Química Geral · Liquids, solids and solutions
Líquidos e pressão de vapor
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O que você vai aprender
- Describe vapor pressure as a dynamic equilibrium that depends only on the liquid and the temperature, and relate it to intermolecular forces.
- Define the boiling point and the normal boiling point, and predict how boiling changes with external pressure.
- Use the two-point Clausius–Clapeyron equation to find ΔHvap, a vapor pressure or a boiling point, and read ΔHvap from the slope of ln P against 1/T.
- Explain surface tension, viscosity and capillary action in terms of cohesive and adhesive forces.
- Calculate the heat for each segment of a heating or cooling curve with q = mcΔT and q = nΔH, and combine phase-change enthalpies.
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Vapor pressure is a dynamic equilibrium
In a sealed container, molecules at the surface of a liquid that have enough kinetic energy escape into the gas phase, and vapor molecules that strike the surface are recaptured. When the two rates become equal, the pressure of the vapor stops changing: that pressure is the vapor pressure. It depends only on the identity of the liquid and the temperature, not on the volume of the container, the amount of liquid or the surface area, as long as some liquid remains. If the container is enlarged, more liquid evaporates until the same pressure is restored. Weaker intermolecular forces mean more molecules can escape, so the vapor pressure is higher: at 25 °C diethyl ether (dispersion and weak dipole–dipole forces) has a vapor pressure of about 537 torr, while water (an extensive hydrogen-bond network) has 23.8 torr. Vapor pressure rises steeply with temperature because the fraction of molecules in the high-energy tail of the kinetic-energy distribution grows rapidly as the temperature rises.
Boiling and the normal boiling point
A liquid boils when its vapor pressure equals the external pressure: bubbles of vapor can then form and grow throughout the liquid, not only at its surface. The normal boiling point is the boiling point at exactly 1 atm (760 torr); for water it is 100 °C, for ethanol 78.4 °C. At lower external pressure the boiling point is lower: water's vapor pressure is 233.7 torr at 70 °C and 355.1 torr at 80 °C, so where the air pressure is 250 torr water boils between 70 and 80 °C. A pressure cooker at about 2 atm raises the boiling point of water to about 120 °C, and vacuum distillation lets a compound that would decompose at its normal boiling point distil at a lower temperature. While a pure liquid boils at constant pressure its temperature stays fixed; adding heat faster only boils it away faster.
The Clausius–Clapeyron equation
The vapor pressure P of a liquid follows ln P = −ΔHvap/(RT) + C, so a plot of ln P against 1/T (T in kelvin) is a straight line with slope −ΔHvap/R. A steeper line means a larger enthalpy of vaporization and stronger intermolecular forces. For two points, ln(P₂/P₁) = −(ΔHvap/R)(1/T₂ − 1/T₁), with R = 8.314 J mol⁻¹ K⁻¹, ΔHvap in J/mol and both temperatures in kelvin; the pressures may be in any unit, because only their ratio appears. The equation assumes that ΔHvap is constant over the range, that the vapor is ideal and that the volume of the liquid is negligible. Worked example: ethanol (drawn) has a vapor pressure of 400 torr at 63.5 °C (336.65 K) and 760 torr at 78.4 °C (351.55 K). ln(760/400) = 0.6419 and 1/336.65 − 1/351.55 = 1.259 × 10⁻⁴ K⁻¹, so ΔHvap = 8.314 × 0.6419 / (1.259 × 10⁻⁴) = 4.24 × 10⁴ J/mol = 42.4 kJ/mol. To find a boiling point, set P₂ equal to the external pressure and solve for 1/T₂.
Surface tension, viscosity and capillary action
A molecule inside a liquid is pulled equally in all directions by its neighbours; a molecule at the surface has neighbours only beside and below it, so it feels a net inward pull. Enlarging the surface therefore costs energy, and the energy per unit area is the surface tension. Water's surface tension (72.8 mN/m at 20 °C) is high because of hydrogen bonding; it is high enough to support a carefully placed paper clip, and detergents lower it. Viscosity is resistance to flow: it rises with stronger intermolecular forces and with longer molecules that tangle, so glycerol, with three O–H groups, is more than a thousand times as viscous as water, and viscosity falls as the temperature rises. Capillary action is the rise of a liquid in a narrow tube when adhesion between the liquid and the wall is stronger than cohesion within the liquid. Water wets glass, forms a concave meniscus and rises; mercury, whose cohesive metallic bonding is far stronger than its attraction to glass, forms a convex meniscus and is pushed down. The height of rise is h = 2γ cos θ/(ρgr), so it is inversely proportional to the tube radius.
