Enthalpies of Physical Change Enthalpies of Chemical Change Hess’ Law

  Thermochemistry Sections 2.7-2.9 of Atkins Standard Enthalpy Changes

Chapter 2 of Atkins: The First Law: Concepts

  Enthalpies of Physical Change Enthalpies of Chemical Change Hess’ Law Standard Enthalpies of Formation Changes

  Reaction Enthalpy & Enthalpy of Formation Group Contributions Temperature Dependence of Reaction Enthalpies

  Thermochemistry

  Thermochemistry is the branch of thermodynamics which studies heats of reaction: heat produced by or required for a chemical reaction. In thermochemistry, chemical reactions are divided into two categories:

  exothermic reaction

  q < 0; heat is produced by the reacting system (i.e., the temperature _rxn of the system is higher right after the reaction than initially; heat must be transferred from the system to the surroundings in order to return the system to its initial temperature)

  endothermic reaction

  q > 0; heat is absorbed by the reacting system (i.e., the temperature _rxn of the system is lower right after the reaction than initially; heat must be transferred from the surroundings to the system in order to return the system to its initial temperature) These reactions can also be described in terms of enthalpy, )H

  Standard Enthalpy Changes

  Numerical values describing )U or )H of a system when some chemical or physical change occurs depend upon the nature of the reaction, as well as the physical states of reactants and products _o It is useful to define a standard enthalpy change, )H , which is the change in enthalpy for a process (chemical or physical) where initial and final substances are in standard states

  standard states: pure form of a substance at specified temperature at

  pressure of 1 bar, e.g. standard state of liquid water at 298 K is pure liquid water at 298 K and 1 bar _o

  Examples:The standard enthalpy of vapourization, ) H , is change in _vap

  enthalpy per mole when pure liquid vapourizes to pure gas at _o pressure of 1 bar. The standard enthalpy of fusion, ) H , is _fus enthalpy change accompanying change from liquid to solid _o

• _-1 H O(l)
₂

  6 H O(g) ) H (373 K) = +40.66 kJ mol _{2 vap o}

• _-1 H O(s) O(l) ) H (273 K) = +6.01 kJ mol _o
₂

  6 H _{2 fus}

  Enthalpy of Physical Change _o standard enthalpy of transition, ) H :

_trs

  Standard enthalpy change accompanying a phase change (A) Enthalpy is a state function, independent of path between initial and _o final states: same value of )H occurs regardless of how change occurs! _o melting H O(s) O(l) ) H ₂

  6 H _{2 fus o} boiling H O(l) ₂

  6 H O(g) ) H _{2 vap o o o}

• sublimation H O(s) H O(g) ) H = ) H ) H
₂

  6 _{2 sub fus vap o} (B) Enthalpy is a state function, so )H differs only in sign for forward and reverse processes _{o o}

  )H (A

6 B) = -)H (B

  6 A)

  Example: At 298 K, _{o -1}

  condensing H O(g) O(l) ) H = -44 kJ mol ₂

  6 H _{2 vap o -1} boiling H O(l) O(g) ) H = +44 kJ mol

6 H

  Graphical Depiction of Enthalpies of Transition

  ) _fus

  H ^o

  ) _vap

  H ^o

  ) _sub

  H ^o

  gas liquid solid

  (A) Same )H ^o , regardless of pathway (B) Forward & reverse processes,

  )H ^o differs only in sign

  

Enthalpies of Fusion and Vapourization

  See Table 2.3 Atkins 6th Ed. at back of book for a listing of enthalpies of fusion and vapourization, with freezing and boiling temperatures

  Enthalpies of Transition †

  H

  H, ) _diss H

  Ionization X(g)

  6 X ⁺ (g) + e-(g) ) _ion

  H

  Electron gain X(g) + e-(g)

  6 X ^- (g)

  ) _eg

  Reaction Reactants 6 products ) _r

  H

  H

  Combustion Cmpd(s,l,g) + O ₂ (g)

  6 CO ₂ (g) + H ₂ O(l,g) ) _c

  H

  Formation Elements 6 compound ) _f

  H

  Activation Reactants 6 activated complex ) ^‡

  Atomization Species(s,l,g) 6 atoms(g) ) _at

  ) _hyd

  There are many different types of transitions, each of which has an associated change in enthalpy

  H

  Transition Process Symbol

  Transition Phase " 6 Phase $

  ) _trs

  H

  Fusion s 6 l ) _fus

  H

  Vapourization l 6 g ) _vap

  Sublimation s 6 g ) _sub

  6 X ^± (aq)

  H

  Mixing fluids Pure 6 mixture ) _mix

  H

  Solution Solute 6 solution ) _sol

  H

  Hydration

  X ^± (g)

  H

  Enthalpies of Chemical Change _o standard reaction enthalpy, ) H : _r

  Change in enthalpy when reactants in standard states change to products in standard states pure unmixed reactants in pure separated products their standard states their standard states

  Example: _{o -1}

  CH (g) + 2O (g) _{4 2}

6 CO (g) + 2H O(l) ) H = -890 kJ mol

  _{2 2 r} The change in enthalpy for the above thermochemical equation is for 1 mole of pure CH (g) reacting with 2 moles of pure O (g) at 1 bar to _{4 2} produce 1 mole of pure CO (g) and 2 moles of pure H O(l) at 1 bar _{2 2} Changes in enthalpies of mixing and separation are insignificant compared to the standard reaction enthalpy, and may be neglected in this

  Standard Molar Enthalpies

  Consider the reaction:

