All practice pages/Interatomic theory

Compounds

Formulas, models, empirical against molecular, isomers, ions and the lattice, hydrates, and naming both directions.

Wednesday 23 September

Monday laid out the rules: ionic against covalent, the charges you read off a column, Roman numerals, and the Greek prefixes. Parts d and e of the sheet are set for Wednesday, and the rest of it is here to work through.

Homework: the two open Chapter 2 sets, 11:59 pm on Sunday the 27th. Lumen types a subscript as an underscore, CaCl_2.

Read what a compound is made of first. Whether the atoms trade electrons or share them settles the counting, the drawing and the name.

What a formula says

A chemical formula gives the elements in a substance and how many atoms of each go into one unit of it. Three marks do all the work: a subscript belongs to the symbol in front of it, a subscript after a bracket multiplies everything inside the bracket, and a raised dot adds whole water molecules on the end.

FormulaAtoms in one unitWhere they come from
H₂O2 hydrogen, 1 oxygenA symbol with no subscript means one of it.
Ca(NO₃)₂1 calcium, 2 nitrogen, 6 oxygenThe 2 outside multiplies the N and the O₃ both.
(NH₄)₂SO₄2 nitrogen, 8 hydrogen, 1 sulfur, 4 oxygenTwo ammoniums at four hydrogens each.
CuSO₄ · 5H₂O1 copper, 1 sulfur, 9 oxygen, 10 hydrogenFive waters ride along: 10 more H and 5 more O.

Try

Five ways to draw one molecule

Methane, five times over. Each drawing keeps what the one before it had and adds something: connections, then direction, then size. The formula on its own says nothing about shape, which is the whole reason the other four exist.

CH4
Molecular formulaHow many atoms of each element, and nothing else.
CH HHH
Structural formulaWhich atom is bonded to which, drawn flat.
CH HHH
Perspective drawingA wedge comes toward you, hashes go back.
Ball and stickThe angles between the bonds, in three dimensions.
Space fillingHow much room each atom actually takes up.

A ball and stick model is not a photograph. The sticks are not real objects and their length is not to scale, and the space filling model is the closest of the five to how a molecule behaves when it bumps into another one.

Elements on their own

Most elements are written as a bare symbol, one atom at a time: sodium is Na, copper is Cu, argon is Ar. Seven are never found that way. In nature they come in pairs, and the pair is what you write.

H₂   N₂   O₂   F₂   Cl₂   Br₂   I₂

Learn these seven. They sit in a rough 7 on the table, with hydrogen tacked on. Write them as pairs whenever you mean the pure element, so chlorine gas is Cl₂ and not Cl.

A few elements go further and bond in larger groups. Sulfur comes as a ring of eight, S₈, and white phosphorus as a cluster of four, P₄.

This is the trap in the book's first question of the section: O and O₂ are not the same thing on paper. O is the element, and one atom of it. O₂ is a molecule with two atoms in it. Sulfur tempts you into writing S₂ by the same pattern, and sulfur is S₈.

Empirical against molecular

The molecular formula counts the atoms in one molecule. The empirical formula gives the same atoms in the smallest whole number ratio. Divide every subscript by the largest number that goes into all of them.

CompoundMolecularDivide byEmpirical
glucoseC₆H₁₂O₆6CH₂O
caffeineC₈H₁₀N₄O₂2C₄H₅N₂O
hydrogen peroxideH₂O₂2HO
benzeneC₆H₆6CH
sucroseC₁₂H₂₂O₁₁1C₁₂H₂₂O₁₁

Sucrose is the reminder that plenty of formulas are already in lowest terms. Nothing but 1 goes into 12, 22 and 11 together, so the two formulas are the same, and that is a real answer.

Going the other way is not possible on its own. CH₂O is the empirical formula of glucose, C₆H₁₂O₆, and also of acetic acid, C₂H₄O₂. The ratio does not tell you which molecule you have.

