Write formulas and names for compounds, draw Lewis structures and predict shapes with VSEPR

Learning goal: Predict formulas of ionic compounds from the periodic table and given polyatomic ions, name ionic compounds, binary covalent compounds and acids from their formulas and write formulas from names, construct Lewis structures for molecules of hydrogen, carbon, nitrogen, oxygen, phosphorus, sulfur and the halogens, predict three-dimensional shapes with valence shell electron pair repulsion theory, and choose the representation that best suits a purpose.

A formula is a claim about ratio. The formula of an ionic compound states the simplest whole-number ratio of ions that makes the total charge zero. The charges come from the periodic table: group 1 forms 1+, group 2 forms 2+, aluminum 3+, group 17 forms 1−, oxygen and sulfur 2−, nitrogen 3−, hydrogen 1+ with nonmetals and 1− in metal hydrides. Polyatomic ions are groups of covalently bonded atoms that carry a charge as a unit; their formulas and charges are given to you: nitrate NO₃⁻, sulfate SO₄²⁻, carbonate CO₃²⁻, phosphate PO₄³⁻, hydroxide OH⁻, ammonium NH₄⁺. Cross the charges to get subscripts, then reduce to the simplest ratio. Calcium 2+ with chloride 1− needs two chlorides: CaCl₂. Aluminum 3+ with oxide 2− needs a total of 6+ and 6−: Al₂O₃. Magnesium 2+ with nitrate 1− needs two nitrates, and a polyatomic ion taken more than once goes in parentheses: Mg(NO₃)₂. Ammonium 1+ with sulfate 2−: (NH₄)₂SO₄. A formula such as Mg₂O₂ is wrong because it is not reduced; the compound's ratio is one to one.

Naming ionic compounds. Name the cation, then the anion with its ending changed to -ide for a single element: NaCl is sodium chloride, Al₂O₃ aluminum oxide, K₂S potassium sulfide. Polyatomic ions keep their names: Mg(NO₃)₂ is magnesium nitrate. No prefixes are used, because the charges already fix the ratio. Metals that form more than one ion, mainly transition metals, need a Roman numeral giving the charge: FeCl₂ is iron(II) chloride and FeCl₃ is iron(III) chloride; CuSO₄ is copper(II) sulfate because sulfate is 2− and one copper must balance it. To find the numeral from the formula, work backwards from the anion charge: in Fe₂O₃ three oxides carry 6−, so two irons carry 6+, and each is 3+.

Naming binary covalent compounds. When two nonmetals combine there are no charges to fix the ratio, so Greek prefixes state the number of each atom: mono- (usually dropped for the first element), di-, tri-, tetra-, penta-, hexa-. CO₂ is carbon dioxide, CO carbon monoxide, N₂O₄ dinitrogen tetroxide, SF₆ sulfur hexafluoride, PCl₃ phosphorus trichloride. Going the other way, dinitrogen pentoxide is N₂O₅. The presence of a metal is the signal to switch systems: NaCl is not monosodium monochloride.

Naming acids. Acids are hydrogen compounds that release hydrogen ions in water. A binary acid, hydrogen with one other nonmetal, takes hydro- plus the root plus -ic acid: HCl is hydrochloric acid, HBr hydrobromic acid, H₂S hydrosulfuric acid. An oxyacid contains a polyatomic ion with oxygen and is named from the ion: an -ate ion gives an -ic acid (H₂SO₄ from sulfate is sulfuric acid, HNO₃ from nitrate is nitric acid, H₃PO₄ from phosphate is phosphoric acid), and an -ite ion gives an -ous acid (H₂SO₃ from sulfite is sulfurous acid, HNO₂ from nitrite is nitrous acid). To write the formula from the name, reverse the rule: chloric acid contains chlorate, ClO₃⁻, and needs one hydrogen: HClO₃. The number of hydrogens equals the charge on the anion.

Lewis structures. A Lewis structure shows every valence electron in a molecule as a dot or a bond line, and it is the starting point for shape and polarity. The rules for molecules built from hydrogen, carbon, nitrogen, oxygen, phosphorus, sulfur and the halogens are: (1) add the valence electrons of all atoms; (2) place the least electronegative atom (never hydrogen) in the center and join each outer atom to it with a single bond, two electrons each; (3) distribute the remaining electrons as lone pairs on the outer atoms to complete their octets (hydrogen takes only two); (4) put any electrons left on the central atom; (5) if the central atom is still short of an octet, move a lone pair from an outer atom in to make a double or triple bond. Check at the end that the total number of electrons drawn equals the count from step 1.

A worked model: carbon dioxide and water. CO₂ has 4 + 6 + 6 = 16 valence electrons. Carbon is central with two C–O single bonds (4 electrons), and the remaining 12 go as three lone pairs on each oxygen. Carbon then has only 4 electrons. Move one lone pair from each oxygen into a bond: O=C=O, with two lone pairs on each oxygen. Count: two double bonds (8) plus four lone pairs (8) equals 16. H₂O has 2 + 6 = 8 electrons: oxygen central, two O–H bonds (4), and the remaining 4 as two lone pairs on oxygen. Count 8. The two structures look similar on paper, but one has no lone pairs on the central atom and the other has two, and that difference decides their shapes.

