Química Geral · Bonding theories
Ligação iônica e energia reticular
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O que você vai aprender
- Classify bonds as nonpolar covalent, polar covalent or ionic from electronegativity differences, and assign partial charges.
- Estimate percent ionic character from a dipole moment and bond length, and explain why ionic character is a continuum.
- Use Coulomb's law to compare ion-pair energies and predict lattice-energy trends from ion charge and size.
- Construct Born–Haber cycles from given data to find a lattice energy, an electron affinity or an enthalpy of formation.
- Explain the melting points, brittleness, conductivity and solubility of ionic compounds from their lattice structure.
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Ionic and covalent bonds: a continuum
In a covalent bond two atoms share an electron pair; in an ionic bond one atom has effectively transferred electrons to the other, and the resulting cation and anion hold together by electrostatic attraction. Most real bonds lie in between, and the electronegativity difference, ΔEN, measures where. A common rule of thumb on the Pauling scale: ΔEN below 0.4 is nonpolar covalent, 0.4 to 2.0 is polar covalent, and above 2.0 is mostly ionic. These cut-offs are conventions, not sharp boundaries. In a polar bond the more electronegative atom carries the partial negative charge (δ−): in H–Cl (ΔEN = 3.16 − 2.20 = 0.96) chlorine is δ−, but in Li–H (ΔEN = 2.20 − 0.98 = 1.22) hydrogen is δ−. Sodium chloride (drawn as its ions), with ΔEN = 3.16 − 0.93 = 2.23, is a typical ionic compound.
Percent ionic character
If a diatomic molecule were fully ionic, its dipole moment would be μ(ionic) = e × d, one electron charge (1.602 × 10⁻¹⁹ C) separated by the bond length. Percent ionic character = μ(measured) ÷ μ(ionic) × 100%. For HF, μ = 1.82 D and d = 91.7 pm: e × d = 1.602 × 10⁻¹⁹ C × 9.17 × 10⁻¹¹ m = 1.469 × 10⁻²⁹ C·m = 4.40 D (1 D = 3.336 × 10⁻³⁰ C·m), so HF is about 1.82 ÷ 4.40 = 41% ionic. Percent ionic character rises smoothly with ΔEN, but no bond reaches 100%: even gas-phase alkali halide molecules have dipoles smaller than e × d, because the cation pulls the anion's electron cloud back toward itself. That polarization is strongest for small, highly charged cations and large anions, which is why AlCl₃ behaves largely as a covalent substance while AlF₃ is an ionic solid.
Coulomb's law
The potential energy of two ions is E = kQ₁Q₂/d, where Q₁ and Q₂ are the ion charges (in units of e), d is the distance between their centres and k = 2.31 × 10⁻¹⁹ J·nm. Opposite charges give a negative energy: the pair is more stable than the separated ions. Energy varies as 1/d, so doubling the distance halves the energy; it is the force that varies as 1/d². For a K⁺–Cl⁻ pair at d = 0.319 nm (138 + 181 pm), E = 2.31 × 10⁻¹⁹ J·nm × (+1)(−1) ÷ 0.319 nm = −7.24 × 10⁻¹⁹ J per ion pair, or −7.24 × 10⁻¹⁹ J × 6.022 × 10²³ mol⁻¹ = −436 kJ/mol. Doubling both charges multiplies the energy by four, while ionic radii change d only modestly, so charge usually dominates size.
Lattice energy trends
In this topic the lattice energy is the energy needed to separate one mole of an ionic solid into its gaseous ions, for example NaCl(s) → Na⁺(g) + Cl⁻(g), so it is always positive; some textbooks quote the reverse process with a negative sign. Lattice energy grows with the product of the ion charges and falls as the ions get larger. Charge first: CaO (2+ and 2−, 3401 kJ/mol) has almost five times the lattice energy of KCl (1+ and 1−, 715 kJ/mol); the fourfold charge product accounts for most of this and the somewhat shorter ion separation (240 vs 319 pm) for the rest. Then size: with the same charges, smaller ions sit closer, so KF (821) > KCl (715) > KBr (682) > KI (649). A crystal's lattice energy is larger than the energy of one isolated ion pair at the same distance, because every ion is surrounded by several oppositely charged neighbours; repulsions from like ions further away reduce, but do not cancel, this gain.
