Energy Balance on
Reactive Processes
Content
 Introduction
 Heat of Reaction or Enthalpy of Reaction
 Relationship Between Enthalpy Change and Heat of
Reaction
 Properties of Heat of Reaction
 Hess’s Law
 Heats of Formation
 Heats of Combustion
 Energy Balance on Reactive Processes
Introduction



In any reaction:
 Energy is required to break the reactant chemical bond
 Energy is released when product chemical bond is formed
Exothermic reaction
 If energy required to break the reactant chemical bond is less
than energy released when product chemical bond is formed
 the product molecules have lower internal energies than the
reactants at the same T and P (i.e ΔH=-ve)
 Heat of reaction must be released as heat or work to maintain
the operation temperature
Endothermic reaction
 If energy required to break the reactant chemical bond is
larger than energy released when product chemical bond is
formed
 the product molecules have higher internal energies than the
reactants at the same T and P (i.e ΔH=+ve)
 Energy is need by the process to maintain the operation
temperature
Heat of Reaction or Enthalpy of Reaction: ΔĤr (T,P)

Heat of reaction or enthalpy of reaction
- Enthalpy change for a process in which stoichiometric
quantities of reactant at T & P reacted completely in single
reaction to form a products at the same T & P.
- Stoichiometric quantities of reactant means molar amount of
the reactant numerically equal to their stoichiometric
coefficient.

In




simple word;
Reactants and products: stoichiometric quantities
Complete Reaction
Reactants are fed at T,P
Products are emerging at T,P
Hˆ r (T , P)  H products  H reactants
Heat of Reaction : Per mole of what ?
2A + B  3C
ΔĤr (100C, 1 atm) =-50 kJ/mol
Meaning that:
Hˆ r 
 50kJ
 50kJ
 50kJ


2 mol A reacted 1 mol B reacted 3 mol C produced
If 150 mol C/s is generated, enthalpy change is
ΔH=
-50 kJ
3 mol C generated
150 mol C generated
s
=
-2500
kJ/s
Relationship Between Enthalpy Change
and Heat of Reaction


Although the Heat of Reaction is defined so, the actual enthalpy
change of the reaction depends on how many moles of reactant
has been consumed (Extent of reaction). Therefore:
Where:
vA
- stoichiometric coefficient
ξ
- extent of reaction
nA,r
- moles of A consumed or generated
Hˆ r (T , P)
H 
nA , r
vA

(n A,out  n A,in )
vA
H  Hˆ r (T , P)
nA , r

vA
Properties of Heat of Reaction
1. Standard heat of reaction (ΔĤr°) - heat of reaction when both
reactants and products are at reference conditions (usually 25 C
and 1 atm)
2. At low and moderate pressure, ΔĤr is nearly independent of
pressure
3. Exothermic (ΔĤr= -ve) and Endothermic (ΔĤr= +ve)
4. ΔĤr depends on how the stoichiometric equation is written
CH4 (g) + 2O2(g)  CO2(g) + 2H2O(l)
ΔĤr1 (25C)= -890.3 kJ/mol  for 1 CH4
2CH4 (g) + 4O2(g)  2CO2(g) + 4H2O(l)
ΔĤr2 (25C)= -1780.6 kJ/mol  for 2 CH4
5. ΔĤr depends on the states of aggregation (gas, liquid, or solid)
CH4 (g) + 2O2(g)  CO2(g) + 2H2O(l)
ΔĤr1 (25C)= -890.3 kJ/mol
CH4 (g) + 2O2(g)  CO2(g) + 2H2O(g)
ΔĤr2 (25C)= -802.3 kJ/mol
Internal Energy of Reaction

For a reaction takes place in a closed reactor or constant volume
ΔÛ r (T)  U products  U reactant


ˆ
ˆ
U r (T )  H r (T )  RT   vi   vi
gaseous
 gaseous
 products reactants






Example for the reaction
C6H14 (l) + 19/2 O2 (g)  6 CO (g) + 7 H2O (v)
Uˆ r (T )  Hˆ r (T )  RT (6  7  19 / 2)
 Hˆ (T )  7 / 2 RT
r
Hess’s Law (Cal’tion of Reaction Heat


