[{"data":1,"prerenderedAt":196},["ShallowReactive",2],{"topic-molecular-geometry-and-bonding-theories":3},{"topic":4,"prev":181,"next":188},{"id":5,"slug":6,"title":7,"shortTitle":8,"lesson":5,"category":9,"description":10,"metaDescription":11,"objectives":12,"conceptSections":25,"workedExample":94,"oerSources":104,"selfStudyQuestions":108,"relatedTopicSlugs":137,"relatedElements":140,"relatedReferences":146,"howTo":148,"conceptProbe":157,"practiceTeaser":161,"gatedContent":168,"seoKeywords":171,"lastAlignmentAudit":179,"objectiveCount":180},15,"molecular-geometry-and-bonding-theories","Molecular Geometry and Bonding Theories","Molecular Shape","bonding-structure","Predict molecular geometry using VSEPR theory, determine polarity, understand hybridization with sigma and pi bonds, and build molecular-orbital diagrams to find bond order and magnetism.","Predict molecular geometry with VSEPR theory. Determine molecular polarity, bond angles, and hybridization (sp, sp2, sp3). Free chemistry study guide.",[13,16,19,22],{"id":14,"text":15},"15.1","Use VSEPR theory to predict electron-pair geometry and molecular geometry from a Lewis structure",{"id":17,"text":18},"15.2","Predict whether a molecule is polar or nonpolar from its geometry and bond polarity",{"id":20,"text":21},"15.3","Determine the hybridization of a central atom (sp, sp², sp³, sp³d, sp³d²) and use it to count sigma and pi bonds in single, double, and triple bonds",{"id":23,"text":24},"15.4","Construct molecular orbital (MO) diagrams for homonuclear diatomics, calculate bond order, and use the configuration to predict magnetism",[26,35,43,51,60,69,77,86,90],{"heading":27,"content":28,"relatedObjectives":29,"deepDive":31},"VSEPR Theory Overview","\u003Cp>\u003Cstrong>VSEPR\u003C/strong> (Valence Shell Electron Pair Repulsion) theory predicts the three-dimensional shape of a molecule by assuming that electron groups around a central atom repel each other and arrange themselves as far apart as possible to minimize repulsion.\u003C/p>\u003Cp>An \u003Cstrong>electron group\u003C/strong> is any region of electron density bonded to the central atom: a single bond, a double bond, a triple bond, or a lone pair. All of these count equally when determining the arrangement. The number of electron groups around the central atom determines the \u003Cstrong>electron-pair geometry\u003C/strong> — the spatial arrangement of \u003Cem>all\u003C/em> electron groups, including lone pairs.\u003C/p>\u003Cp>To apply VSEPR: (1) draw the Lewis structure, (2) count electron groups on the central atom, (3) identify the electron-pair geometry, and (4) name the molecular geometry based on the positions of the \u003Cem>atoms\u003C/em> only (ignoring lone pairs in the name).\u003C/p>\u003Cp>For a polyatomic \u003Cem>ion\u003C/em>, account for the overall charge before counting electron groups: add one electron per unit of negative charge or remove one per unit of positive charge to the total valence-electron pool, then build the Lewis structure on that adjusted count. The ICl\u003Csub>4\u003C/sub>\u003Csup>−\u003C/sup> ion, for example, ends up with 12 valence electrons around iodine (4 bonding pairs + 2 lone pairs = 6 electron groups), giving an octahedral electron-pair geometry and a square-planar molecular geometry once the two lone pairs are placed trans to each other.\u003C/p>",[30],116,[32],{"label":33,"body":34},"Why this matters: drugs work by shape","\u003Cp>A medicine molecule works by fitting a target protein the way a key fits a lock, and the key’s cut is exactly what VSEPR predicts: the three-dimensional arrangement of atoms. Pharmaceutical chemists routinely design molecules around a shape first and a formula second, because two compounds with identical formulas but different geometries can be a cure and a dud. Your nose runs on the same principle: receptor proteins respond to molecular shapes and charge distributions. The two-dimensional Lewis structures of the previous topic were the wiring diagram; this topic builds the actual sculpture.