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Química Geral · Exam review

Revisão para a prova: líquidos, sólidos e soluções

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O que você vai aprender

  • Identify the intermolecular forces in a pure substance or a mixture and use them to rank boiling points, vapor pressures and melting points.
  • Use the two-point Clausius–Clapeyron equation to find ΔHvap, a vapor pressure or a boiling temperature, and apply vapor pressure to condensation and dew-point problems.
  • Calculate the heat for each segment of a heating curve and read phase diagrams, including triple points, critical points and the slope of the solid–liquid line.
  • Count atoms and formula units in cubic unit cells and interconvert density, edge length and atomic radius.
  • Convert between molarity, molality, mole fraction and mass percent, using density where needed.
  • Calculate and compare colligative properties, including Raoult's law for one or two volatile components and molar masses from colligative data.

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Intermolecular forces: the decision rules

Every molecule has London dispersion forces, and they grow with the number of electrons and with contact area. A polar molecule adds dipole–dipole forces. Hydrogen bonding needs an H bonded to N, O or F on one molecule and a lone pair on N, O or F of another; an H on carbon never counts, so pure dimethyl ether and pure acetone have no hydrogen bonds, although both accept hydrogen bonds from water. In solutions, ions attract the dipoles of a polar solvent (ion–dipole forces). At similar molar mass the order is dispersion only < dipole–dipole < hydrogen bonding: ethanol boils at 78 °C and dimethyl ether (drawn beside it, same formula C₂H₆O) at −24 °C. Size can beat polarity: nonpolar Cl₂ (34 electrons) boils at −34 °C, above polar HCl (18 electrons) at −85 °C. Ionic solids melt highest when the ions are small and highly charged: MgO melts near 2850 °C, NaCl at 801 °C. Stronger forces mean a higher boiling point, a larger ΔHvap and a lower vapor pressure.

Vapor pressure and the Clausius–Clapeyron equation

The vapor pressure of a pure liquid depends only on temperature. It does not depend on how much liquid is present or on the volume above it, as long as some liquid remains. A liquid boils when its vapor pressure equals the external pressure; the normal boiling point is the temperature at which it equals 1 atm (760 torr). Between two temperatures, ln(P₂/P₁) = −(ΔHvap/R)(1/T₂ − 1/T₁) with R = 8.314 J mol⁻¹ K⁻¹, T in kelvin and the natural logarithm. Worked example: water has 23.8 torr at 25.0 °C and ΔHvap = 44.0 kJ/mol, so at 35.0 °C ln(P₂/23.8) = (44 000/8.314)(1/298.15 − 1/308.15) = 0.576, and P₂ = 23.8 × 1.779 = 42.3 torr. A gas phase can hold a vapor only up to its vapor pressure: water condenses (dew forms) when the air cools to the temperature at which the vapor pressure equals the partial pressure of water present. Traps: Celsius temperatures, log₁₀ instead of ln (which makes ΔHvap 2.303 times too small) and J versus kJ.

Heating curves and phase diagrams

On a heating curve, sloped segments warm one phase: q = m·c·ΔT. Flat segments are phase changes at constant temperature: q = n·ΔH. Worked example: 10.0 g of ice at −10.0 °C to liquid water at 25.0 °C takes 10.0 × 2.09 × 10.0 = 209 J, then (10.0/18.02) × 6010 = 3335 J to melt, then 10.0 × 4.18 × 25.0 = 1045 J, in total 4.59 kJ. At constant heating power, the segment with the largest specific heat rises most slowly. Melting only loosens the attractions while vaporizing separates the molecules completely, so ΔHfus < ΔHvap; and ΔHsub = ΔHfus + ΔHvap at the same temperature, so ΔHsub is the largest of the three. A supercooled liquid that suddenly freezes warms to its freezing point by the heat its partial freezing releases. On a phase diagram, each line is a two-phase equilibrium. Below the triple-point pressure no liquid exists, so heating a solid there makes it sublime; above the critical temperature no pressure can liquefy the gas, which becomes a supercritical fluid. A solid–liquid line that tilts right means the solid is denser than the liquid; water's tilts left because ice is less dense.

Solids and cubic unit cells

Types of solid: molecular (dispersion, dipole or hydrogen-bond forces), ionic, covalent network and metallic. In a cubic cell a corner atom counts 1/8, an edge atom 1/4, a face atom 1/2 and a body atom 1. Simple cubic: 1 atom, coordination number 6, a = 2r, 52 % filled. Body-centred cubic: 2 atoms, coordination number 8, atoms touch along the body diagonal so √3·a = 4r, 68 % filled. Face-centred cubic: 4 atoms, coordination number 12, atoms touch along the face diagonal so √2·a = 4r, 74 % filled. Density ρ = n·M/(NA·a³), with a converted from pm to cm (1 pm = 10⁻¹⁰ cm). Worked example: copper is fcc with a = 361.5 pm, so ρ = 4 × 63.55/(6.022 × 10²³ × (3.615 × 10⁻⁸ cm)³) = 8.94 g/cm³. Many ionic solids are an fcc array of anions with cations in holes; per fcc cell there are 4 octahedral and 8 tetrahedral holes. Rock salt (NaCl, drawn) fills every octahedral hole (4 NaCl per cell), zinc blende (ZnS) half the tetrahedral holes (4 ZnS per cell), and fluorite (CaF₂) has Ca²⁺ in the fcc positions with F⁻ in all 8 tetrahedral holes (4 CaF₂ per cell).