VSEPR: electron pairs repel. Valence shell electron pair repulsion theory says that the groups of electrons around a central atom, whether bonding pairs (a double or triple bond counts as one group) or lone pairs, move as far apart as they can. Two groups spread 180° apart, a linear arrangement; three groups spread 120° apart in a trigonal planar arrangement; four groups point to the corners of a tetrahedron, 109.5° apart. That is the electron-pair geometry. The molecular geometry, the shape you would see, describes only the positions of the atoms. With four groups and no lone pairs, as in methane, the molecule is tetrahedral. With four groups and one lone pair, as in ammonia, the atoms form a trigonal pyramid, and the lone pair squeezes the H–N–H angles to about 107°. With four groups and two lone pairs, as in water, the atoms form a bent shape with an angle of about 104.5°. Carbon dioxide, with two groups and no lone pairs, is linear at 180°; formaldehyde, CH₂O, with three groups, is trigonal planar at about 120°. Lone pairs repel more strongly than bonding pairs, which is why the angles close slightly.

Shape decides molecular polarity. Once the shape is known, add the bond dipoles as arrows. In the linear CO₂ molecule two equal opposite dipoles cancel, so the molecule is nonpolar; in bent water they do not, so water is polar; ammonia's trigonal pyramid leaves a net dipole toward the lone pair, so it is polar; methane's symmetric tetrahedron of nearly nonpolar C–H bonds is nonpolar. The same method applied to a large molecule such as caffeine works piece by piece: each carbon with four single bonds is tetrahedral, each carbon with a double bond is trigonal planar, and each nitrogen with three bonds and a lone pair is trigonal pyramidal or, when part of a flat ring, planar. Worked example 5 carries out this piece-by-piece analysis on dopamine.

Choosing a representation. Each model shows something and hides something. A chemical formula gives composition and ratio but no structure; it is the right choice for a stoichiometry calculation or an ionic lattice, where there is no molecule to draw. A Lewis structure shows bonds and lone pairs and is the right choice for predicting shape, polarity and reactivity of a molecule; it is a poor choice for a metal or an ionic solid. A ball-and-stick model shows the three-dimensional arrangement and angles at the cost of hiding lone pairs and exaggerating the gaps between atoms; it is the right choice for judging shape and how molecules might fit together. Ask what question you are answering before choosing.

Where the rest of the standards is taught. C.PM.3 is shared with the bonding lesson, which teaches bond energy, bond formation from electron configurations and the bond-type continuum; this lesson applies bonding to formulas, Lewis structures and shapes.

Investigation: build shapes and measure angles. Materials: gumdrops or modeling clay in two colors, toothpicks, a protractor, and four balloons. Steps: build methane with one central ball and four sticks, arranging the sticks so that every pair is as far apart as possible, and measure the angles between sticks with the protractor; build ammonia by removing one stick and marking where the lone pair sits; build water by removing another; build carbon dioxide with two sticks in a line and formaldehyde with three in a plane. Then tie four inflated balloons together at their necks and observe the shape they settle into; untie one to leave three, then two, and observe each time. Record the shape name and measured angle for each model. A result that supports the claim: the balloons, which really do push one another apart, settle by themselves into tetrahedral, trigonal planar and linear arrangements (about 109.5°, 120° and 180°), an analogy for electron groups repelling. The stick models do not settle into anything: you placed the sticks, so they illustrate the geometry and do not test it; compare your measured stick angles with the measured molecular angles in this lesson's table (109.5° in methane, about 107° in ammonia, about 104.5° in water). What the model cannot show: sticks are rigid while real bonds vibrate, the sticks exaggerate the gaps between atoms, whose electron clouds in reality fill most of that space, lone pairs have no ball, and pulling a stick out of a rigid model does not close the remaining angles, so the model cannot show the slightly smaller angles that lone pairs cause in ammonia and water. Organic naming and molecules with atoms beyond the listed elements are reserved for later courses.

Worked example 1 — formulas from names. Aluminum sulfate: Al³⁺ and SO₄²⁻; the lowest common charge is 6, so two aluminum (6+) and three sulfate (6−): Al₂(SO₄)₃. Iron(III) oxide: Fe³⁺ and O²⁻, so Fe₂O₃. Ammonium phosphate: NH₄⁺ and PO₄³⁻, so (NH₄)₃PO₄. Sodium hydroxide: Na⁺ and OH⁻, NaOH, no parentheses needed for a single polyatomic ion. Check each by adding the charges: 2(3+) + 3(2−) = 0; 2(3+) + 3(2−) = 0; 3(1+) + (3−) = 0; (1+) + (1−) = 0.