\u003C/p>",{"heading":36,"content":37,"relatedObjectives":38,"deepDive":39},"Electron-Pair and Molecular Geometries","\u003Cp>The five fundamental electron-pair geometries correspond to 2 through 6 electron groups:\u003C/p>\u003Ctable>\u003Cthead>\u003Ctr>\u003Cth>Electron Groups\u003C/th>\u003Cth>Electron-Pair Geometry\u003C/th>\u003Cth>Ideal Bond Angles\u003C/th>\u003C/tr>\u003C/thead>\u003Ctbody>\u003Ctr>\u003Ctd>2\u003C/td>\u003Ctd>Linear\u003C/td>\u003Ctd>180°\u003C/td>\u003C/tr>\u003Ctr>\u003Ctd>3\u003C/td>\u003Ctd>Trigonal planar\u003C/td>\u003Ctd>120°\u003C/td>\u003C/tr>\u003Ctr>\u003Ctd>4\u003C/td>\u003Ctd>Tetrahedral\u003C/td>\u003Ctd>109.5°\u003C/td>\u003C/tr>\u003Ctr>\u003Ctd>5\u003C/td>\u003Ctd>Trigonal bipyramidal\u003C/td>\u003Ctd>90° and 120°\u003C/td>\u003C/tr>\u003Ctr>\u003Ctd>6\u003C/td>\u003Ctd>Octahedral\u003C/td>\u003Ctd>90°\u003C/td>\u003C/tr>\u003C/tbody>\u003C/table>\u003Cp>When all electron groups are bonding pairs, the molecular geometry matches the electron-pair geometry. When lone pairs are present, the molecular geometry is a subset: for example, four electron groups with one lone pair give a \u003Cstrong>trigonal pyramidal\u003C/strong> shape (NH\u003Csub>3\u003C/sub>), and four groups with two lone pairs give a \u003Cstrong>bent\u003C/strong> shape (H\u003Csub>2\u003C/sub>O).\u003C/p>",[30],[40],{"label":41,"body":42},"Prove the five geometries with balloons","\u003Cp>Tie two, three, four, five, or six balloons together at their necks and let go: they settle, on their own, into a line, a flat triangle, a tetrahedron, a trigonal bipyramid, and an octahedron. Nothing chemical is happening; each balloon simply shoves the others as far away as it can, and those five shapes are the geometric solutions to “maximize the angles between N crowded things.”\u003C/p>\u003Cp>That is the entire content of VSEPR: electron groups behave like the balloons. The five geometries are not chemistry facts to memorize but geometry facts that electron repulsion is forced to obey, which is why the same table works for every central atom in the periodic table.\u003C/p>",{"heading":44,"content":45,"relatedObjectives":46,"deepDive":47},"The Effect of Lone Pairs on Shape","\u003Cp>Lone pairs occupy more space than bonding pairs because they are held closer to the nucleus and spread out more broadly. This extra repulsion \u003Cstrong>compresses\u003C/strong> bond angles below their ideal values. In methane (CH\u003Csub>4\u003C/sub>), all four groups are bonding and angles are 109.5°. In ammonia (NH\u003Csub>3\u003C/sub>), one lone pair pushes the three N–H bonds closer together, reducing the angle to about 107°. In water (H\u003Csub>2\u003C/sub>O), two lone pairs compress the H–O–H angle further to about 104.5°.\u003C/p>\u003Cp>For five electron groups, removing bonding pairs in favor of lone pairs produces progressively distorted shapes: \u003Cstrong>seesaw\u003C/strong> (4 bonds, 1 lone pair), \u003Cstrong>T-shaped\u003C/strong> (3 bonds, 2 lone pairs), and \u003Cstrong>linear\u003C/strong> (2 bonds, 3 lone pairs). For six groups: \u003Cstrong>square pyramidal\u003C/strong> (5 bonds, 1 lone pair) and \u003Cstrong>square planar\u003C/strong> (4 bonds, 2 lone pairs). Lone pairs preferentially occupy equatorial positions in trigonal bipyramidal systems because equatorial sites have more room.\u003C/p>",[30],[48],{"label":49,"body":50},"Common mistake: naming the shape after the invisible pairs","\u003Cp>Water’s four electron groups adopt a tetrahedral \u003Cem>electron-pair\u003C/em> geometry, so students answer “tetrahedral” when asked for its shape. But molecular geometry names the arrangement of \u003Cem>atoms\u003C/em> only, and water’s three atoms form a bent shape. The lone pairs dictate the geometry from backstage, compressing the angle to 104.5°, but they never appear in the shape’s name.\u003C/p>\u003Cp>Keep the two questions separate: electron-pair geometry counts every group (it sets the angles and the hybridization); molecular geometry describes what a microscope would see. Exams love the gap between the two, and so do the ammonia (trigonal pyramidal, not tetrahedral) and SO\u003Csub>2\u003C/sub> (bent, not trigonal planar) classics.