Concentration units and conversions

Molarity M = mol solute per litre of solution; molality m = mol solute per kilogram of solvent; mole fraction χ = mol of one component ÷ total mol; mass percent = mass solute ÷ mass solution × 100; ppm = mass solute ÷ mass solution × 10⁶. Molality, mole fraction and mass percent do not change with temperature; molarity does, because the volume does. To convert, pick a convenient amount and use density to link mass and volume. Worked example: 10.0 % NaCl by mass, density 1.071 g/mL. Take 100.0 g of solution: 10.0 g NaCl = 0.1711 mol and 90.0 g water, so m = 0.1711/0.0900 = 1.90 mol/kg. The 100.0 g occupies 100.0/1.071 = 93.4 mL, so M = 0.1711/0.0934 = 1.83 mol/L. Trap: molality divides by the mass of solvent, never by the mass of solution.

Colligative properties

Colligative properties depend on the concentration of dissolved particles. Raoult's law: P(solvent) = χ(solvent)·P°(solvent). For two volatile liquids each obeys its own Raoult's law, the total is the sum, and the vapor is richer in the more volatile liquid: y(A) = P(A)/P(total). A total vapor pressure above the Raoult's-law value (positive deviation) means A–B attractions are weaker than the average of A–A and B–B and mixing is endothermic; a lower one means stronger A–B attractions. ΔTf = i·Kf·m and ΔTb = i·Kb·m (water: Kf = 1.86 and Kb = 0.512 °C kg/mol), and π = i·M·R·T with R = 0.08206 L atm mol⁻¹ K⁻¹. The ideal van 't Hoff factor i counts ions per formula unit (glucose, drawn, 1; NaCl 2; CaCl₂ 3); real electrolytes fall a little short because of ion pairing. Worked example: ideal 0.100 m Na₂SO₄ has ΔTf = 3 × 1.86 × 0.100 = 0.558 °C and freezes at −0.558 °C. For a molar mass, find moles of solute from the measured effect, then divide grams by moles; osmotic pressure is the method of choice for large molecules because even tiny molarities give measurable pressures.

What to carry forward

Name the forces first: dispersion always, dipole–dipole for polar molecules, hydrogen bonding only for H on N, O or F, ion–dipole in salt solutions; stronger forces mean higher boiling points and lower vapor pressures. Use ln(P₂/P₁) = −(ΔHvap/R)(1/T₂ − 1/T₁) with kelvin and natural logs. On heating curves use m·c·ΔT on slopes and n·ΔH on plateaus. Count unit-cell atoms with 1/8, 1/4, 1/2 and 1, pair sc, bcc and fcc with a = 2r, √3·a = 4r and √2·a = 4r, and use ρ = n·M/(NA·a³) in cm. Convert concentrations by choosing a basis and using density, and for colligative properties count particles: ΔT = i·K·m, π = i·M·R·T and P = χ·P°.

Problemas de prática (40)

Praticar é grátis com uma conta.

Preveja o produto 1

  • Does iodine sublime when heated at 1 atm?Use the triple-point pressure to predict whether a solid melts or sublimes when heated at 1 atm.

Classificar 6

Concentration and colligative properties

  • Which concentration goes in which equation?Match the freezing-point, osmotic-pressure and Raoult's-law equations with the concentration unit each requires.

Solids and unit cells

  • Which unit-cell statement is true?Identify the correct atom count, coordination number, touching direction or packing efficiency for cubic unit cells.
  • What holds solid argon together?Classify a noble-gas solid by the only attractive force available between its atoms.

Intermolecular forces and vapor pressure

  • Hydrogen bonds between two different moleculesDecide whether two different molecules in a mixture can hydrogen-bond, by checking for a donor H on N, O or F and an acceptor lone pair.
  • Which vapor-pressure statement is true?Identify the correct statement about what does and does not change the vapor pressure of a pure liquid.

Phase changes and phase diagrams

  • Which phase-diagram statement is true?Identify the correct statement about triple points, critical points, normal boiling points and the melting line of water.

Comparar 4

Concentration and colligative properties

  • Freezing points of four aqueous solutionsRank aqueous solutions by freezing point using the product of van 't Hoff factor and molality.

Solids and unit cells

  • Unit-cell edges of four cubic metalsRank cubic metals by unit-cell edge length by combining each atomic radius with the touching direction of its cell type.