Heating and cooling curves
On a heating curve, sloped segments warm one phase, q = mcΔT, and flat segments are phase changes at constant temperature, q = nΔH. During a flat segment the added energy separates molecules against their attractions while their average kinetic energy stays constant. Sign convention: q is positive for heat absorbed by the sample and negative for heat released. Melting, vaporization and sublimation absorb heat; freezing, condensation and deposition release the same amounts. Water data: c(ice) 2.09 J/(g·°C), c(liquid) 4.184 J/(g·°C), c(steam) 2.01 J/(g·°C), ΔHfus 6.01 kJ/mol at 0 °C, ΔHvap 40.7 kJ/mol at 100 °C, M = 18.02 g/mol. ΔHvap is much larger than ΔHfus because vaporization separates the molecules completely, whereas melting only loosens the hydrogen-bond network. Worked example: warming 10.0 g of ice from −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 × 4.184 × 25.0 = 1046 J, a total of 4590 J = 4.59 kJ. Because enthalpy is a state function, ΔHsub = ΔHfus + ΔHvap when both are taken at the same temperature.
What to carry forward
Vapor pressure is set by the liquid and the temperature alone; weaker intermolecular forces give higher vapor pressure, lower boiling points, lower surface tension and lower viscosity. A liquid boils when its vapor pressure equals the external pressure. Use ln(P₂/P₁) = −(ΔHvap/R)(1/T₂ − 1/T₁) with kelvin temperatures and ΔHvap in J/mol. On heating and cooling curves, add mcΔT for each sloped segment and nΔH for each flat one, keeping the sign of q for heat absorbed or released.
Problemas de prática (40)
Praticar é grátis com uma conta.
Preveja o produto 2
Surface tension, viscosity and capillarity
- A drop of detergent near a floating needlePredict the effect of a surfactant on an object supported by surface tension.
Vapor pressure and boiling
- Doubling the space above a liquidPredict that the vapor pressure returns to its equilibrium value after the volume above a liquid changes while liquid remains.
Classificar 4
Heating curves and phase-change heat
- Which phase change releases heat?Classify phase changes as endothermic or exothermic from whether intermolecular attractions are formed or broken.
Surface tension, viscosity and capillarity
- Which liquid is pushed down in a glass tube?Classify a liquid as wetting or non-wetting toward glass from the balance of cohesive and adhesive forces.
Vapor pressure and boiling
- What makes 61 °C special for chloroform?Identify the normal boiling point as the temperature at which the vapor pressure equals 1 atm.
Clausius–Clapeyron equation
- Which plot is a straight line?Identify ln P against 1/T as the linear form of the Clausius–Clapeyron equation.
Comparar 5
Vapor pressure and boiling
- Two alcohols of almost equal massCompare the vapor pressures of a diol and an alcohol of similar molar mass by counting hydrogen-bonding groups.
- Rank vapor pressures at 25 °CRank the vapor pressures of liquids at one temperature from their normal boiling points and intermolecular forces.
Clausius–Clapeyron equation
- Same boiling point, different ΔHvapCompare vapor pressures below the boiling point for two liquids that share a normal boiling point but differ in ΔHvap.
Surface tension, viscosity and capillarity
- Rank liquids by viscosityRank liquids by viscosity from the number of hydrogen-bonding groups and the size of the molecules.
- Why water's surface tension beats ethanol'sCompare the surface tensions of two hydrogen-bonding liquids from hydrogen bonds per molecule and the groups exposed at the surface.
Calcular 13
Clausius–Clapeyron equation
- Normal boiling point of benzene from two vapor pressuresFind ΔHvap from two vapor pressures and use it to extrapolate the normal boiling point.
