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Chemistry 231
Thermodynamics in Reacting
Systems
Enthalpy Changes for
Reactions

The shorthand form for a chemical
reaction
0    J J
J
J = chemical formula for substance J
J = stoichiometric coefficient for J
Reaction Enthalpy Changes

The enthalpy change for a chemical
reaction
 r H   n J H m J 
J
Hm [J] = molar enthalpies of substance J
nJ = number of moles of J in the reaction
The Enthalpy Change

Reaction beginning and ending with
equilibrium or metastable states
 r H  H final  H initial
  n J H m J 
J
Note – Initial and final states have the
same temperature and pressure!
Reaction Enthalpies (cont’d)

We note that 1 mole of a reaction
occurs if
n J   J
 r H    J H m J 
J
A Standard State Reaction


A reaction that begins and ends with all
substances in their standard states
The degree sign, either  or 



P = 1.00 bar
[aqueous species] = 1.00 mol/ kg
T = temperature of interest (in data tables
- 25C or 298 K).
Standard Reaction Enthalpies

We note that for 1 mole of a reaction
under standard conditions
r H


 J H m J 

J

The Formation Reaction


A "chemical thermodynamic reference
point."
For CO and CO2
C (s) + O2 (g)  CO2 (g)
C (s) + ½ O2 (g)  CO (g)
The Formation Reaction

The formation reaction




1 mole of a compound
constituent elements
stable state of aggregation at that temperature.
Formation of 1.00 mole of Na2SO3(s)
2 Na(s) + S(s) + 3/2 O2 (g)  Na2SO3 (s)

‘Formation enthalpy of Na2SO3(s)’,
fH°[Na2SO3 (s)]
The Significance of the
Formation Enthalpy


fH° is a measurable quantity!
Compare CO (g) with CO2 (g)
C (s) + 1/2 O2 (g)  CO (g)
fH° [CO(g)] = -110.5 kJ/mole
C (s) + O2 (g)  CO2 (g)
fH° [CO2(g)] = - 393.5 kJ/mole
Formation Enthalpies

Formation enthalpies - thermodynamic
reference point!



Hom [J] = fH [J]
Hm [elements] = 0 kJ / mole.
Use the tabulated values of the
formation enthalpies
The General Equation

The enthalpy change for a given
reaction is calculated from the
formation enthalpies as
r H 


Notes


 J f H J 

J

Reverse a reaction
Multiply a reaction by an integer
The Calorimeter


A calorimeter - device containing water
and/or another substance with a known
heat capacity
Calorimeters – either truly or
approximately adiabatic systems
Two major types of calorimeters.

The constant volume (bomb)
calorimeter.


U = qv.
The constant pressure calorimeter.

H = qp.
The Constant Volume (Bomb)
Calorimeter
The Constant Pressure
Calorimeter
Relating H and U


The enthalpy and the internal energy
both represent quantities of heat.
U = qv.
H = qp.
Relate the two state functions using the
following relationship
U = H -  PV
Other Important Enthalpy
Changes




Enthalpy
Enthalpy
Enthalpy
Enthalpy
of
of
of
of
solution
dilution
fusion
vapourisation
The Solution Enthalpy


solH - heat absorbed or released when
a quantity of solute is dissolved in fixed
amount of solvent
solH = Hm(sol’n) – Hm(component)


H(component) = Hm(solid) + Hm(solvent)
Two definitions


Standard
Limiting
The Dilution Enthalpy


For the process,
HCl (aq, 6 M)  HCl (aq, 1 M).
The Enthalpy of dilution of the acid.
dilH = Hm(sol’n 2) – Hm(sol’n ,1)
Reaction Enthalpy Changes
With Temperature

Differentiate the reaction enthalpy with
temperature
r H 

 J H m J 

J
dr H
d

dT
dT


J  J H m J 

The Result
r H T   r H 298 K   r C p T




rCp - the heat capacity change for the
reaction
r C p 

 J C p J 

J

Internal Energy Changes in
Chemical Reactions


Examine a chemical reaction.
C (s) + O2 (g)  CO2 (g)
U = U[CO2 (g)] – U[C(s)] – U[O2(g)]
Note - rH = -393.5 kJ/mole
 r U    J f U J 


J
 r H    r U   n g RT
Enthalpies and Hess’s Law


Use tabulated values of formation
enthalpies to obtain rH°.
May also estimate reaction enthalpies
using an indirect method.
Hess’s Law

Hess’s Law –

the enthalpy change for a given reaction is
the same whether the reaction occurs in a
single step or in many steps.
The Entropy Change in a
Chemical Reaction

Burning ethane!
C2H6 (g) + 7/2 O2 (g)  2 CO2 (g) + 3 H2O (l)

The entropy change is calculated in a
similar fashion to that of the enthalpies
 rS    J S J 


m
J
Some Generalizations


For any gaseous reaction (or a reaction
involving gases).
ng > 0, rS > 0 J/(K mole).
ng < 0, rS < 0 J/(K mole).
ng = 0, rS  0 J/(K mole).
For reactions involving only solids and
liquids – depends on the entropy values
of the substances.
The Gibbs Energy Change for
a Chemical Reaction

The standard Gibbs energy change for a
chemical reaction is obtained as follows
r G    J f G J 


J
The Gibbs Energy Change

For the methane combustion reaction
1 CH4(g) + 2 O2(g)  1 CO2(g) + 2 H2O(l)
rG =  np fG (products) -  nr fG
(reactants)
= 2 fG [H2O(l)] + 1 fG [CO2(g)] - (7/2
fG [O2(g)] + 1 fG [CH4(g)] )
The Formation Gibbs Energies


fG (elements) = 0 kJ / mole.
Tabulated values at SATP used to obtain
the Gibbs energy changes for chemical
reactions.
A Caveat!!!


rG° refers to standard conditions only!
For non-standard conditions - rG
rG < 0 - reaction moves in the forward
direction
rG > 0 - reaction moves in the reverse
direction
rG = 0 - reaction is at equilibrium
Bond Energies

Examine the following reactions
H2 (g)  H (g) + H (g) U° = 433.9 kJ
Cl2 (g)  Cl (g) + Cl (g) U° = 239.5 kJ


Bond dissociation energies.
Enthalpy changes are designated D (HH) and D (Cl-Cl).
For Polyatomic Molecules
CO2 (g)  C (g) + 2 O (g) U = 740 kJ


H of this reaction D(C=O)
What about dissociating methane into C
+ 4 H’s?
CH4(g)  C(g) + 4 H(g) U° = 1640 kJ

4 C-H bonds in CH4 \ D (C-H)  410
kJ/mol
Make or Break!!

Note: all chemical reactions involve the
breaking and reforming of chemical bonds



Bonds break - we add energy.
Bonds form - energy is released.
rU°   D(bonds broken) -  D(bonds
formed)
A Word of Caution
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These are close but not quite exact. Why?
The bond energies we use are averaged bond
energies !
This is a good approximation for reactions
involving diatomic species.
Can only use the above procedure for
GAS PHASE REACTIONS ONLY!!!