\u003C/p>",{"heading":52,"content":53,"relatedObjectives":54,"deepDive":56},"Molecular Polarity","\u003Cp>A molecule is \u003Cstrong>polar\u003C/strong> if it has a net dipole moment — an overall uneven distribution of electron density. Two conditions must both be met:\u003C/p>\u003Col>\u003Cli>The molecule must contain \u003Cstrong>polar bonds\u003C/strong> (bonds between atoms with different electronegativities, producing individual bond dipoles). A bond between two identical atoms (H–H, Cl–Cl) is nonpolar by definition. A bond between two \u003Cem>different\u003C/em> elements that happen to share the same Pauling electronegativity value is also nonpolar — H and P, for example, are both assigned a Pauling EN of about 2.1, which is why the H–P bond in PH\u003Csub>3\u003C/sub> is treated as nonpolar. One distinction worth keeping straight: the ΔEN scale used to \u003Cem>classify\u003C/em> bonds (nonpolar covalent below ~0.4, polar covalent up to ~1.7, ionic beyond) answers a different question than the one asked here. A pair like Cl–Br (Δχ ≈ 0.2) falls in the “nonpolar covalent” \u003Cem>bin\u003C/em> on that classification scale, yet the bond still carries a small, real dipole (≈0.6 D) — any nonzero electronegativity difference does. When a problem asks whether a \u003Cem>bond\u003C/em> is polar, it is asking about the dipole: only identical atoms or same-EN pairs give a truly nonpolar bond.\u003C/li>\u003Cli>The molecular geometry must be \u003Cstrong>asymmetric\u003C/strong> so that the individual bond dipoles do not cancel.\u003C/li>\u003C/ol>\u003Cp>Symmetry is the key factor. CO\u003Csub>2\u003C/sub> has two polar C=O bonds, but its linear geometry makes the dipoles point in opposite directions and cancel — the molecule is nonpolar. H\u003Csub>2\u003C/sub>O also has two polar bonds, but its bent shape leaves a net dipole pointing from H toward O — the molecule is polar.\u003C/p>\u003Cp>Similarly, CCl\u003Csub>4\u003C/sub> (tetrahedral, all identical bonds) is nonpolar because of perfect symmetry, while CHCl\u003Csub>3\u003C/sub> (one H replaces a Cl) is polar because the symmetry is broken. Molecular polarity governs many physical properties including boiling point, solubility, and interactions with other molecules.\u003C/p>",[55],115,[57],{"label":58,"body":59},"Why this matters: your microwave oven is a polarity detector","\u003Cp>A microwave oven works because water is polar. The oscillating field reverses direction billions of times per second, and every water molecule, carrying its permanent dipole, keeps twisting to realign; that frantic rotation, jostling neighboring molecules, becomes heat. Nonpolar substances have no handle for the field to grab: a perfectly dry, nonpolar plastic plate stays cool while the food on it steams.\u003C/p>\u003Cp>The same polarity analysis you are doing with arrows on paper decides real material behavior: which solvents mix, which plastics insulate, and why oil refuses to warm in a microwave nearly as fast as soup.\u003C/p>",{"heading":61,"content":62,"relatedObjectives":63,"deepDive":65},"Hybridization of Atomic Orbitals","\u003Cp>\u003Cstrong>Hybridization\u003C/strong> is the mixing of standard atomic orbitals (s, p, d) on a central atom to form a new set of equivalent \u003Cstrong>hybrid orbitals\u003C/strong> oriented to match the observed molecular geometry. The type of hybridization is determined by the number of electron groups:\u003C/p>\u003Ctable>\u003Cthead>\u003Ctr>\u003Cth>Electron Groups\u003C/th>\u003Cth>Hybridization\u003C/th>\u003Cth>Geometry\u003C/th>\u003Cth>Example\u003C/th>\u003C/tr>\u003C/thead>\u003Ctbody>\u003Ctr>\u003Ctd>2\u003C/td>\u003Ctd>sp\u003C/td>\u003Ctd>Linear\u003C/td>\u003Ctd>BeCl\u003Csub>2\u003C/sub>, CO\u003Csub>2\u003C/sub>\u003C/td>\u003C/tr>\u003Ctr>\u003Ctd>3\u003C/td>\u003Ctd>sp\u003Csup>2\u003C/sup>\u003C/td>\u003Ctd>Trigonal