpsitin. A mlecule is nnplar when all individual bnd plarities are cunterbalanced by ther identical bnd plarities. A mlecule is plar when any ne f its individual bnd plarities is nt cunterbalanced by identical bnd plarities. Lack f cunter balancing plarities may result frm a less symmetrical shape (shape). Lack f cunterbalancing plarities als may result frm
a unique bnd in the mlecule, having a different bnd strength r bnding t a different element (cmpsitin). In highly symmetric binary mlecules (tw elements), individual bnd plarities may cancel, leaving the mlecule with n net diple mment, as in all f the fllwing cases. If a binary mlecule has a gemetry that gives it a sense f up r dwn r right and left it is plar. If a ternary mlecule has its bnds asymmetrically arranged, it may be plar even thugh its shape wuld be nnplar fr a binary mlecule. The fllwing cases have shapes that wuld be nnplar fr binary mlecules but which are plar because there are tw different kinds f bnds arund the central atm that are nt symmetrically arranged.
Key Questins 5. Fr all the mlecules r ins whse shapes yu determined in Key Questin 3. indicate whether r nt the species is plar. 6. Cnsider the fllwing Lewis structures fr sme simple rganic cmpunds. (Lne pairs n pendant atms have been mitted fr simplicity.) Redraw each f these n the basis f VSEPR cnsideratins, and indicate whether r nt the mlecule is plar. 4 7. A certain cmpund with a frmula AB is fund t be plar. Mrever, it is determined that there are tw different bnd lengths, tw lng nes and tw shrt nes. What is the prbable shape f the mlecule? Explain yur reasning.
Appendix A: Shapes f Mlecules fr Varius Electrn Dmain (ED) Gemetries ED Dmain Gemetry Bnd Dmains Lne Pairs Mlecular Shape Examples 2 linear 2 0 linear MX2 BeF 2, CO2 3 trignal planar 3 0 trignal planar MX3 BF 3, NO 3 2 1 bent MX 2 (<120 ) SnCl 2, NO2 4 tetrahedral 4 0 tetrahedral MX4 CH4 3 1 trignal pyramidal MX3 NH3 2 2 bent MX 2 (<109.5 ) H2O 5 trignal bipyramidal 5 0 trignal bipyramidal MX5 PCl5 4 1 irregular tetrahedrn MX4 SF4 3 2 T-shaped MX3 ClF3 2 3 linear MX2 XeF2 6 ctahedral 6 0 ctahedral MX6 SF6 5 1 square pyramid MX5 IF5 4 2 square planar MX4 XeF4 Nte: In this table, bnd means a linkage between tw atms in a mlecule. Thus, a single-, duble-, r triple-bnd cnstitutes nly ne bnd.
Appendix B: Pssible Shapes f Mlecules with Frmulas MX n, n = 2 6 Frmula Case Shape Example MX2 2 bnds + 0 lne pairs linear BeF2 2 bnds + 1 lne pair bent (<120 ) SnCl 2 2 bnds + 2 lne pairs bent (<109.5 ) H2O 2 bnds + 3 lne pairs linear XeF 2 MX3 3 bnds + 0 lne pairs trignal planar BF3 3 bnds + 1 lne pair trignal pyramidal NH 3 3 bnds + 2 lne pairs T-shape ClF 3 MX4 4 bnds + 0 lne pairs tetrahedral CH4 4 bnds + 1 lne pair irregular tetrahedrn SF 4 4 bnds + 2 lne pairs square planar XeF 4 MX5 5 bnds + 0 lne pairs trignal bipyramid (tbp) PF5 5 bnds + 1 lne pair square pyramid IF 5 MX6 6 bnds + 0 lne pairs ctahedral SF6 Nte: In this table, bnd means a linkage between tw atms in a mlecule. Thus, a single-, duble-, r triple-bnd cnstitutes nly ne bnd.