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Química Geral · Liquids, solids and solutions

Soluções e unidades de concentração

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O que você vai aprender

  • Predict whether a solute dissolves in a solvent from the intermolecular forces each one has.
  • Build the enthalpy of solution from solute separation, solvent separation and mixing, and explain why some endothermic dissolutions still happen.
  • Describe how the solubility of solids and gases changes with temperature and use solubility data to classify and crystallize solutions.
  • Apply Henry's law to find dissolved gas concentrations from partial pressures and the reverse.
  • Calculate molarity, molality, mole fraction, mass percent, ppm and ppb, and convert between them using the solution density.

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Like dissolves like

A solution forms when solute–solvent attractions can replace the solute–solute and solvent–solvent attractions that must be broken. Nonpolar substances held together by dispersion forces mix with each other: iodine (drawn with hexane) dissolves in hexane to give a violet solution but barely dissolves in water, because a nonpolar molecule cannot replace the hydrogen bonds it would break in water. Polar molecules that hydrogen bond, such as ethanol, mix with water in all proportions. In a homologous series the nonpolar part grows and water solubility falls: ethanol is miscible with water, 1-butanol dissolves to roughly 70 g/L, 1-hexanol to about 6 g/L and hexane almost not at all. Ionic solids dissolve in water through ion–dipole attractions: the oxygen end of water points at cations and the hydrogen end at anions.

The energy of dissolving

Think of dissolving in three steps. Separating the solute particles absorbs energy (ΔH₁ > 0), making room in the solvent absorbs energy (ΔH₂ > 0), and letting solute and solvent attract each other releases energy (ΔH₃ < 0). The enthalpy of solution is the sum, ΔHsoln = ΔH₁ + ΔH₂ + ΔH₃; a positive value means the solution cools as the solute dissolves. For an ionic solid the first step is the lattice enthalpy and the last two are combined into the hydration enthalpy of the ions. For NaCl (drawn) the lattice enthalpy is +788 kJ/mol and the hydration enthalpy is −784 kJ/mol, so ΔHsoln ≈ +788 − 784 = +4 kJ/mol. Small and highly charged ions are hydrated most strongly, so hydration enthalpies grow more negative from Cs⁺ to Li⁺ and are several times larger again for Mg²⁺. An endothermic dissolution can still be spontaneous because dispersing the solute raises the entropy: ammonium nitrate (ΔHsoln ≈ +26 kJ/mol) dissolves readily and cools the water, which is how instant cold packs work.

Solubility and temperature

Solubility is the amount of solute in a saturated solution, often quoted in g per 100 g of water. A solution holding less is unsaturated; one that holds more than the solubility, without crystals, is supersaturated and crystallizes when seeded. Most solids become more soluble as the temperature rises, some steeply and some hardly at all. Potassium nitrate dissolves about 31.6 g per 100 g of water at 20 °C and about 110 g at 60 °C, so cooling a saturated 60 °C solution of 100 g water to 20 °C deposits 110 − 31.6 = 78.4 g of crystals. Sodium chloride changes only from about 36 g to about 38 g between 20 °C and 80 °C, so it is recovered by evaporating the water rather than by cooling. Gases behave the opposite way: dissolving a gas has no solute–solute attractions to overcome and is usually exothermic, so a gas becomes less soluble as the water warms. Warm water holds less oxygen, and a warm soft drink goes flat faster.

Henry's law

At constant temperature the concentration of a dissolved gas is proportional to its partial pressure above the solution: S = kH × P(gas). With kH(O₂) = 1.3 × 10⁻³ mol L⁻¹ atm⁻¹ at 25 °C and air at 1.00 atm containing 21 % O₂, P(O₂) = 0.21 atm and S = 1.3 × 10⁻³ × 0.21 = 2.7 × 10⁻⁴ mol/L, which is 2.7 × 10⁻⁴ × 32.00 = 8.7 × 10⁻³ g/L, or 8.7 mg/L. Use the partial pressure, not the total pressure: for a gas mixture P(gas) = x(gas) × P(total). Doubling the partial pressure doubles the solubility, which is why a sealed soft drink holds much more CO₂ than an open one and why divers breathing compressed air take up extra nitrogen. Henry's law works best for dilute solutions of gases that do not react with the solvent; very soluble, reactive gases such as ammonia and hydrogen chloride do not follow it.

