Now let’s apply the heat stuff to real-world stuff like phase changes and the energy or cost it takes to carry it out. A “heating curve”.......a plot of temperature of a substance vs heat added to a substance. emperature ˚C T Heat Added (Joules) Here’s the same curve now applying the conservation of energy (sum of the heats) q = mice ∆Hfus q = mH2O ∆Hvap q = sstm mstm ∆T q = sice mice ∆T q = sH2O mH2O ∆T Phase Phase F 220 transition transition Temperature does Temperature does not change during not change during a phase transition. a phase transition. Steam Heating Ice + Water 100 solid ice Water D Water + E to 0˚C mix steam mix 0 C Ice B emperature ˚C Heating Boiling all T Heating water to water to Melting steam past boiling steam -100 solid ice to 100˚C A 0˚C water 100˚C 100˚C 4.12 38 79.3 305 309 Heat Added (kJ/mole) Calculate the amount of heat required to convert 500 grams of ice at -20.0˚C to steam at 120.˚C. The specific heat capacities of water, ice and water vapor are 4.18, 2.06 and 1.84 J/g ˚C respectively, and the latent heat of fusion and vaporization, ΔHf and ΔHv, are 6.02 and 40.7 kJ/mol respectively. n qi = 0 sum the q’s baby i=1 ! q = si mi ΔT for heating non-phase transitions qsolid=>liquid = (# moles) ΔH˚fusion for phase transitions qliquid=>gas = (# moles) ΔH˚vaporization Calculate the amount of heat required to convert 500 grams of ice at -20˚C to steam at 120˚C. The specific heat capacities of water, ice and water vapor are 4.18, 2.06 and 1.84 J/g ˚C respectively, and the latent heat of fusion and vaporization, ΔHf and ΔHv, are 6.02 and 40.7 kJ/mol respectively. 1. Heat ice from -20˚C to ice at 0˚C = 500. g x 2.06 J/g ˚C x 20˚C 2. Melt ice at 0˚C to water at 0˚C = 500. g/(18 g/mol) x 6.02 kJ/mol 3. Heat water from 0˚C to water at 100˚C= 500. g x 4.18 J/g ˚C x 100˚C 4. Evap water at 100˚C to vap at 100˚C = 500. g/(18 g/mol) x 40.7 kJ/mol 5. Heat vap from 100˚C to vap at 120˚C = 500. g x 1.84 J/g ˚C x 20˚C 1. = 20.6 kJ 2. = 167.2 kJ 3. = 209.0 kJ 4. = 1130.5 kJ 5. = 18.4 kJ Total = 1545.6 kJ Bunker fuel C, coal and rice hulls are the most widely used fuels in the Philippines (world too) used in create steam in nearly all industries worldwide. Look up the heating value of each of these fuels. By hook or by crook find the price per liter or price per kg of each of these fuels. Which fuel is the cheapest fuel to produce steam? What is the approximate cost to produce a MT steam at 120˚C starting from 24˚C assuming the efficiencies of all the heating processes are the same, and the cost of boilers are the same as well? Unfortunately not everything is simple economics. What other factors might one consider with each of these fuels assuming 15MT of steam is produced per day 7 days a week, 30 days a month and 12 months a year? The concept of vapor pressure The equilibrium vapor pressure is the pressure exerted by a vapor over its liquid phase (measured under vacuum) when dynamic equilibrium exists between condensation and evaporation. Evaporation Vapor Pressure Liquid Liquid In open containers, In closed containers, molecules molecules that have vaporize and condense until there enough KE can overcome is no further change in IMF’s at the surface and concentration in each phase. “evaporate” into the This forms an equilibrium “vapor atmosphere. pressure” over the liquid. Dynamic chemical equilibrium is reached when there is no net change in the number of molecules: the rate of evaporation and the rate of condensation are equal. Molecules vaporizing and Molecules in liquid begin condensing at such a rate to vaporize that no net change in numbers occure Dynamic equilibria is also reached in melting and sublimation and also in most chemical reactions. At the melting point a solid begins to change into a liquid as heat is added. As long no heat is added or removed melting (red arrows) and freezing (black arrows) occur at the same rate an the number of particles in the solid remains constant. aA + bB cC + dD Reactants Products Reaction Rate of the forward reaction = = Rate of Reverse reaction Because kinetic energy (of molecules in any phase) depends on temperature, so does vapor pressure of a liquid. Relates molecular 3 properties of molecules KE = Ek = RT to bulk properties that 2 we observe! Kinetic Energy Temperature More molecules escape at high temp At higher temperatures, a larger fraction of molecules have enough KE to escape the liquid phase. The vapor pressure of a pure liquid (bulk property) depends on the intermolecular forces between molecules. The stronger the attractive forces in the liquid phase the lower the vapor pressure--and the less volatile it is. Which of the following has the highest vapor pressure at 1 atm? 2 atm Which is the least volatile at 1 atm? .66 atm water boils at 75˚C at 300 torr = .4 atm Vapor Pressure of Some Liquids The following diagram shows a close-up view of part of the vapor-pressure curves for a solvent (red curve) and a solution of the solvent with a second liquid (green curve). Which solvent is more volatile? The boiling point of a pure liquid is the temperature at which the equilibrium vapor pressure of a liquid over its liquid phase is equal to the external pressure on the liquid. The normal boiling point is the temperature at which a liquid boils when the external pressure is 1 atm. Evaporation Boiling If we plot vapor pressure vs temperature we observe a linear relationship between ln P and 1/T. Vapor pressure plotted as ln (vapor pressure) plotted a function of temperature as a function of 1/Temp • The Clausius-Claperyron equation relates the vapor pressure (P) of a pure liquid to the liquid’s temperature (T) and the liquids molar heat of vaporization (∆Hvap). -ΔHvap 1 slope = ∆H /R ln P = + C vap R T y = m x + b (note R = 8.31 J/K mol) ln P • By taking measurements at two temps, we get: 1/T P2 -ΔHvap 1 1 ln = − P R T T 1 2 1 Vapor pressure of pure etOH is 115 torr at 34.9˚C. If ΔHvap = 40.5 kJ/mol calculate the temperature when the vapor pressure of etOH is 760 torr. R is the gas constant given at 8.314 J/mol K .