Ionic compounds only ever get written as the empirical formula, because there is no molecule to count. NaCl means one sodium for every chlorine, not a pair sitting together.

Two spots to be careful: H₂O₂ goes to HO, not to H or HO₂, and a subscript of 1 is never written. C₉H₈O₄, aspirin, has nothing in common between 9, 8 and 4, so it stays as it is.

Read it off the drawing

The homework hands you a structure and asks for both formulas. Count every atom in the picture, including the hydrogens hanging off the ends, and that is the molecular formula. Then reduce it, and that is the empirical one.

OCO
HCCH
CC HH HH
SOO OH OH

Two of the four reduce to themselves, which is the point of putting them here. An answer of "it stays as it is" is a real answer, and the question is written to see whether you check.

Same formula, different substance

Isomers have the same molecular formula and are not the same compound. C₃H₆O₂ is two different liquids depending on how the atoms are joined, and they do not behave alike.

Propanoic acidMethyl ethanoate
FormulaC₃H₆O₂C₃H₆O₂
Density0.9954 g/mL0.92 g/mL
Melting point−20.8 °C−98.05 °C
Boiling point141 °C57 °C

A gap of 84 degrees in boiling point, from the same nine atoms.

Structural isomers are joined up differently. Propanoic acid and methyl ethanoate are one pair. C₂H₆O is another: ethanol, with its oxygen on the end, and dimethyl ether, with the oxygen in the middle.

Spatial isomers are joined up the same way and sit differently in space. L‑alanine and D‑alanine are mirror images that cannot be laid on top of each other, the way your hands cannot.

Not every formula has an isomer. Two carbons and six hydrogens can only be put together one way, so C₂H₆ is ethane and nothing else.

Why an ion has the charge it has

An ion is an atom that has lost or gained electrons. The protons never move, so the charge is only ever an electron count. A main group element takes whatever charge lands it on the electron count of the nearest noble gas, which is why the charge can be read straight off the group.

AtomElectronsWhat it doesEnds up likeIon
sodium11loses 1neon, 10Na⁺
magnesium12loses 2neon, 10Mg²⁺
aluminum13loses 3neon, 10Al³⁺
nitrogen7gains 3neon, 10N³⁻
oxygen8gains 2neon, 10O²⁻
chlorine17gains 1argon, 18Cl⁻
calcium20loses 2argon, 18Ca²⁺

A cation is positive, made by losing electrons, and keeps the element's name: the calcium ion. An anion is negative, made by gaining them, and takes an -ide ending: the chloride ion.

Metals are on the left and have few electrons to shed, so they go positive. Nonmetals are on the right and are close to a full count already, so they go negative. Group 8A is already there and forms no ions worth naming.

This is a main group rule only. The transition metals in the B groups do not have one predictable charge, which is exactly why their names carry a Roman numeral.

An ionic compound is a lattice, not a molecule

Opposite charges pull on each other, and that pull is the ionic bond. It does not join two ions into a private pair. Every sodium ion in table salt is surrounded by chloride ions, every chloride by sodium ions, and the pattern repeats in all three directions for as far as the crystal goes.

So there is no molecule of NaCl to point at. What the formula gives is a formula unit: the smallest whole number ratio of the ions, and enough of each to make the charge come out to zero.

Say formula unit for ionic compounds and molecule for covalent ones. The exam has asked which word belongs.

Na⁺Cl⁻Na⁺Cl⁻Cl⁻Na⁺Cl⁻Na⁺Na⁺Cl⁻Na⁺Cl⁻Cl⁻Na⁺Cl⁻Na⁺one formula unit, written NaCl
Put togetherIonsCharge to cancelFormula unit
sodium and chlorineNa⁺ and Cl⁻1 and 1, already evenNaCl
magnesium and chlorineMg²⁺ and Cl⁻2+ needs two 1−MgCl₂
magnesium and oxygenMg²⁺ and O²⁻2 and 2, already evenMgO

The three the lecture works through. Mg²⁺ with O²⁻ is MgO and never Mg₂O₂, because the ratio has to come down to the smallest whole numbers.