planar\u003C/td>\u003Ctd>BF\u003Csub>3\u003C/sub>, C\u003Csub>2\u003C/sub>H\u003Csub>4\u003C/sub>\u003C/td>\u003C/tr>\u003Ctr>\u003Ctd>4\u003C/td>\u003Ctd>sp\u003Csup>3\u003C/sup>\u003C/td>\u003Ctd>Tetrahedral\u003C/td>\u003Ctd>CH\u003Csub>4\u003C/sub>, NH\u003Csub>3\u003C/sub>, H\u003Csub>2\u003C/sub>O\u003C/td>\u003C/tr>\u003Ctr>\u003Ctd>5\u003C/td>\u003Ctd>sp\u003Csup>3\u003C/sup>d\u003C/td>\u003Ctd>Trigonal bipyramidal\u003C/td>\u003Ctd>PCl\u003Csub>5\u003C/sub>\u003C/td>\u003C/tr>\u003Ctr>\u003Ctd>6\u003C/td>\u003Ctd>sp\u003Csup>3\u003C/sup>d\u003Csup>2\u003C/sup>\u003C/td>\u003Ctd>Octahedral\u003C/td>\u003Ctd>SF\u003Csub>6\u003C/sub>\u003C/td>\u003C/tr>\u003C/tbody>\u003C/table>\u003Cp>The quick rule: count all electron groups (bonding \u003Cem>and\u003C/em> lone pairs) on the central atom. Two groups = sp, three = sp\u003Csup>2\u003C/sup>, four = sp\u003Csup>3\u003C/sup>, and so on. Water has four electron groups (2 bonds + 2 lone pairs), so oxygen is sp\u003Csup>3\u003C/sup> hybridized even though its molecular shape is bent.\u003C/p>",[64],117,[66],{"label":67,"body":68},"Hybridization is a patch, and a brilliant one","\u003Cp>Carbon’s ground-state configuration (two paired 2s electrons, two unpaired 2p) predicts an atom that forms two bonds at right angles. Methane laughs at that prediction: four bonds, all identical, at 109.5°. Hybridization is the repair: mix the one s and three p orbitals into four equivalent sp\u003Csup>3\u003C/sup> hybrids pointing at tetrahedral corners, and the observed molecule reappears.\u003C/p>\u003Cp>Notice the direction of the logic: the geometry is the experimental fact, and hybridization is chosen to match it, not the other way around. That is why the recipe is “count electron groups, then assign hybridization” and never “derive the shape from hybridization first.”\u003C/p>",{"heading":70,"content":71,"relatedObjectives":72,"deepDive":73},"Sigma and Pi Bonds","\u003Cp>Hybrid orbitals form \u003Cstrong>sigma (σ) bonds\u003C/strong> — bonds with electron density concentrated directly between the two nuclei along the internuclear axis. Every single bond is a sigma bond, and every double or triple bond contains exactly one sigma bond.\u003C/p>\u003Cp>The additional bonds in a double or triple bond are \u003Cstrong>pi (π) bonds\u003C/strong>, formed by the side-by-side overlap of unhybridized p orbitals. A double bond consists of one σ bond + one π bond. A triple bond consists of one σ bond + two π bonds.\u003C/p>\u003Cp>In ethylene (C\u003Csub>2\u003C/sub>H\u003Csub>4\u003C/sub>), each carbon is sp\u003Csup>2\u003C/sup> hybridized with three sigma bonds (two C–H and one C–C). The remaining unhybridized p orbital on each carbon overlaps to form the pi bond, locking the molecule into a planar geometry. Pi bonds prevent rotation around the bond axis, which is why geometric (cis/trans) isomerism occurs in molecules with C=C double bonds.\u003C/p>\u003Cp>\u003Cstrong>Different atoms can have different hybridizations.\u003C/strong> When a molecule contains atoms with different electron-group counts, each atom's hybridization is determined independently from its own count. Propyne (H\u003Csub>3\u003C/sub>C–C≡CH) has an sp\u003Csup>3\u003C/sup> methyl carbon (4 single bonds → 4 electron groups) and two sp alkyne carbons (each has 2 electron groups along the triple bond axis). Allene (H\u003Csub>2\u003C/sub>C=C=CH\u003Csub>2\u003C/sub>) has two sp\u003Csup>2\u003C/sup> terminal carbons (3 electron groups each) and one sp central carbon (2 electron groups). Apply the count-and-match rule per atom, not once per molecule.\u003C/p>",[64],[74],{"label":75,"body":76},"Why this matters: pi bonds lock the shape of fats","\u003Cp>A single (sigma) bond is like an axle: the two ends spin freely. Add a pi bond and rotation is locked, because twisting would tear the side-by-side orbital overlap apart. That lock creates cis/trans isomerism: groups frozen on the same side or opposite sides of a double bond, permanently.\u003C/p>\u003Cp>Fats make it visible at the grocery store. Natural unsaturated oils are mostly cis: the kink keeps molecules from packing tightly, so they stay liquid. Industrial partial hydrogenation produced trans fats, whose straightened chains pack like saturated fat, raising both shelf stability and cardiovascular risk, which is why regulators drove them off the market. All of that traces back to one pi bond refusing to rotate.