- Boiling water in a mountain townCalculate the boiling point of a liquid at a reduced external pressure with the Clausius–Clapeyron equation.
- ΔHvap of ethanol from two vapor pressuresCalculate an enthalpy of vaporization from vapor pressures measured at two temperatures.
- How much does a 10 °C rise raise the vapor pressure?Calculate the ratio of vapor pressures at two temperatures from ΔHvap without knowing either pressure.
- Vapor pressure of water at 70 °CEstimate a vapor pressure at a new temperature from the normal boiling point and ΔHvap.
Surface tension, viscosity and capillarity
- How high does water climb a capillary?Calculate the capillary rise of water from its surface tension, density and the tube radius.
Vapor pressure and boiling
- Cooling a flask that holds air and waterCombine Dalton's law with the vapor pressure of water to find the total pressure in a sealed flask after cooling.
- How much water stays liquid?Use the vapor pressure and the ideal gas law to find how much of a liquid evaporates into a closed, evacuated flask.
Heating curves and phase-change heat
- Making ice in a freezerCalculate the total heat removed along a cooling curve that includes freezing.
- From ice at −15 °C to steam at 120 °CCalculate the total heat for a five-segment heating curve from solid to superheated vapor.
- How long until the kettle boils dry?Combine sensible heat and heat of vaporization with heater power to find the time to boil a liquid away.
- Enthalpy of sublimation of iceCombine enthalpies of fusion and vaporization measured at the same temperature to obtain an enthalpy of sublimation.
- Heat to boil away ethanolCalculate the heat needed to vaporize a mass of liquid at its boiling point from the molar enthalpy of vaporization.
Encontre o erro 2
Clausius–Clapeyron equation
- A suspiciously small ΔHvapDiagnose an incorrect enthalpy of vaporization caused by using Celsius temperatures in the Clausius–Clapeyron equation.
Vapor pressure and boiling
- Turning up the burner under boiling waterDiagnose the error in expecting a stronger flame to raise the temperature of a boiling liquid.
Interprete as evidências 7
Surface tension, viscosity and capillarity
- Viscosity and surface tension along an alkane seriesInterpret viscosity and surface-tension data for a homologous series in terms of dispersion forces and chain entanglement.
Heating curves and phase-change heat
- Where does the heat go on a flat segment?Interpret a flat segment of a heating curve as energy absorbed by a phase change at constant temperature.
- ΔHvap from the length of a plateauInterpret the duration of a heating-curve plateau at constant heater power to obtain a molar enthalpy of vaporization.
- A dip below the freezing pointInterpret the dip and recovery on a cooling curve as supercooling followed by exothermic freezing.
Vapor pressure and boiling
- Boiling water on a high summitRead a vapor-pressure table to find the boiling point of water at a reduced external pressure.
Clausius–Clapeyron equation
- Read ΔHvap from a slopeInterpret the slope of a ln P against 1/T plot to obtain the enthalpy of vaporization.
- Two lines on a Clausius–Clapeyron plotInterpret the relative slopes of ln P against 1/T lines as relative enthalpies of vaporization.
Trabalhe de trás para frente 1
- How cold was the ice?Work backwards along a heating curve from the total heat absorbed to the starting temperature of a solid.
Planeje uma síntese 1
- Distilling a heat-sensitive liquidPlan a distillation that keeps a heat-sensitive liquid below its decomposition temperature by lowering the external pressure.
Explique por quê 5
Heating curves and phase-change heat
- Why boiling costs far more than meltingExplain why the enthalpy of vaporization of a substance is much larger than its enthalpy of fusion.
Surface tension, viscosity and capillarity
- Why a narrower tube lifts water higherExplain the inverse dependence of capillary rise on tube radius by balancing the surface force against the weight of the column.
- A paper clip resting on waterExplain how surface tension can support a dense object on a water surface.
- Why warm syrup pours fasterExplain the decrease of a liquid's viscosity with rising temperature.
Vapor pressure and boiling
- Why vapor pressure climbs so fastExplain the steep rise of vapor pressure with temperature using the distribution of molecular kinetic energies.
Travou em líquidos e pressão de vapor? 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.
Depois, Scan Standard: /mês