IonicCovalent
Held bypull between + and − chargesa shared pair of electrons
Smallest piecea formula unita molecule
Made froma metal and a nonmetaltwo nonmetals
Formula comes fromcharges cancellingthe prefixes in the name

Build an ionic formula

    The subscripts are whatever makes the charges add to zero, in the smallest whole numbers. Mg²⁺ with S²⁻ is MgS, never Mg₂S₂. Parentheses go around a polyatomic ion only when there is more than one of it.

    Take the compound apart

    The other direction, and the one the homework leans on hardest: given the formula, write the two ions with their charges. A covalent compound has no ions to write, which is half of what the question is testing.

    CompoundCationAnion
    BaOBa²⁺O²⁻
    Na₂ONa⁺O²⁻
    (NH₄)₂CO₃NH₄⁺CO₃²⁻
    Sr(H₂PO₄)₂Sr²⁺H₂PO₄⁻
    NF₃covalent, so no ions
    IBrcovalent, so no ions

    The subscript is a count, not a charge. The 2 outside the bracket in Sr(H₂PO₄)₂ says there are two dihydrogen phosphate ions. Each one still carries 1−. Writing H₂PO₄²⁻ because of that 2 is the mistake the question is set to catch.

    Work it from the side you know. Strontium is group 2, so it is Sr²⁺; the compound is neutral, so the two anions have to carry 2− between them, which is 1− each.

    An ion made of one atom, like Ba²⁺ or O²⁻, is a monatomic ion. One built from a central atom with oxygens around it, like CO₃²⁻ or SO₄²⁻, is an oxyanion, and that is the family the -ate and -ite endings name.

    Hydrates

    Some ionic compounds crystallise with water caught in the lattice. The water is written after a raised dot, with a number in front of it for how many go with each formula unit, and the name ends in a Greek prefix plus the word hydrate.

    FormulaName
    LiClO₄ · 3H₂Olithium perchlorate trihydrate
    CuSO₄ · 5H₂Ocopper(II) sulfate pentahydrate
    MgSO₄ · 7H₂Omagnesium sulfate heptahydrate
    CoCl₂ · 6H₂Ocobalt(II) chloride hexahydrate
    Na₂CO₃ · 10H₂Osodium carbonate decahydrate

    Name the compound exactly as you would without the water, Roman numeral and all, then add the prefix and hydrate.

    That water is not held tightly. Heat the crystal and it leaves as steam, and what is left is the anhydrous compound. Copper(II) sulfate is the one everybody remembers: blue with its five waters, white without them.

    The prefixes are the same ones covalent names use, mono through deca, and here the mono is kept: a compound with one water is a monohydrate.

    Wednesday's lab is the dehydration of a hydrate, where the water driven off is weighed to find how many went with each formula unit. Worth having the dot straight before then.

    Covalent compounds share electrons

    Two nonmetals have no reason to hand electrons over, because neither one is inclined to give them up. Instead they share a pair, and the shared pair is the covalent bond. What it makes is a real molecule, a fixed group of atoms with a size and a shape.

    H₂O   CH₄   CO   CO₂

    Because nothing has to cancel, the formula cannot be worked out from charges. There is no rule that says carbon and oxygen must meet one to one, and so CO and CO₂ both exist and are different gases.

    That is why covalent names carry prefixes and ionic names do not. The prefix is carrying the information that the charges would have carried.

    Which kind is it?

    Ionicmetal + nonmetal

    Electrons are handed over, and the pull between the ions that are left is the ionic bond. Charges cancel, so no prefixes are ever used. Ammonium takes the metal's place, and the piece you count is a formula unit, never a molecule.

    NaCl, Ca₃N₂, (NH₄)₂SO₄
    Covalent, also called molecularnonmetal + nonmetal

    Neutral atoms share a pair of electrons, and the shared pair is the covalent bond. What it makes is a molecule. The formula cannot be worked out from charges, so prefixes tell you how many of each.

