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3. High Temperature Gases 3. High Temperature Gases FPK1 2009/MZ 1/23 Terms and Concepts . Dissociation . Diatomic element gases . Bond energy, dissociation energy (enthalpi) . Flood’s dissociation diagram . Vaporization, evaporation, boiling, sublimation . Heat of evaporation, enthalpy of evaporation FPK1 2009/MZ 2/23 Bond dissociation enthalpy . Only a limited number of enthalpies of formation have been o measured, and there are many reactions for which ∆H f data is not available for one or more reagent. o . When this happens, ∆H rxn for the reaction can not be predicted. The enthalpy of reaction can be estimated using bond- dissociation enthalpies. By definition, the bond-dissociation enthalpy for an X-Y bond is the enthalpy of the gas-phase reaction in which this bond is broken to give isolated X and Y atoms. XY(g)↔X(g) + Y(g) FPK1 2009/MZ 3/23 Bond dissociation enthalpy . The bond-dissociation enthalpy for a C-H bond can be calculated by o combining ∆H f data to give a net equation in which the only thing that happens is the breaking of C-H bonds in the gas phase. CH4(g)→ C(s) + 2 H2(g) ∆Ho = 1 mol x 74.81 kJ/mol CH4 C(s)→C(g) ∆Ho = 1 mol x 716.68 kJ/mol C 2 H2(g)→4 H(g) ∆Ho = 4 mol x 217.65 kJ/mol H CH4(g)→C(g) + 4 H(g) ∆Ho = 1662.09 kJ . If it takes 1662 kJ/mol to break the four moles of C-H bonds in a mole of CH4, the average bond-dissociation enthalpy for a single C-H bond is about 415 kJ/mol. Bond-dissociation enthalpies are always positive numbers because it takes energy to break a bond. When a table of bond energies is used to estimate the enthalpy associated with the formation of a bond, the sign becomes negative because energy is released when bonds are formed. FPK1 2009/MZ 4/23 Reference: Huheey, pps. A-21 to A-34; T.L. Cottrell, "The Strengths of Chemical Bonds," 2nd ed., Butterworths, London, 1958; B. deB. Darwent, "National Standard Reference Data Series," National Bureau of Standards, No. 31, Washington, DC, 1970; S.W. Benson, J. Chem. Educ., 42, 502 (1965). FPK1 2009/MZ 5/23 Element gases Many elements form two-atomic molecules; these dissociate: O2 2 O Na2 2 Na (g) Equilibrium: (I) 2 p Na K P p Na2 (II) ni pi ptot ntot (III) , degree of dissociation 1 nNa 2 1 n n 2 Na Na2 FPK1 2009/MZ 6/23 Degree of dissociation vs Kp . The degree of dissociation in gases is denoted by the symbol α where α refers to the percentage of gas molecules which dissociate. Various relationships between Kp and α exist depending on the stoichiometry of the equation. FPK1 2009/MZ 7/23 Degree of dissociation vs Kp: example . N2O4(g)→2NO2(g) . When assuming 1 mol N2O4 that dissociates . Left N2O4 will be (1-α), NO2 formed will be 2 α . Thus nN2O4=(1- α); nNO2=2 α . ntot = nN2O4+nNO2=1- α +2 α =1+ α 2 . Kp=(pNO2) /pN2O4 FPK1 2009/MZ 8/23 Degree of dissociation vs Kp 2 2 2 2 2 2 p NO 2 x 1 4 4 K NO2 .p p p p p x tot 1 tot 1 1 tot 1 2 N 2O4 N 2O4 1 And rearranging gives 2 2 2 2 2 K p 1 ptot 4 K p K p ptot 4 4 ptot K p K p K K 2 p p 4 ptot K p 4 ptot K p FPK1 2009/MZ 9/23 Degree of dissociation vs Kp K p 4 ptot K p 0 0 We approximate: ln K H 298 S 298 p RT R 0 cal and further: S 298 25 K mol 0 H 298 We can generalize: f , ptot T 0 Degree of dissociation can be estimated if we know H 298 and specify T and ptot (see Flood’s diagram). FPK1 2009/MZ 10/23 FPK1 2009/MZ 11/23 FPK1 2009/MZ 