Born–Haber cycles
Lattice energies cannot be measured directly, so they are found with Hess's law. Form the solid from its elements in two ways: directly (ΔH°f), or in steps that make gaseous ions and then let them condense into the lattice. For NaBr: sublime sodium, Na(s) → Na(g), +107 kJ/mol; ionize it, Na(g) → Na⁺(g) + e⁻, +496; make gaseous bromine atoms from liquid bromine, ½ Br₂(l) → Br(g), +112; add an electron, Br(g) + e⁻ → Br⁻(g), −325 (the electron affinity); then the ions form the solid, releasing the lattice energy U. Since the two routes have the same overall enthalpy, ΔH°f = 107 + 496 + 112 − 325 − U = −361 kJ/mol, so U = 361 + 107 + 496 + 112 − 325 = 751 kJ/mol. Count every atom: a dihalide MX₂ needs IE₁ + IE₂ for the metal, the full X–X bond enthalpy (two atoms) and two electron affinities. Forming O²⁻ costs energy overall (EA₁ ≈ −141, EA₂ ≈ +744 kJ/mol), and the much larger lattice energy of a 2+/2− solid pays for it.
Properties of ionic compounds
Melting an ionic solid means overcoming attractions between every ion and its neighbours, so ionic compounds melt high (NaCl 801 °C, MgO 2852 °C), and melting points broadly follow lattice energy. Ionic crystals are hard but brittle: sliding one layer along by a single ion position brings like charges face to face, and the repulsion splits the crystal. Solid ionic compounds do not conduct electricity because the ions are locked in place; molten salts and aqueous solutions conduct because the ions can move. Dissolving separates the ions (costing the lattice energy) and hydrates them (releasing the hydration enthalpy): ΔH(soln) = U + ΔH(hydration). For KCl, 717 kJ/mol − 700 kJ/mol = +17 kJ/mol, a slightly endothermic dissolution. Whether a salt dissolves depends on that balance and on entropy, so ions that pack very tightly, such as Li⁺ with F⁻, often give poorly soluble salts.
What to carry forward
Bond character runs continuously from nonpolar covalent to ionic as ΔEN grows, and no bond is 100% ionic. Coulomb's law, E = kQ₁Q₂/d, explains lattice energy: charge product first, ion size second. A Born–Haber cycle is Hess's law: ΔH°f = sublimation + ionization + atomization + electron affinity − U, with every atom and every charge counted. Large lattice energies explain high melting points, and moving ions explain why melts and solutions conduct while the solid does not.
Problemas de prática (40)
Praticar é grátis com uma conta.
Preveja o produto 4
Coulomb's law and lattice energy
- Pulling an ion pair apartPredict how the Coulomb energy of an ion pair changes when the distance between the ions doubles.
Properties of ionic compounds
- Which salt melts highest?Predict the highest-melting ionic solid from ion charges and sizes.
Ionic and covalent bonds
- Which end of Li–H is negative?Assign the partial charges in a bond where hydrogen is the more electronegative atom.
Born–Haber cycles
- Why is there no NaCl₂?Use ionization energies and lattice energies to predict which cation charge a metal adopts in its chloride.
Classificar 5
Born–Haber cycles
- Which step releases energy?Classify the steps of the NaCl Born–Haber cycle that lead to gaseous ions as endothermic or exothermic.
- Which equation is the lattice energy?Identify the process whose enthalpy change is the lattice energy of an ionic solid.
Ionic and covalent bonds
- Which bond is polar covalent?Classify bonds as nonpolar covalent, polar covalent or ionic using electronegativity-difference cut-offs.
- A bond with no ionic characterRecognize that only a bond between identical atoms has exactly zero ionic character.
Properties of ionic compounds
- Which sample conducts electricity?Classify samples as electrical conductors or non-conductors from whether they contain mobile ions.
Comparar 6
Coulomb's law and lattice energy
- Charge versus size in lattice energyRank lattice energies of salts that differ in both ion charge and ion size.
- Rank ion pairs by Coulomb attractionRank isolated ion pairs by Coulomb energy when charge and distance pull in different directions.