\u003C/p>",{"heading":78,"content":79,"relatedObjectives":80,"deepDive":82},"Molecular Orbital (MO) Theory and Bond Order","\u003Cp>Valence-bond theory (the hybridization picture above) is excellent for explaining geometry but cannot easily account for properties like the paramagnetism of O\u003Csub>2\u003C/sub> or the existence of one-electron and three-electron bonds. \u003Cstrong>Molecular orbital (MO) theory\u003C/strong> takes a different starting point: instead of localizing electrons in pairs between two atoms, MO theory combines atomic orbitals from the whole molecule into \u003Cem>molecular\u003C/em> orbitals that span the entire structure, and then fills those MOs with electrons.\u003C/p>\u003Cp>\u003Cstrong>Bonding and antibonding orbitals.\u003C/strong> When two atomic orbitals on neighboring atoms overlap, they combine in two ways. Constructive overlap concentrates electron density between the two nuclei and lowers the energy of the resulting orbital below the energy of the parent atomic orbitals — this is a \u003Cstrong>bonding\u003C/strong> molecular orbital. Destructive overlap puts a node between the two nuclei and raises the energy of the resulting orbital above the parents — this is an \u003Cstrong>antibonding\u003C/strong> orbital, written with an asterisk (e.g., σ*\u003Csub>1s\u003C/sub>). The number of MOs you produce always equals the number of atomic orbitals you started with: combining two 1s orbitals gives one σ\u003Csub>1s\u003C/sub> bonding MO and one σ*\u003Csub>1s\u003C/sub> antibonding MO.\u003C/p>\u003Cp>\u003Cstrong>Sigma and pi MOs from p orbitals.\u003C/strong> When two atoms’ p orbitals overlap end-on along the bond axis, they form a σ bonding MO and a σ* antibonding MO. When the remaining two pairs of p orbitals overlap side-by-side, they form two degenerate π bonding MOs and two degenerate π* antibonding MOs. So combining the 2p subshells of two atoms gives 6 MOs in total: one σ\u003Csub>2p\u003C/sub>, two π\u003Csub>2p\u003C/sub> (degenerate), two π*\u003Csub>2p\u003C/sub> (degenerate), and one σ*\u003Csub>2p\u003C/sub>.\u003C/p>\u003Cp>\u003Cstrong>Filling rules.\u003C/strong> MOs fill from lowest to highest energy following the same three rules as atomic orbitals: \u003Cem>Aufbau\u003C/em> (lowest first), \u003Cem>Pauli\u003C/em> (max two electrons per MO with opposite spins), and \u003Cem>Hund\u003C/em> (one electron in each degenerate orbital before pairing). For polyatomic ions, adjust the total electron count first — add an electron for each unit of negative charge, remove one for each unit of positive charge.\u003C/p>\u003Cp>\u003Cstrong>Bond order.\u003C/strong> Once the MOs are filled, the strength of the resulting bond is summarized by the \u003Cstrong>bond order\u003C/strong>:\u003C/p>\u003Cp style=\"text-align:center;\">bond order = ½ (number of bonding electrons − number of antibonding electrons)\u003C/p>\u003Cp>A higher bond order means a shorter, stronger bond. A bond order of 1 corresponds to a single bond, 2 to a double bond, 3 to a triple bond. Fractional bond orders are also meaningful (e.g., O\u003Csub>2\u003C/sub>\u003Csup>−\u003C/sup> has a bond order of 1.5 — weaker than O\u003Csub>2\u003C/sub>’s double bond, stronger than O\u003Csub>2\u003C/sub>\u003Csup>2−\u003C/sup>’s single bond). When a fully filled bonding subshell is matched by a fully filled antibonding subshell at lower n (for example, all four 1s electrons in a second-row diatomic), those subshells contribute zero net to the bond order and can be excluded from the calculation; counting only the valence (2s and 2p) MOs gives the same answer with less arithmetic.\u003C/p>\u003Cp>\u003Cstrong>The 2p ordering switch.