Worked example 2 — names from formulas. Cu₂O: oxide is 2−, so two coppers share 2+, each is 1+: copper(I) oxide. P₂O₅: two nonmetals, so prefixes: diphosphorus pentoxide. Ca(OH)₂: calcium hydroxide, no numeral because calcium is always 2+. HNO₂: an oxyacid from nitrite, so nitrous acid; HNO₃ from nitrate is nitric acid. H₂S dissolved in water: a binary acid, hydrosulfuric acid. The first decision each time is whether a metal is present and whether the compound is an acid.

Worked example 3 — Lewis structure and shape of ammonia, NH₃. Valence electrons: 5 + 3 = 8. Nitrogen is central with three N–H bonds, using 6; the remaining 2 form one lone pair on nitrogen. Count 8. Four electron groups around nitrogen give a tetrahedral electron-pair geometry; with one lone pair the three hydrogens form a trigonal pyramid, and the H–N–H angle is about 107°, a little less than 109.5° because the lone pair repels more strongly. The N–H bonds are polar (difference 0.84) and the pyramid is not symmetric, so ammonia is polar with the negative end at nitrogen.

Worked example 4 — a triple bond: hydrogen cyanide, HCN. Valence electrons: 1 + 4 + 5 = 10. Carbon is central (hydrogen is never central, and carbon is less electronegative than nitrogen): H–C–N uses 4, and the remaining 6 go on nitrogen as three lone pairs. Carbon then has only 4 electrons. Move two lone pairs from nitrogen into bonds: H–C≡N with one lone pair left on nitrogen. Count: single bond 2, triple bond 6, lone pair 2, total 10. Two electron groups around carbon give a linear molecule, 180°. The C≡N bond is polar and there is nothing on the other side to cancel it, so HCN is polar.

Worked example 5 — several shapes inside one larger molecule: dopamine. Dopamine, C₈H₁₁NO₂, is a signaling molecule in the brain. Its structure, as usually drawn for the uncharged molecule, is supplied here in words: a ring of six carbon atoms; two neighboring ring carbons each carry an O–H group; a third ring carbon carries a two-carbon chain, –CH₂–CH₂–, that ends in an NH₂ group; and the other three ring carbons each carry one hydrogen. A large molecule has no single shape, so apply VSEPR to each atom that has more than one neighbor. Each ring carbon is bonded to three atoms and has no lone pairs (one of its bonds to a ring neighbor is drawn as a double bond, which counts as one group): three groups, trigonal planar, about 120°, which is why the ring is flat. Each CH₂ carbon has four single bonds: four groups, tetrahedral, about 109.5°. The nitrogen has three bonds and one lone pair: four groups, trigonal pyramidal, with angles predicted to be a little under 109.5°, as in ammonia. Each O–H oxygen has two bonds and two lone pairs: four groups, bent, as in water. So one molecule contains a flat region, two tetrahedral centers, a pyramidal center and two bent ones. The same atom-by-atom method describes caffeine, serotonin or a protein; only the number of centers grows.

Representation task: a naming and formula grid. Make a grid with the cations Na⁺, Ca²⁺, Al³⁺, Fe³⁺ and NH₄⁺ down the side and the anions Cl⁻, O²⁻, NO₃⁻, SO₄²⁻ and PO₄³⁻ across the top. Fill every cell with the correct formula and name, using parentheses and Roman numerals where they belong. Then write the formula and name of five binary covalent compounds and five acids chosen by your teacher, and check each answer against the rules in the lesson. Then read the ingredient labels of household products without opening them and develop the formula from each compound's name, for example sodium chloride (table salt), calcium carbonate (antacid tablets and chalk), magnesium hydroxide (milk of magnesia), magnesium sulfate (Epsom salt) and sodium hydroxide (drain cleaner; read the label only). Then construct a prototype of a card or board game that practices formula writing and nomenclature, for example matching ion cards to build formulas and scoring correct names, play it with classmates, and allow other students to evaluate and critique the appropriateness of the game: whether its rules reward the real decisions (metal or nonmetal, fixed or variable charge, acid or not) rather than guessing. Revise the game using their critique.

Independent performance: Lewis structures, models and a representation choice. For CH₄, NH₃, H₂O, CO₂, CH₂O and PCl₃: count valence electrons, draw the Lewis structure, state the number of electron groups and lone pairs on the central atom, name the electron-pair geometry and the molecular shape with its approximate angle, and state whether the molecule is polar. Build ball-and-stick models of at least three and measure the angles. Then, for the larger molecule lactic acid, CH₃–CH(OH)–C(=O)–O–H, state the number of electron groups and the local shape at each of the three carbons and at each of the two O–H oxygens. Success criteria: each Lewis structure accounts for exactly the counted electrons; each shape is justified by counting groups and lone pairs, not recalled; each polarity decision refers to both bond polarity and symmetry; and a closing paragraph explains, for a sodium chloride crystal, a water molecule and a copper wire, which representation (formula, Lewis structure, ball-and-stick) is most useful and what each one hides.