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Química Geral · Liquids, solids and solutions

Diagramas de fases da água e do CO₂

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O que você vai aprender

  • Read a pressure–temperature phase diagram: name the phase in each region, the two-phase equilibrium on each line, the normal melting and boiling points, the triple point and the critical point.
  • Explain the negative solid–liquid slope of water and the positive slope of carbon dioxide from the densities of the solid and the liquid.
  • Predict the sequence of phase changes along a path of constant pressure or constant temperature, including sublimation, deposition and supercritical behaviour.
  • Calculate with phase-diagram data: unit conversions of triple and critical points, enthalpies of sublimation, the Clapeyron slope of the melting line and vapor pressures from the Clausius–Clapeyron equation.

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Regions and lines

A phase diagram plots pressure against temperature and shows which phase is stable at each combination. Solid is stable at low temperature and high pressure, gas at high temperature and low pressure, and liquid in between. Each line marks the conditions at which two phases coexist in dynamic equilibrium: molecules still cross between the phases, but the rates in the two directions are equal. The solid–liquid line is the melting curve, the liquid–gas line the vaporization (vapor-pressure) curve, and the solid–gas line the sublimation curve. Where the vaporization curve crosses 1 atm you read the normal boiling point; where the melting curve crosses 1 atm, the normal melting point. While two phases coexist at fixed pressure, added heat changes the amounts of the phases, not the temperature.

Triple point, critical point and supercritical fluids

The three lines meet at the triple point, the single temperature and pressure at which solid, liquid and gas coexist. For water it is 0.01 °C and 611.7 Pa (0.00604 atm, 4.59 torr); below this pressure liquid water cannot exist, so ice heated at constant pressure sublimes. The vaporization curve stops at the critical point (water 374 °C and 218 atm; CO₂ 31.0 °C and 72.8 atm). There the liquid and the vapor reach the same density and the meniscus disappears. Above the critical temperature no pressure, however high, can liquefy the gas, because the molecules' kinetic energy outweighs their attractions; a substance above both its critical temperature and its critical pressure is a supercritical fluid, with a density close to a liquid's but flowing and diffusing like a gas. Stronger intermolecular attractions give higher critical temperatures: helium 5.2 K, methane 191 K, ammonia 405 K, water 647 K. Because the vaporization curve ends, a liquid can be turned into a gas without boiling by taking a path around the critical point.

Water: a melting line that leans left

Ice (0.917 g/cm³) is less dense than liquid water (1.000 g/cm³ at 0 °C), so a given mass of water takes up more room as ice: for the same mass, V(ice)/V(liquid) = ρ(liquid)/ρ(ice). Raising the pressure favours the phase with the smaller volume, the liquid, so the melting point of ice falls as pressure rises and the solid–liquid line slopes up to the left. The Clapeyron equation gives the slope: dP/dT = ΔHfus/(T·ΔV). Per mole, V(liquid) = 18.02 cm³ and V(ice) = 18.02/0.917 = 19.65 cm³, so ΔV = −1.63 cm³/mol = −1.63 × 10⁻⁶ m³/mol, and dP/dT = 6010 J/mol ÷ (273.15 K × −1.63 × 10⁻⁶ m³/mol) = −1.35 × 10⁷ Pa/K = −133 atm/K. Each extra atmosphere therefore lowers the melting point by only about 0.0075 °C: at 100 atm ice melts at 0 − 99/133 = −0.74 °C. The same slope explains why the triple point (0.01 °C, 0.006 atm) lies slightly above the normal melting point (0.00 °C, 1 atm). Most substances, carbon dioxide included, have a denser solid and a melting line that slopes up to the right.

Carbon dioxide and sublimation

The triple point of CO₂ is −56.6 °C and 5.11 atm. Because 1 atm is below the triple-point pressure, solid CO₂ (dry ice) at 1 atm never melts: it sublimes at −78.5 °C. Liquid CO₂ exists only above 5.11 atm and only between the triple-point temperature and the critical temperature, 31.0 °C. Heated at 20 atm from −80 °C, CO₂ melts just above −56.6 °C (its melting line leans right), boils near −20 °C and is a gas at room temperature. Sublimation (solid → gas) and its reverse, deposition, follow the solid–gas line. By Hess's law, ΔHsub = ΔHfus + ΔHvap at the same temperature: for ice near 0 °C, 6.01 + 45.0 = 51.0 kJ/mol. Freeze-drying uses this line: frozen food is held below the triple-point pressure so its ice sublimes instead of melting. Snow and freezer ice shrink below 0 °C for the same reason, whenever the surrounding air holds less water vapor than the ice's sublimation pressure.