\u003C/strong> For the heavier second-row diatomics — O\u003Csub>2\u003C/sub>, F\u003Csub>2\u003C/sub>, Ne\u003Csub>2\u003C/sub> — the σ\u003Csub>2p\u003C/sub> bonding MO sits below the two π\u003Csub>2p\u003C/sub> bonding MOs, and the standard filling order is σ\u003Csub>2p\u003C/sub> < π\u003Csub>2p\u003C/sub> < π*\u003Csub>2p\u003C/sub> < σ*\u003Csub>2p\u003C/sub>. For the lighter second-row diatomics — B\u003Csub>2\u003C/sub>, C\u003Csub>2\u003C/sub>, N\u003Csub>2\u003C/sub> — mixing between the 2s and 2p orbitals raises the σ\u003Csub>2p\u003C/sub> above the π\u003Csub>2p\u003C/sub>, so the order is reversed: π\u003Csub>2p\u003C/sub> fills \u003Cem>before\u003C/em> σ\u003Csub>2p\u003C/sub>. Whenever you build an MO diagram for a B/C/N diatomic, swap the σ\u003Csub>2p\u003C/sub> and π\u003Csub>2p\u003C/sub> rungs of the ladder.\u003C/p>\u003Cp>\u003Cstrong>Carbon monoxide and the heteronuclear precedent.\u003C/strong> Carbon monoxide (CO) is the one heteronuclear diatomic that appears in this topic, and it is treated as \u003Cem>isoelectronic with N\u003Csub>2\u003C/sub>\u003C/em>: both species have 10 valence electrons (5 from each atom in N\u003Csub>2\u003C/sub>; 4 from carbon plus 6 from oxygen in CO). Because the electron count drives the molecular-orbital pattern, CO uses the reversed B/C/N order — π\u003Csub>2p\u003C/sub> fills before σ\u003Csub>2p\u003C/sub> — not the heavier-second-row order. Apply N\u003Csub>2\u003C/sub>'s MO diagram directly to CO when computing bond order and magnetism. Other heteronuclear diatomics that are not isoelectronic with a B/C/N homonuclear diatomic (HF, HCl, NO) require a more general MO treatment that is outside the scope of this topic.\u003C/p>\u003Cp>\u003Cstrong>Magnetism: paramagnetic vs diamagnetic.\u003C/strong> A species with one or more unpaired electrons in its MO configuration is \u003Cstrong>paramagnetic\u003C/strong> — it is weakly attracted to a magnetic field. A species with all electrons paired is \u003Cstrong>diamagnetic\u003C/strong> and is weakly repelled. The classic case is O\u003Csub>2\u003C/sub>: with 16 electrons filling through (π*\u003Csub>2p\u003C/sub>)\u003Csup>2\u003C/sup>, Hund’s rule places one electron in each of the two degenerate π*\u003Csub>2p\u003C/sub> orbitals, leaving two unpaired electrons. The valence-bond Lewis structure (a simple O=O double bond with two lone pairs on each oxygen) cannot explain this paramagnetism — it predicts all electrons paired. MO theory gets the right answer because it treats the antibonding electrons explicitly. Bond order: (10 − 6)/2 = 2, matching the double bond seen in the Lewis structure, but with the paramagnetism added on top.\u003C/p>\u003Cp>\u003Cstrong>Reading off properties from an MO diagram.\u003C/strong> Once you have the configuration, the diagram tells you (1) the bond order, (2) whether the species is diamagnetic or paramagnetic, and (3) how the species compares to neighbors when you add or remove electrons. Removing an antibonding electron raises the bond order (cation is more strongly bound); adding an electron to an antibonding orbital lowers the bond order (anion is less strongly bound). This is why O\u003Csub>2\u003C/sub>\u003Csup>+\u003C/sup> has a bond order of 2.5 (stronger than O\u003Csub>2\u003C/sub>) while O\u003Csub>2\u003C/sub>\u003Csup>2−\u003C/sup> has a bond order of 1 (the peroxide single bond, weaker than O\u003Csub>2\u003C/sub>).\u003C/p>",[81],118,[83],{"label":84,"body":85},"Why this matters: liquid oxygen clings to a magnet","\u003Cp>Pour liquid oxygen between the poles of a strong magnet and it sticks there, hanging in the gap until it boils away. Nothing in the Lewis picture predicts that: a tidy double-bonded O\u003Csub>2\u003C/sub> structure pairs every electron, and paired electrons are not magnetic. MO theory gets it right, placing O\u003Csub>2\u003C/sub>’s last two electrons unpaired in separate antibonding orbitals: the molecule is paramagnetic.\u003C/p>\u003Cp>This classic demonstration is why the topic bothers with a second bonding theory at all: a model is judged by the experiments it survives, and the magnet is an experiment valence-bond theory fails.