12/23 Boiling point . The boiling point of a liquid is the temperature at which the vapor pressure of the liquid equals the environmental pressure surrounding the liquid . A liquid in a vacuum environment has a lower boiling point than when the liquid is at atmospheric pressure. A liquid in a high pressure environment has a higher boiling point than when the liquid is at atmospheric pressure. In other words, the boiling point of liquids varies with and depends upon the surrounding environmental pressure. FPK1 2009/MZ 13/23 Heat of vaporisation . The enthalpy of vaporization, (symbol ∆vH), also known as the heat of vaporization or heat of evaporation, is the energy required to transform a given quantity of a substance into a gas. It is often measured at the normal boiling point of a substance; although tabulated values are usually corrected to 298 K, . The heat of vaporization is temperature-dependent, though a constant heat of vaporization can only be assumed for small temperature ranges . The heat of vaporization diminishes with increasing temperature and it vanishes completely at the critical temperature (Tr=1) because above the critical temperature the liquid and vapor phases don't coexist anymore. FPK1 2009/MZ 14/23 Determining Tb Vaporization equilibrium: NaCl (s,l) ⇄ NaCl (g) G0 H0 S0 v v v RT RT R Kp pNaCle e e Clausius Clapeyron 0 0 v H v S At ’boiling point’ (TB), ln p 0 NaCl RT R pNaCl = 1 atm, thus: B H 0 S 0 v v RTB R 0 v H 0 v S TB 0 v H TB 0 v S FPK1 2009/MZ 15/23 For ideal gases: cal S0 25 K mol We get: 1 K mol TB v H 25 cal Boiling point (very) roughly linearly dependant on H0. FPK1 2009/MZ 16/23 ∆vH FPK1 2009/MZ 17/23 ∆vH . Hydrogen bonding gives larges ∆vH . Polar substances have higher ∆vH than similar non polar substances . Similar bonding in similar compounds gives similar ∆vH . NH3 lowest ∆vH amonh hydrogen bounded molecules . F, Cl, Br, I regular increase in ∆vH . Methane, ethane, propane regular increase in ∆vH FPK1 2009/MZ 18/23 Determining Tb and ∆vH: Neat approach . ∆vH can be determined by measuring px at different temperatures. Tb = boiling temp at 1 atm (1bar) H 0 S 0 ln p v v RT R p1 v H 1 1 ln p2 R T2 T1 p R ln 1 p 2 H 1 1 v T2 T1 FPK1 2009/MZ 19/23 Ex. A liquid has vapour pressure of 254mmHg at 25°C and 648mmHg at 45°C. What is ∆vH and Tb? FPK1 2009/MZ 20/23 Heat of sublimation . The heat of sublimation, or enthalpy of sublimation, is defined as the heat required to sublime one mole of the substance at a given combination of temperature and pressure, usually standard temperature and pressure (STP). The enthalpy of sublimation is the heat of sublimation for vaporizing one mole of the solid substance under three specific conditions: – (1) the pressure remains constant, – (2) the only possible work that occurs is expansion against the atmosphere (so-called PdV work) and – (3) the temperature remains constant during the process. A heat of sublimation for a substance is only valid for conversion of the pure solid to the pure gaseous state of the substance. FPK1 2009/MZ 21/23 FPK1 2009/MZ 22/23 Terms and Concepts . Dissociation . Diatomic element gases . Bond energy, dissociation energy (enthalpi) . Flood’s dissociation diagram . Vaporization, evaporation, boiling, sublimation . Heat of evaporation, enthalpy of evaporation FPK1 2009/MZ 23/23.
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