Numbers from the curves

Along a solid–gas or liquid–gas line, the Clausius–Clapeyron equation links the equilibrium pressure to temperature: ln(P₂/P₁) = −(ΔH/R)(1/T₂ − 1/T₁), with ΔH the enthalpy of sublimation or vaporization in J/mol, R = 8.314 J mol⁻¹ K⁻¹ and T in kelvins. Example: ice at its triple point has a vapor pressure of 611.7 Pa at 273.16 K. With ΔHsub = 51.0 kJ/mol, at −10 °C (263.15 K): 1/263.15 − 1/273.16 = 1.393 × 10⁻⁴ K⁻¹, ΔH/R = 6134 K, so ln(P₂/611.7) = −0.854 and P₂ = 260 Pa. Heat for a phase change is moles × molar enthalpy: subliming 50.0 g of dry ice (ΔHsub = 25.2 kJ/mol) takes 50.0/44.01 × 25.2 = 28.6 kJ. For pressure units use 1 atm = 101.325 kPa = 760 torr and 1 bar = 100 kPa.

Following a path across the diagram

Trace the path the conditions take and note each line crossed; every crossing is a phase change at that line's temperature and pressure. Heating at constant pressure is a horizontal path: water at 1 atm melts at 0 °C and boils at 100 °C, but water at 0.001 atm, below its triple-point pressure, goes straight from ice to vapor. Compressing at constant temperature is a vertical path: water vapor at −0.5 °C first deposits as ice, and because the melting line leans left the ice melts again near 1 + 0.5 × 133 = 67.5 atm. A sealed container of liquid and vapor at fixed temperature always returns to the same vapor pressure after a disturbance; changing the volume only shifts how much of each phase is present. Above the critical temperature a vertical path never crosses a line, and the fluid simply becomes denser.

What to carry forward

Lines are two-phase equilibria, the triple point is the only place all three phases coexist, and the vaporization curve ends at the critical point, beyond which the fluid is supercritical. Water's melting line slopes left (about −133 atm/K) because ice is less dense than liquid water; carbon dioxide's slopes right, and its triple point above 1 atm makes dry ice sublime at −78.5 °C. Read any process as a path across the diagram, and use ΔHsub = ΔHfus + ΔHvap and the Clapeyron and Clausius–Clapeyron equations for numbers.

Problemas de prática (40)

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Preveja o produto 8

Water and carbon dioxide compared

  • A CO₂ cylinder warmed in the sunPredict the state of a sealed liquid–vapor CO₂ sample warmed past its critical temperature.
  • Squeezing two melting equilibriaPredict the opposite responses of ice–water and solid–liquid CO₂ equilibria to an increase in pressure.

Following phase changes

  • Heating solid CO₂ at 10 atmPredict the sequence of phase changes of carbon dioxide heated at a pressure above its triple point.
  • Compressing CO₂ gas at 0 °COrder the stages of isothermal compression of a gas below its critical temperature.
  • Warming dry ice at 1 atmPredict the phase change of solid carbon dioxide warmed at atmospheric pressure.
  • Pushing the piston on water and its vaporPredict how a liquid–vapor equilibrium responds to compression at constant temperature.
  • Compressing water vapor at −1.0 °CPredict the phase sequence when water vapor below 0 °C is compressed, using the left-leaning melting curve.
  • Heating ice at 0.0040 atmPredict that ice heated below water's triple-point pressure sublimes instead of melting.

Classificar 5

Reading a phase diagram

  • CO₂ at 20 °C and 80 atmClassify a state above the critical pressure but below the critical temperature as liquid, not supercritical.
  • CO₂ at −70 °C and 1 atmClassify the stable phase of carbon dioxide at a low temperature and 1 atm using its sublimation point.
  • CO₂ at 40 °C and 100 atmClassify a state above both the critical temperature and the critical pressure as a supercritical fluid.
  • Which point is liquid water?Use water's negative melting slope, triple point and critical point to classify points on its phase diagram.
  • Water at 0.01 °C and 0.00604 atmIdentify the triple point of water as the only condition at which ice, liquid and vapor coexist.