\u003C/p>",{"heading":87,"content":88,"relatedObjectives":89},"Predicting Shape, Polarity, and Hybridization Together","\u003Cp>For any molecule, a systematic four-step approach connects Lewis structure to full three-dimensional properties:\u003C/p>\u003Col>\u003Cli>\u003Cstrong>Draw the Lewis structure\u003C/strong> to identify bonding pairs, lone pairs, and multiple bonds on the central atom.\u003C/li>\u003Cli>\u003Cstrong>Count electron groups\u003C/strong> to determine the electron-pair geometry and hybridization.\u003C/li>\u003Cli>\u003Cstrong>Identify the molecular geometry\u003C/strong> by considering only the positions of atoms (excluding lone pairs from the shape name).\u003C/li>\u003Cli>\u003Cstrong>Assess polarity\u003C/strong> by checking whether bond dipoles cancel given the molecular geometry.\u003C/li>\u003C/ol>\u003Cp>For example, sulfur dioxide (SO\u003Csub>2\u003C/sub>): the Lewis structure shows two double bonds and one lone pair on S (3 electron groups). Electron-pair geometry: trigonal planar. Hybridization: sp\u003Csup>2\u003C/sup>. Molecular geometry: bent (2 atoms + 1 lone pair). Polarity: the S=O dipoles do not cancel in the bent arrangement, so SO\u003Csub>2\u003C/sub> is polar. This integrated approach works for any molecule.\u003C/p>",[55,30,64,81],{"heading":91,"content":92,"relatedObjectives":93},"VSEPR and Polarity: Common Mistakes and Decision Path","\u003Cp>A systematic approach to molecular geometry and polarity:\u003C/p>\u003Col>\u003Cli>\u003Cstrong>Draw the Lewis structure first\u003C/strong>. Geometry predictions depend on knowing the number of electron groups.\u003C/li>\u003Cli>\u003Cstrong>Count electron groups\u003C/strong> (bonding pairs + lone pairs) around the central atom. Double and triple bonds each count as one group.\u003C/li>\u003Cli>\u003Cstrong>Determine electron-pair geometry\u003C/strong> from the total number of electron groups (2 = linear, 3 = trigonal planar, 4 = tetrahedral, 5 = trigonal bipyramidal, 6 = octahedral).\u003C/li>\u003Cli>\u003Cstrong>Determine molecular geometry\u003C/strong> by considering only the positions of atoms (not lone pairs).\u003C/li>\u003Cli>\u003Cstrong>Assess polarity\u003C/strong>: if all outer atoms are identical and there are no lone pairs on the central atom, the molecule is likely nonpolar. Otherwise, check whether dipole moments cancel.\u003C/li>\u003C/ol>\u003Cp>Common mistakes: counting a double bond as two electron groups, confusing electron-pair geometry with molecular geometry, assuming all tetrahedral molecules are nonpolar (bent and trigonal pyramidal are subsets of tetrahedral electron-pair geometry but are polar), and misidentifying hybridization by not matching it to the electron-pair geometry.\u003C/p>",[55,30,64],{"title":95,"problem":96,"steps":97,"answer":103},"Predicting Geometry, Polarity, and Hybridization","Determine the electron-pair geometry, molecular geometry, hybridization, and polarity of sulfur dioxide (SO₂).",[98,99,100,101,102],"Draw the Lewis structure: S is central with 2 double bonds to O and 1 lone pair. Total electron groups on S = 3 (2 double bonds + 1 lone pair).","Electron-pair geometry: 3 groups → trigonal planar.","Molecular geometry: 2 bonding groups + 1 lone pair → bent.","Hybridization: 3 electron groups → sp².","Polarity: The S=O bonds are polar (O is more electronegative). The bent shape means dipoles do not cancel → SO₂ is polar.","SO₂ has a trigonal planar electron-pair geometry, bent molecular geometry, sp² hybridization, and is a polar molecule.",[105,106,107],"OpenStax Chemistry 2e, Ch 7.6: Molecular Structure and Polarity (CC BY 4.0)","OpenStax Chemistry 2e, Ch 8.2: Hybrid Atomic Orbitals (CC BY 4.0)","OpenStax Chemistry 2e, Ch 8.4: Molecular Orbital Theory (CC BY 4.0)",[109,111,114,116,118,120,122,124,126,128,130,132,135],{"question":110},"What is VSEPR theory and what does it predict?",{"question":112,"hint":113},"What is the difference between electron-pair geometry and molecular geometry?","Consider how lone pairs affect the shape you actually see.",{"question":115},"What are the five basic electron-pair geometries?",{"question":117},"How do lone pairs affect molecular shape compared to bonding pairs?",{"question":119},"What determines whether a molecule is polar