  2A + B 6 3C + D Standard enthalpy is calculated from:

  o o o ' & ) H <H <H j m j m r products reactants

  where < are stoichiometric coefficients. Thus,

  o o o o o ) H ' [3H (C) % H (D)] & [2H (A) % H (B)] m m m m _o r where H (J) is standard molar enthalpy of species J. _m

  Symbolically, we write 0 = 3C + D - 2A - B, or

  

0 ' J

< j J

  J

  Here J denotes substances and < the stoichiometric numbers, _J

  ' &2 ' &1 ' %3 ' %1 < < < <

A B C D

o o

  '

  Thus, standard reaction enthalpy is: ) H < H (J)

  m r j J

  † Hess’ Law

  The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions into which the overall reaction may be divided - Individual steps may not be “real” reactions, but must balance _-1 Standard reaction enthalpy for hydrogenation of propene: -124 kJ mol

  CH =CHCH (g) + H (g) CH CH (g) _{2 3 2}

6 CH

  _{3 2 3 -1} Standard reaction enthalpy for combustion of propane: -2220 kJ mol

  CH CH CH (g) + 5O (g) (g) + 4H O(l) _{3 2 3 2} 6 3CO _{2 2} Calculate the standard enthalpy of combustion of propene: C H (g) + (9/2)O (g) (g) + 3H O(l) _{3 6 2} 6 3CO _{2 2 o -1}

  ) H /kJ mol _f C H (g) + H (g) H (g)

• 124
_{3 6 2}

  6 C _{3 8} C H (g) + 5O (g) (g) + 4H O(l) -2220 _{3 8 2} 6 3CO _{2 2} H O(l) (g) + ½O (g)

• 286
₂

  6 H _{2 2} C H (g) + (9/2)O (g) (g) + 3H O(l) -2058

  Standard Enthalpies of Formation _o standard enthalpy of formation, ) H : _f

  Change in enthalpy for formation of compound from its constituent elements in their reference states

  

reference state: the most stable state of an element at the specified

  temperature and 1 bar pressure

  elements Examples:

  nitrogen N (g) ₂ mercury Hg(l) carbon C(s) (graphite)

  6 C _{6 6} ) H = +49.0 kJ mol _r

  6C(s,graphite) + 3H H (l) _{o -1 2}

  reactants _o ) H _r

  N (g) N (g) _{2 o}

  6 ₂

  products

  (J)

  = [ ) _f

  H o

  ) f

  < J

  ' j J

  H o

  ) r

  (NO, g)] = [-187.78 + 4(0)] - [2(264.0) + 2(90.25)] kJ mol ^-1 = -896.3 kJ mol ^-1

  H ^o

  (HN ₃ , l) + 2 ) _f

  H ^o

  (N ₂ , g)]

  H ^o

  (H ₂ O ₂ , l) + 4 ) _f

  H ^o

  H ^o

  

Reaction Enthalpy in Terms of Formation

  6 H ₂ O ₂ (l) + 4N ₂ (g) ) _r

  2HN ₃ (l) + 2NO(g)

  Example

  H o

  <) f

  & j reactants

  

H

o

  <) f

  ' j products

  H o

  ) r

  for reaction is sum of forming and “unforming” enthalpies

  H ^o

  Conceptual Reaction: Decompose the reactants into their elements, form these elements into products Value of ) _r

• [2 ) _f

  

Group Contributions

  Sometimes it is difficult to exactly thermodynamically break enthalpies of formation down into contributions from individual atoms and bonds

  mean bond enthalpies, )H(A-B)

  enthalpy change associated with breaking of a specific bond, A-B A-B(g) A(g) + B(g) )H(A-B)

  6 This is an unreliable method, since )H(A-B) are average values for series of unrelated compounds (different geometries, isomers, etc.)

  thermochemical groups

  atom or physical group of atoms bound to at least two other atoms enthalpy of formation is associated with sum of contributions associated with all of the thermochemical groups into which the molecule can be divided - sometimes called Benson thermochemical groups

  Benson Group Contributions _{o -1 o -1 -1}

  Group ) H /kJ mol C /J K mol _{r p,m} C(H) (C) -42.17 ₃

  25.9 C(H) (C) -20.7 _{2 2}

  22.8 C(H)C -6.19 ₃

  18.7 C(C) +8.16 ₄

  18.2 C(C) C(H) (C) _{4 2 2} Example Estimate standard enthalpy of formation for hexane (g & l) at 298 K: Decomposition: two C(H) (C) groups and four C(H) (C) groups _{o 3 2 2}

  ) H (C H ,g) = 2(-42.17)+4(-20.7) _{f 6 14}

• _{-1 o}

  = -167.1 kJ mol _-1 ) H (C H ) = 28.9 kJ mol _{vap o 6 14}

  ) H (C H ,l) = -167.1 - 28.9 _{f 6 14}

• _-1 = -196.0 kJ mol _-1

  Temperature Dependence of Reaction Enthalpies

  Standard enthalpies have been measured at many temperatures for many substances - however, in absence of such information, the standard enthalpies of formation may be estimated from heat capacities

  T ₂ H(T ) ' H(T C dT

  2 1 p ) % m

  T ₁ Here, we have heated from T to T , no phase _{1 2} transitions. Kirchoff’s Law is written as T ₂

o

o o

  ) H (T ) ' ) H (T ) C dT p r 2 r 1 r

  ) % m _o T ₁

  ) C is the difference in heat capacities between _{r p} reactants and products under standard conditions, weighed by stoichiometric coefficients

  o o o o ' ' &

  ) C <C <C < C (J) p p,m p,m j p,m r j j J products reactants J