Concentration units

Molarity, M = mol solute per litre of solution. Molality, m = mol solute per kilogram of solvent. Mole fraction, x(A) = mol A ÷ total mol of all components. Mass percent = mass solute ÷ mass solution × 100 %. Parts per million and per billion are mass ratios multiplied by 10⁶ and 10⁹; for dilute aqueous solutions, whose density is close to 1.00 g/mL, 1 ppm ≈ 1 mg/L and 1 ppb ≈ 1 µg/L. Example: 10.0 g of urea (drawn, 60.06 g/mol) in 90.0 g of water is 10.0/100.0 = 10.0 % by mass; it contains 10.0/60.06 = 0.1665 mol urea, so the molality is 0.1665/0.0900 kg = 1.85 m; water is 90.0/18.015 = 4.996 mol, so x(urea) = 0.1665/(0.1665 + 4.996) = 0.0323. Molality, mole fraction and the mass-based units depend only on masses and amounts, so they do not change with temperature; molarity does, because the solution volume expands on warming.

Converting with density

Pick a convenient amount of solution, then use the density to switch between its mass and its volume. Choose the basis that makes the unit you are given or want simple: 1 L of solution for a molarity, 1 kg of solvent for a molality, 100 g of solution for a mass percent. Example: 20.0 % NaOH by mass has a density of 1.22 g/mL. One litre has a mass of 1220 g, of which 20.0 % is NaOH: 244 g ÷ 40.00 g/mol = 6.10 mol, so the solution is 6.10 M. For the molality take 100 g of solution: 20.0 g NaOH is 0.500 mol dissolved in 80.0 g of water, so the molality is 0.500/0.0800 kg = 6.25 m. The two numbers differ because a litre of solution is not a kilogram of solvent. Going from molality to molarity runs the other way: mass of solution = 1000 g solvent + mass of solute, then volume = mass ÷ density.

What to carry forward

A solute dissolves when solute–solvent attractions can pay for the attractions that are broken, and entropy can carry a slightly endothermic dissolution. Solids usually become more soluble when heated; gases become less soluble, and their solubility is proportional to partial pressure (S = kH·P). For concentrations, write each unit as a fraction (mol per L of solution, mol per kg of solvent, mol per total mol, g per 100 g of solution), choose a convenient basis, and use the density to turn solution mass into volume.

Problemas de prática (40)

Praticar é grátis com uma conta.

Preveja o produto 3

Solubility, temperature and gases

  • Which gas breaks Henry's law?Predict which gas departs from Henry's law from its solubility and its reaction with water.
  • Oxygen in a warmed riverPredict how warming water changes the amount of a gas it can hold at saturation.

How solutions form

  • What dissolves in hexane?Predict which solute dissolves in a nonpolar solvent from the intermolecular forces of solute and solvent.

Classificar 4

Converting units with density

  • What links molarity and molality?Identify the measured property needed to convert between a volume-based and a mass-based concentration.

Solubility, temperature and gases

  • Classify a potassium nitrate solutionClassify a solution as unsaturated, saturated or supersaturated by comparing its composition with the solubility.

Concentration units

  • Which unit changes on warming?Classify concentration units by whether they depend on temperature.

How solutions form

  • Which steps of dissolving absorb energy?Assign the sign of the enthalpy change to each step of the three-step model of dissolution.

Comparar 4

How solutions form

  • Rank by solubility in waterRank alcohols and an alkane by water solubility from the balance of hydrogen-bonding and nonpolar parts.
  • Rank ions by hydration enthalpyRank ions by the magnitude of their hydration enthalpy using charge and ionic radius.
  • Fat-soluble or water-soluble vitamin?Compare the water solubility of two vitamins from the proportion of hydrogen-bonding groups in their structures.