Phase changes and phase diagrams

  • Three phase-change enthalpies of waterRank the enthalpies of fusion, vaporization and sublimation using what each change does to intermolecular attractions.

Intermolecular forces and vapor pressure

  • Four compounds of almost equal massRank the boiling points of compounds of similar molar mass from their dipole moments and hydrogen-bonding ability.

Calcular 18

Intermolecular forces and vapor pressure

  • Acetone boiling under reduced pressureUse the Clausius–Clapeyron equation and a normal boiling point to find the boiling temperature at a reduced pressure.
  • Dew point of humid summer airFind the dew point of air from its relative humidity using vapor pressure and the Clausius–Clapeyron equation.
  • Hexane vapor in a flask moved to an ice bathDecide whether a vapor condenses on cooling and calculate the mass of liquid formed, using Clausius–Clapeyron and the ideal gas law.
  • ΔHvap of methanol from its normal boiling pointCombine a vapor pressure with the normal boiling point in the Clausius–Clapeyron equation to obtain ΔHvap.

Solids and unit cells

  • Atomic radius of aluminum from its densityFind an atomic radius from density by first obtaining the face-centred cubic edge length and then using the face-diagonal contact.
  • Formula units in the fluorite cellCount the ions in an ionic unit cell with sharing fractions and convert the count into formula units.
  • Density of molybdenum from its atomic radiusCalculate the density of a body-centred cubic metal from its atomic radius using the body-diagonal contact.
  • Edge length of the KCl cell from its densityCalculate the edge length of a rock-salt unit cell from the density and molar mass of the compound.
  • Density of zinc blendeDeduce the number of formula units in a zinc blende cell from hole occupancy and use it to calculate the density.

Phase changes and phase diagrams

  • Boiling away benzene with a steady heaterUse the length of one heating-curve plateau to find the heater power, then time the remaining segments.
  • Melting gallium in the handAdd a warming step and a melting step to find the heat needed to melt a metal that starts below its melting point.
  • Supercooled water that suddenly freezesUse an energy balance to find how much of a supercooled liquid freezes when it returns to its freezing point.

Concentration and colligative properties

  • Boiling point of a calcium chloride solutionCalculate the boiling point of an electrolyte solution from mass data, molality and the ideal van 't Hoff factor.
  • Mole fraction of ethanol in a 40 % mixtureConvert a mass composition into a mole fraction.
  • Vapor above equal masses of methanol and ethanolCombine a mass-to-mole-fraction conversion with Raoult's and Dalton's laws to find the vapor composition above an ideal liquid mixture.
  • Mass percent of a 2.50 m KI solutionConvert a molality into a mass percent by choosing one kilogram of solvent as the basis.
  • Molar mass of a protein from osmotic pressureDetermine the molar mass of a macromolecule from the osmotic pressure of a dilute solution.
  • Molality of 0.500 M sucroseConvert molarity into molality using the solution density and the mass of solute.

Encontre o erro 2

Intermolecular forces and vapor pressure

  • A ΔHvap that is too smallDiagnose a Clausius–Clapeyron error by recomputing what each common slip would give.

Phase changes and phase diagrams

  • Find the missing step on a heating curveFind the omitted segment in a multistep heating-curve calculation.

Interprete as evidências 4

Concentration and colligative properties

  • A mixture above Raoult's lineInterpret a positive deviation from Raoult's law in terms of the relative strengths of unlike and like intermolecular attractions.
  • How many chlorides does the metal carry?Use a measured freezing-point depression to find the van 't Hoff factor and deduce the formula of an ionic solute.

Phase changes and phase diagrams

  • Which part of water's heating curve climbs slowest?Relate the slopes of a heating curve to the specific heats of the phases at constant heating power.
  • Reading the phase diagram of substance QUse triple-point, critical-point and melting-line data to predict the phases a substance passes through along different paths.

Trabalhe de trás para frente 2

Concentration and colligative properties

  • Molecular formula from a camphor freezing pointWork back from a freezing-point depression to the molar mass and then to the molecular formula of a compound with a known empirical formula.

Solids and unit cells

  • Formula of an oxide from its filled holesWork backward from hole occupancy in a face-centred cubic anion array to the formula and cation charge of an ionic compound.

Planeje uma síntese 1

  • Making saline that matches bloodPlan the mass of an electrolyte needed for a solution of a target osmotic pressure, using the van 't Hoff factor.

Explique por quê 2

Intermolecular forces and vapor pressure

  • Why nonpolar Cl₂ boils above polar HClExplain why a larger nonpolar molecule can boil higher than a smaller polar one by comparing dispersion and dipole–dipole forces.
  • Why KBr dissolves in water but not in hexaneExplain the solubility of an ionic solid in water but not in a nonpolar solvent in terms of ion–dipole forces and lattice energy.

Travou em revisão para a prova: líquidos, sólidos e soluções? Escaneie o problema.

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