- NaCl or KCl: larger lattice energy?Compare the lattice energies of two salts with equal charges from the size of the cation.
- Rank the sodium halides by lattice energyRank salts with the same cation by lattice energy from anion size.
Ionic and covalent bonds
- Rank metal and carbon chlorides by ionic characterRank bonds to the same nonmetal by ionic character from the electronegativity of the other atom.
- Most ionic bond: charge or electronegativity?Judge bond ionic character by electronegativity difference rather than by ion charges.
Calcular 11
Ionic and covalent bonds
- Electronegativity difference in an Al–Cl bondCalculate the electronegativity difference of a metal–nonmetal bond and see that it can fall in the polar covalent range.
- Percent ionic character of HClCalculate percent ionic character from a measured dipole moment and bond length.
Born–Haber cycles
- Lattice energy of CaF₂Calculate the lattice energy of an MX₂ salt, counting two halogen atoms and two electron affinities.
- Electron affinity of chlorine from a KCl cycleUse a Born–Haber cycle in reverse to find an unknown electron affinity.
- Enthalpy of formation of LiF from its lattice energyCalculate an enthalpy of formation by running a Born–Haber cycle forward from a known lattice energy.
- Lattice energy of MgOCalculate the lattice energy of a 2+/2− oxide from a Born–Haber cycle with two ionization and two electron-gain steps.
- Lattice energy of NaCl from a Born–Haber cycleCalculate the lattice energy of a 1:1 salt from a Born–Haber cycle.
Coulomb's law and lattice energy
- Coulomb energy of a mole of Mg²⁺–O²⁻ pairsConvert a single ion-pair Coulomb energy for doubly charged ions into kJ per mole of pairs.
- How much stronger is the Mg²⁺–O²⁻ attraction?Use Coulomb's law to calculate the ratio of two ion-pair energies with different charges and distances.
- Energy of one Na⁺–Cl⁻ ion pairCalculate the Coulomb potential energy of a single ion pair with its sign.
Properties of ionic compounds
- Enthalpy of solution of NaClCalculate an enthalpy of solution from the lattice energy and the hydration enthalpy of the ions.
Encontre o erro 3
Ionic and covalent bonds
- Is a polar covalent bond 0% ionic?Find the error in reasoning that treats a polar covalent bond as having no ionic character.
Coulomb's law and lattice energy
- More ionic means larger lattice energy?Diagnose the error of predicting lattice energy from electronegativity difference instead of charge and distance.
Born–Haber cycles
- Find the error in a Na₂O cycleDiagnose a stoichiometry error in a Born–Haber calculation for an M₂X compound.
Interprete as evidências 2
Properties of ionic compounds
- Which unknown solid is ionic?Interpret melting point and conductivity data to identify an ionic solid among other solid types.
Coulomb's law and lattice energy
- Reading lattice energies of isoelectronic saltsInterpret lattice-energy data for isoelectronic salts to separate the effect of charge from that of distance.
Trabalhe de trás para frente 1
- Which compound does this cycle describe?Work backwards from the steps of a Born–Haber cycle to the ionic compound it describes.
Planeje uma síntese 1
- Choosing a furnace liningChoose an ionic solid for a high-temperature application from its lattice energy and melting point.
Explique por quê 7
Ionic and covalent bonds
- Why AlF₃ and AlCl₃ behave so differentlyExplain how cation polarizing power and anion size give a metal halide substantial covalent character.
- Is any bond 100% ionic?Explain why percent ionic character varies continuously and never reaches 100%.
Properties of ionic compounds
- Why does a salt crystal shatter?Explain the brittleness of ionic crystals from the arrangement of charges in the lattice.
- Why is LiF nearly insoluble?Explain a solubility difference between two salts from the balance of lattice energy and hydration.
- Two chlorides, 900 °C apartExplain why an ionic solid melts far higher than a molecular solid containing a polar covalent bond.
Coulomb's law and lattice energy
- Why the lattice beats the ion pairExplain why a crystal's lattice energy exceeds the Coulomb energy of isolated ion pairs at the same distance.
Born–Haber cycles
- Why do oxides contain O²⁻?Explain why the oxide ion exists in ionic solids although adding a second electron to oxygen is endothermic.
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Depois, Scan Standard: /mês