Normal procedure using calorimeter, however has a limitation
If the stoichiometric equation for reaction 1 can be obtained by
algebraic operations (multiplication by constant, addition, and
subtraction) on stoichiometric equation for reaction 2,3….., then
the heat of reaction ΔĤr1 can be obtained by performing the same
operations on the heats of reactions ΔĤr2 , ΔĤr3 ….
C + 1/2O2(g)  CO (incomplete combustion)
Alternative method
C + O2  CO2 ΔHr1 = -393.51 kJ/mol
CO + ½ O2  CO2 ΔHr2 = -282.99 kJ/mol
C + ½ O2 (+ ½ O2)
H  Hˆ 0 r1
CO (+ ½ O2)
Hˆ
0
r3
CO2
H  Hˆ 0 r 2
Hˆ 0 r 3  Hˆ 0 r1  (Hˆ 0 r 2 )
 393.51  282.99
 110.52kJ / mol
Class Discussion
Example 9.1-1
Example 9.1-2
Example 9.2-1
Heats of Formation




Formation reaction
– reaction in which the compound is formed from its elemental
constituents as they normally occur in nature (e.g. O2 rather
than O)
standard heat of formation (ΔĤ°f )
- Enthalpy change associated with the formation of 1 mole of
compound at a reference temperature (25C) and pressure
(1 atm)
Standard heat of formation are listed in Table B.1.
Standard heat of formation for elemental species (e.g O2) is zero
 Relationship between standard heat of formation and heat
of reaction based on Hess’s Law
Hˆ r   vi Hˆ  fi 
i
ˆ
v

H
 i  fi 
products
ˆ
v

H
 i  fi
reac tan t
Example 9.3-1

Determine the standard heat of reaction for the combustion of
liquid n-pentane assuming H2O (l) is a combustion product.
Heats of Combustion



Standard heat of combustion,
heat of combustion of that substance with oxygen to yield
specified products (e.g. CO2, H2O) with both reactant and
products at 25C and 1 atm.
Several value are listed in Table B.1
Relationship between heat of reaction and heat of combustion
Hˆ r   vi Hˆ ci 
i
ˆ
v

H
 i ci 
reac tan ts
ˆ
v

H
 i ci
products
Example 9.4-1

Calculate the standard heat of reaction for the dehydrogenation of
ethane
C2 H6  C2 H4 + H2
Energy Balance on Reactive Processes
 Method 1: Heat of Reaction Method
preferable when there is a single reaction for which
ΔĤ°r is known
Reactants
ΔH
Tout
Tin
ΔH1
Reactants
T=25 oC
Products
ΔH2
ΔHro
Products
T=25 oC
Method 1: Heat of Reaction Method
1. Complete the material balance
2. Choose reference states for specific enthalpy changes
- reactant and products species at 25C and 1 atm for which ΔĤ°r is known
- For nonreacting species at any convenient temperature, such as reactor inlet
or outlet
3. For a single reaction in a continuous process, calculate the extent of reaction
-choose as species A any reactant or product for which the feed and product
flow rates are known

(n A,out  n A,in )
vA
4. Prepare inlet-outlet enthalpy table
5. Calculate each unknown stream component enthalpy
 for the reactor ; use following eq.
6. Calculate H
H  Hˆ ro   nout Hˆ out  nin Hˆ in (single reaction)
H 
 Hˆ   n
j
o
rj
out
Hˆ out  nin Hˆ in (multiple reactions)
reaction
7. Substitute calculated value
the required calculations.
H
in the energy balance equation and complete
Energy Balance on Reactive Processes
 Method 2: Heat of Formation Method
preferable when there is a multiple reaction and single reaction for
which ΔĤ°r is unknown
Reactants
ΔH
Products
Tin
Tout
ΔH1
ΔH2
Elements
25 oC
Method 2: Heat of Formation Method
1. Complete the material balance
2. Choose reference states for specific enthalpy changes
- elemental species that constitute the reactants and products in the
states in which the elements are found at 25C and 1 atm
- For nonreacting species at any convenient temperature
3. Prepare inlet-outlet enthalpy table
4. Calculate each unknown stream component enthalpy
5. Calculate H for the reactor for single or multiple reaction. Note that
heat of reaction terms are not required if the element are chosen as
references ; use following eq.
H   nout Hˆ out   nin Hˆ in
6. Substitute calculated H value in the energy balance equation and
complete the required calculations.
Example 9.5-1

The standard heat of reaction for the oxidation of ammonia is
given below:
4 NH3 (g) + 5 O2 (g)  4 NO (g) + 6 H2O (v)
ΔĤ°r=-904.7 kJ/mol
100 mol NH3/s and 200 mol O2/s at 25C are fed into a reactor in
which the ammonia is completely consumed. The products gas
emerges at 300C. Calculate the rate at which heat must be
transferred to or from the reactor, assuming operation at
approximately 1 atm.
Class Discussion
Example 9.5-2
Example 9.5.3
Example 9.5.4
GOOD LUCK
FOR YOUR
FINAL EXAM