or nonpolar?",{"question":121},"What is hybridization and how is it related to electron-pair geometry?",{"question":123},"What is the hybridization of a carbon atom in a tetrahedral arrangement?",{"question":125},"What are typical bond angles for linear, trigonal planar, and tetrahedral geometries?",{"question":127},"How can you predict molecular polarity from molecular geometry?",{"question":129},"What is the difference between a bonding and an antibonding molecular orbital?",{"question":131},"How is bond order calculated from a molecular orbital diagram, and what does a higher bond order tell you?",{"question":133,"hint":134},"Which homonuclear diatomics use the reversed 2p ordering (pi below sigma), and which use the standard ordering?","B, C, N use reversed; O, F, Ne use standard.",{"question":136},"Why is O₂ paramagnetic, and how does MO theory account for this where the simple Lewis structure does not?",[138,139],"covalent-bonding-lewis-structures","liquids-solids-intermolecular-forces",[141,142,143,144,145],"C","N","O","S","P",[147],"bond-energies",{"title":149,"steps":150},"How to Predict Molecular Geometry and Polarity",[151,152,153,154,155,156],"Draw the Lewis structure of the molecule to identify bonding pairs, lone pairs, and multiple bonds on the central atom.","Count the total number of electron groups around the central atom (single bonds, double bonds, triple bonds, and lone pairs each count as one group).","Determine the electron-pair geometry from the count: 2 = linear, 3 = trigonal planar, 4 = tetrahedral, 5 = trigonal bipyramidal, 6 = octahedral.","Determine the molecular geometry by considering only the positions of bonded atoms (ignore lone pairs in the shape name).","Assign the hybridization of the central atom: 2 groups = sp, 3 = sp2, 4 = sp3, 5 = sp3d, 6 = sp3d2.","Assess polarity: identify whether bond dipoles cancel based on the molecular geometry. If dipoles do not cancel, the molecule is polar.",{"question":158,"answer":159,"type":160},"Both CO2 and SO2 contain two oxygen atoms bonded to a central atom, and both have polar bonds. Yet CO2 is nonpolar while SO2 is polar. Explain why these two molecules differ in polarity.","CO2 has two electron groups around carbon (two double bonds, no lone pairs), giving it a linear geometry with a 180-degree bond angle. The two equal C=O dipoles point in exactly opposite directions and cancel completely, making the molecule nonpolar. SO2 has three electron groups around sulfur (two double bonds plus one lone pair), giving it a bent molecular geometry. Because the two S=O dipoles are not oriented at 180 degrees, they do not cancel, and the molecule has a net dipole moment, making it polar.","conceptual",[162,165],{"id":163,"problem":164,"type":160},"pt-15-1","Determine the electron-pair geometry, molecular geometry, and hybridization of the central atom in NF3.",{"id":166,"problem":167,"type":160},"pt-15-2","A molecule has the formula XeF4. How many lone pairs are on the central xenon atom, and what is the molecular geometry?",{"workedExampleCount":169,"hasWorksheets":170},8,true,[172,173,174,175,176,177,178],"VSEPR theory","molecular geometry","hybridization","molecular polarity","bond angles","molecular orbital theory","bond order","2026-07-16",4,{"id":182,"slug":183,"lesson":182,"title":184,"shortTitle":185,"description":186,"category":9,"objectiveCount":180,"problemCount":187},14,"chemical-bonding-and-lewis-structures","Chemical Bonding and Lewis Structures","Lewis Structures","Draw Lewis structures for molecules and polyatomic ions that satisfy the regular octet (and the duet for hydrogen), apply the octet rule and identify its exceptions, calculate formal charges, and identify resonance structures.",22,{"id":189,"slug":190,"lesson":189,"title":191,"shortTitle":191,"description":192,"category":193,"objectiveCount":194,"problemCount":195},16,"thermochemistry","Thermochemistry","Study energy changes in chemical reactions: calorimetry, Hess's law, standard enthalpies of formation, bond energies, and stoichiometric enthalpy.","thermodynamics-kinetics",6,40,1785108608123]