    CO, N₂O₄, P₂S₅
    AcidH + anion, in water

    Hydrogen ions bonded to a negative ion. The anion's ending decides the acid's ending.

    HCl, H₂SO₄, HNO₂

    Metals sit on the left of the staircase and the nonmetals on the right. Ammonium, NH₄⁺, is not a metal but stands in for one, so (NH₄)₂SO₄ is ionic.

    Where that rule bends

    The staircase itself

    Silicon and arsenic are metalloids, neither one thing nor the other. SiCl₄ and AsCl₅ are covalent and take prefixes, so silicon tetrachloride, not silicon(IV) chloride.

    The B groups

    CuCl₂ and CrCl₃ are ionic, but the charge cannot be read off the table. That is what the Roman numeral is for: copper(II) chloride, chromium(III) chloride. The numeral goes right against the name with no space: iron(III), never iron (III).

    The book's own exception

    AlCl₃ is a metal with a nonmetal and still behaves covalently. The rule is a good guide rather than a law, and the book says so itself.

    How the two kinds behave

    The homework asks this as often as it asks for a name, and the rules above give you nothing to answer with. It comes down to how hard the pieces are held together.

    Sodium chlorideWater
    Kindioniccovalent
    Melts at801 °C0 °C
    Boils at1413 °C100 °C

    Pulling a lattice of charges apart takes far more heat than separating molecules from one another, so ionic compounds are solids with high melting points and covalent ones are often gases, easily boiled liquids, or solids that melt low.

    Conducting is the careful one. A solid ionic compound does not conduct: the ions are locked in the lattice and nothing can move. Melt it, or dissolve it, and it conducts well, because now the ions can travel.

    So the flat sentence "ionic compounds conduct electricity" is marked wrong. The one that is right says molten or dissolved.

    Covalent compounds have no ions to move at all, so they generally do not conduct in any state. These are strong tendencies rather than laws, and the book hedges them the same way.

    Charges worth knowing on sight

    Where it sitsChargeExample
    Group 1, the alkali metals1+Na⁺, K⁺
    Group 2, the alkaline earths2+Mg²⁺, Ca²⁺
    Group 13, aluminum3+Al³⁺
    Group 153−N³⁻, P³⁻
    Group 162−O²⁻, S²⁻
    Group 17, the halogens1−Cl⁻, Br⁻
    Transition metalsWhat to write
    Silveralways 1+, no numeral
    Zincalways 2+, no numeral
    Cadmium, under zinc and the same in this respectalways 2+, no numeral
    Iron, copper, cobalt, nickel, chromium, manganese, gold, mercury, titaniumRoman numeral for the charge, worked out from the anion
    Tin and lead, which also take two chargesRoman numeral, tin(II) or tin(IV)

    Know these three. Silver 1+, zinc 2+ and aluminum 3+ are the metals whose charge never varies, so their names take no Roman numeral. Every other transition or post-transition metal needs one. Silver(I) chloride is accepted here as well, but silver chloride is the form the worksheet uses.

    Mercury(I) is the odd one out. It travels as a pair of mercury ions sharing a single 2+ charge, written Hg₂²⁺, so mercury(I) chloride is Hg₂Cl₂ and not HgCl. Mercury(II) behaves normally.

    An older set of names is still in use: ferrous and ferric for iron(II) and iron(III), cuprous and cupric for copper(I) and copper(II), stannous and stannic for tin(II) and tin(IV). The -ous ending is the lower charge and -ic the higher. Write the Roman numeral version unless you are asked for the old one.

    Fe₂(SO₄)₃ has three sulfates at 2− each, so 6− in all, shared by two irons: iron(III) sulfate. The numeral is the charge on one metal ion, not the number of them.

    Why those three never vary

    Every other transition metal has a choice about how many electrons to give up, which is what the Roman numeral records. These three have only one way to go, and the configurations show it.

