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  K 1 2  p 4 2  K  K 2  p 4 2  2 4 p  K  K p tot p p tot tot p 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  pNaCle 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