Comparar 4

Water and carbon dioxide compared

  • Four temperatures on CO₂'s phase diagramRank the sublimation, triple, boiling and critical temperatures of carbon dioxide from the pressures of the points.
  • Rank critical temperaturesRank critical temperatures by the strength of intermolecular attractions.
  • Solid–liquid lines of water and CO₂Compare the signs of the solid–liquid line slopes of water and carbon dioxide.
  • Four temperatures on water's phase diagramRank melting, triple and boiling temperatures of water using the left-leaning melting line.

Calcular 11

Calculations from phase diagrams

  • Slope of water's melting lineCalculate the slope of water's solid–liquid line with the Clapeyron equation from densities and the enthalpy of fusion.
  • CO₂ critical pressure in atmospheresConvert the critical pressure of carbon dioxide from megapascals to atmospheres.
  • Temperature range of liquid CO₂Read the temperature range over which liquid carbon dioxide can exist from its triple and critical points.
  • Heat to sublime a kilogram of dry iceCalculate the heat absorbed when a mass of dry ice sublimes from its molar enthalpy of sublimation.
  • Heat to freeze-dry 100 g of iceCombine enthalpies of fusion and vaporization by Hess's law to find the heat needed to sublime a mass of ice.
  • Melting point under 300 m of iceCalculate the pressure-melting point at the base of a glacier from the weight of the overlying ice.
  • Vapor pressure of ice at −20 °CUse the Clausius–Clapeyron equation along the sublimation curve to find the vapor pressure of ice at a lower temperature.
  • Pressure that melts ice at −1.00 °CUse the slope of water's melting line to find the pressure at which ice melts below 0 °C.
  • Why the triple point is 0.01 °CCalculate how far the triple-point temperature of water lies above its melting point at 1 atm from the melting-line slope.
  • Water's triple-point pressure in torrConvert the triple-point pressure of water from pascals to torr.

Water and carbon dioxide compared

  • Volume increase when water freezesCalculate the percentage volume increase of water on freezing from the densities of ice and liquid.

Encontre o erro 1

  • Does blade pressure melt the ice?Diagnose the pressure-melting explanation of skating with the slope of water's melting line.

Interprete as evidências 3

Following phase changes

  • Liquid and vapor at 100 °C and 1 atmInterpret coexistence on a phase boundary as a dynamic equilibrium with equal rates of evaporation and condensation.

Reading a phase diagram

  • Heating substance X at 1 atmRead the phase changes along a 1 atm heating path from the triple point, critical point and solid–liquid density of a substance.
  • What a point on the liquid–gas curve meansInterpret a point on a phase boundary as two phases in dynamic equilibrium.

Trabalhe de trás para frente 2

Following phase changes

  • Which pressure made ice sublime?Work backwards from an observed sublimation to the pressure range in which it was heated.

Reading a phase diagram

  • What a solid that sublimes at 1 atm revealsDeduce the triple-point pressure of a substance from its sublimation under constant pressure.

Planeje uma síntese 2

Following phase changes

  • Setting up a freeze-dryerPlan freeze-drying conditions that remove ice by sublimation below water's triple point.

Reading a phase diagram

  • Liquid to gas without boilingPlan a path around the critical point that turns a liquid into a gas without ever forming two phases.

Explique por quê 4

Water and carbon dioxide compared

  • Why dry ice leaves no puddleExplain from the triple-point pressure why solid carbon dioxide never melts at atmospheric pressure.
  • Why pressure lowers the melting point of iceExplain the negative solid–liquid slope of water from the densities of ice and liquid water.

Following phase changes

  • Shrinking ice cubes in a frost-free freezerExplain the slow loss of ice below 0 °C as sublimation into dry air.

Reading a phase diagram

  • Why the liquid–gas curve stopsExplain why the vaporization curve ends at the critical point instead of continuing to higher temperatures.

Travou em diagramas de fases da água e do CO₂? Escaneie o problema.

Tire uma foto da reação da sua lista ou do livro e desenhe o mecanismo com cada seta corrigida. 1 scan grátis agora, sem cadastro; mais 1 com uma conta gratuita.

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