    MetalIonAtom, then ionWhat is left
    silverAg⁺[Kr]4d¹⁰5s¹ → [Kr]4d¹⁰the single 5s electron goes and the d subshell is full
    zincZn²⁺[Ar]3d¹⁰4s² → [Ar]3d¹⁰both 4s electrons go, and again the d subshell is full
    aluminumAl³⁺[Ne]3s²3p¹ → [Ne]all three outer electrons go, down to neon's core

    A full d subshell is hard to break into. Taking a further electron out of silver's or zinc's 4d or 3d costs far more energy than any bond gives back, so there is no second charge to choose between.

    Aluminum is fixed for the plainer reason: it is a main group metal with three outer electrons, and losing all three leaves it with neon's electron count. That is the same rule that fixes sodium at 1+ and magnesium at 2+.

    Cadmium sits directly under zinc, [Kr]4d¹⁰5s² down to [Kr]4d¹⁰, and behaves the same way. It is not one of the three to memorise, but its name takes no numeral either.

    Prefixes, for covalent compounds only

    FormulaName
    COcarbon monoxide
    SO₃sulfur trioxide
    N₂O₄dinitrogen tetroxide
    SF₆sulfur hexafluoride
    XeCl₅xenon pentachloride

    A few compounds never get their systematic name. H₂O is water, NH₃ is ammonia, CH₄ is methane. Nobody says dihydrogen monoxide outside a joke, and the homework will not either.

    The first element drops mono, so CO₂ is carbon dioxide and not monocarbon dioxide. Before oxide the a or o falls away: monoxide, tetroxide, pentoxide.

    Acids

    Anion endingAcid endingExample
    -idehydro- ... -ic acidCl⁻ chloride → HCl, hydrochloric acid
    -ate-ic acidSO₄²⁻ sulfate → H₂SO₄, sulfuric acid
    -ite-ous acidNO₂⁻ nitrite → HNO₂, nitrous acid

    Enough hydrogens go in front to cancel the charge, which is why carbonate and sulfate take two: H₂CO₃ and H₂SO₄. Acetic acid is the odd one written HC₂H₃O₂, with only the first hydrogen acidic.

    One formula, two names. HCl as a pure compound is a gas, and by the covalent rules it is hydrogen chloride. Dissolved in water it is hydrochloric acid. The same goes for H₂S, hydrogen sulfide as a gas and hydrosulfuric acid in water. Either name is accepted here unless the question says which state it is in.

    Formulas that are written wrong

    Al₂SAl₂S₃

    Aluminum is 3+ and sulfide is 2−. Two aluminums give 6+, so three sulfides are needed to cancel it.

    PNa₃Na₃P

    Right atoms, wrong order. The positive ion is written first, always.

    Mg₂S₂MgS

    The charges already cancel one to one, so the subscripts have to come down to the smallest whole numbers.

    Na₂C₂O₄ reduced to NaCO₂Na₂C₂O₄

    Sodium oxalate is two Na⁺ with one C₂O₄²⁻. Halving every atom gives a real ratio and a wrong formula, because it breaks up the oxalate ion. Reduce the ratio of the ions, never the inside of one.

    Na₂O₂ read as sodium oxidesodium peroxide

    Oxide is O²⁻ and peroxide is O₂²⁻, two oxygens sharing one 2− charge. Sodium oxide is Na₂O, sodium peroxide is Na₂O₂. Hydroxide and peroxide both hold oxygen and neither is an oxyanion, which is why neither takes an -ate or an -ite.

    azide vs nitrideN₃⁻ vs N³⁻

    Azide is three nitrogens sharing one negative charge. Nitride is one nitrogen carrying three. Subscript against superscript, and a different ion.

    calcium nitride vs nitrateCa₃N₂ vs Ca(NO₃)₂

    Nitride is the bare N³⁻ ion. Nitrate is the polyatomic NO₃⁻. One letter, a different compound.