Concentration units

  • Rank glucose solutions given in different unitsRank solutions expressed in different concentration units by converting them to a common unit.

Calcular 17

Solubility, temperature and gases

  • Nitrogen released when a diver surfacesCombine Henry's law and the ideal gas law to find the volume of gas released when the pressure over a solution drops.
  • Methane dissolved from a gas mixtureCombine Dalton's law and Henry's law to find the mass concentration of one gas dissolved from a mixture.
  • Dissolved nitrogen in waterUse Henry's law with a partial pressure to find the concentration of a dissolved gas.
  • CO₂ lost from an opened soft drinkUse Henry's law at two partial pressures to find the mass of gas released from a solution.

Concentration units

  • Molality of an antifreeze solutionCalculate molality from the mass of solute and the mass of solvent.
  • Sodium fluoride for water fluoridationUse a ppm target to find the mass of a salt needed to supply one of its ions.
  • Mole fraction of 30 % hydrogen peroxideConvert a mass percent into a mole fraction using a 100 g basis.
  • Lead in drinking water in ppbExpress a trace contaminant as parts per billion by mass.
  • Mole fraction of glucose from molalityConvert a molality into a mole fraction by choosing 1 kg of solvent as the basis.
  • Mass percent of a sugar solutionCalculate the mass percent of a solute from the masses of solute and solvent.

Converting units with density

  • Molarity from a mole fractionConvert a mole fraction into a molarity through the mass and the volume of a chosen amount of solution.
  • Magnesium in seawater: ppm to mmol/LConvert a ppm-by-mass concentration into a molar concentration using the density of a non-dilute solution.
  • Molality of 2.00 M sodium chlorideConvert a molarity into a molality using the solution density and the solute's molar mass.
  • Molality of concentrated sulfuric acidFind the molality of a concentrated solution from its mass percent and recognise which data are not needed.
  • Molarity of concentrated sulfuric acidConvert a mass percent into a molarity using the solution density.
  • Molarity of 3.00 m ureaConvert a molality into a molarity by building the solution mass on a 1 kg solvent basis.

How solutions form

  • Enthalpy of solution of NaClCombine a lattice enthalpy and a hydration enthalpy to obtain an enthalpy of solution.

Encontre o erro 2

How solutions form

  • Why hexane and water separateFind the flaw in an explanation of why a nonpolar liquid does not mix with water.

Concentration units

  • Check a molality labelFind the error when molality is calculated with the mass of solution instead of the mass of solvent.

Interprete as evidências 2

Converting units with density

  • Read a concentrated ammonia labelRead the mass percent and density on a reagent label and turn them into a molarity.

Solubility, temperature and gases

  • Crystals from cooling a KNO₃ solutionRead solubility data at two temperatures to find the mass that crystallizes when a saturated solution is cooled.

Trabalhe de trás para frente 3

How solutions form

  • Hydration enthalpy of chloride from KClWork backwards through the dissolution cycle to find the hydration enthalpy of one ion.

Converting units with density

  • Mass percent of concentrated nitric acidWork back from a molarity and a density to the mass percent printed on a reagent label.

Solubility, temperature and gases

  • O₂ pressure for a target concentrationRearrange Henry's law to find the partial pressure needed for a required dissolved-gas concentration.

Planeje uma síntese 2

Converting units with density

  • Prepare 0.500 m sodium chlorideChoose the procedure that produces a solution of specified molality rather than molarity.

Solubility, temperature and gases

  • Recovering salt from brineChoose a crystallization method from how strongly a solid's solubility depends on temperature.

Explique por quê 3

How solutions form

  • Why acetone and chloroform warm on mixingExplain an exothermic mixing of two liquids by a solute–solvent attraction absent from both pure liquids.
  • Why does a cold pack work?Explain why an endothermic dissolution can still be spontaneous.

Solubility, temperature and gases

  • Why gases dissolve exothermicallyExplain from the three-step model why dissolving a gas in water is usually exothermic.

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