Mass and Energy Balance
ERT 214
Semester 1 2011/2012
Course Details

Course Outcomes (COs) will be covered


CO3 – Analyze energy balance problems and apply energy
balance concepts to solve problem in chemical and biological
systems
Important Reminder
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


Assignment 4 – Due on Monday, 12 Disember
Assignment 5 – Due on Monday, 19 Disember
Quiz 4 – On Tuesday, 6 Disember
Midterm Test 2 – On Tuesday, 20 Disember
Course Details (cont’d)

Course Contents


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Energy Balances on Nonreactive Processes (Wk 11)
Energy Balances on Reactive Processes (Wk 12-13)
Energy Balance for Biological Process System (Wk 13-14)
Unsteady state Material and Energy Balances (Wk 15)
Chapter 3
Part 4 – Balances on Reactive Processes
Week 13
At the end of this lecture part, you will be
able to:

Define and understand


the concept of heat of reaction and the properties of heat of
reaction, heat of formation, heat of combustion, Hess’s Law
Analyze and calculate problems related to heat of
reaction, heat of formation, heat of combustion, Hess’s
Law
Heat of Reaction

Definition:

The heat of reaction (entalphy of reaction), ΔHr(T,P), is the
entalphy change for a process in which stoichiometric
quantities of reactants at temperature T and pressure P react
completely in a single reaction to form products at the same
temperature and pressure
Heat of Reaction
Consider a reaction:
2H 2  O2  2H 2O
Heat of Reaction (cont’d)


One O-O bond and two H-H bonds broken. System
absorbs energy, Usystem and Hsystem increase from reactants
to transition state
4 O-H bonds are formed. System releases energy, Usystem
and Hsystem decrease from transition state to products
Heat of Reaction (cont’d)
Suppose stoichiometric quantities of the reactants (2 mol
H2 + 1 mol O2) react completely, with the reactants starting
at T and P and the products (2 mol H2O) ending at the
same T and P.
Heat of Reaction (cont’d)
The change in enthalpy from reactants to products,
H products  H reactants  H r T , P 
is the heat of reaction.
For stoichiometric quantities of H2 and O2 reacting
completely at T=25ºC and P =1 atm,



2 mol H 2 g, 25 C, 1 atm  1 mol O 2 g, 25 C, 1 atm

 2 mol H 2 O l, 25 C, 1 atm
H r  571.68


Heat of Reaction (cont’d)
Negative ΔHr  Energy products  Energy reactants 
more energy released by product bond formation than
absorbed when reactant bonds break. The reaction is
therefore exothermic.
For example:
2H 2 g   O 2 g   2H 2 Ol  , H r  571.68 kJ
 571.68 kJ
 571.68 kJ
 571.68 kJ
Δ Hr 


2 mol H 2 react 1 mol O 2 react 2 mol H 2 O react

Heat of Reaction (cont’d)
If 5 mol H2/s react and the reactants and products are at
25°C, then the energy balance is
 5 mol H 2 react   571.68 kJ 



Q  H  

s

 2 mol H 2 react 
kJ
 1430  1430 kW (The reactor must be cooled)
s
Stardard Heat of Reaction


Hˆ r kJ / mol  is the standard heat of reaction, the heat
of the reaction with the given stoichiometry and phases,
reacting completely, at a reference temperature and
pressure of 25°C and 1 atm.
(The “standard” part, which refers to the specified
temperature and pressure, is denoted by the
superscript°.)
Heat of Reaction (cont’d)
If A is a reactant or product, υA is its stoichiometric
coefficient (negative for reactant, positive for product), and
nAr (mol A) is a quantity of A that reacts with reactants and
products at 25°C, then the enthalpy change is
ΔHˆ r kJ 
ΔH kJ   n A,r mol A react 
v A mol A react 
 ξΔHˆ r
where ξ is the extent of reaction. ξ 
n A,out  n A,in
vA

n A, r
vA
For an open system, dots would go above the H, n, and ξ.
Heat of Reaction (cont’d)

Note the properties of the heat of reaction listed on p.
443
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exothermic reaction if negative,
endothermic if positive;
ΔĤr (T, P) nearly independent of pressure at low and moderate
pressures
the standard heat of the reaction 2A→2B is twice that of A→B
Class Discussion
EXAMPLE 9.1-1
Internal Energy of Reaction



If a reaction take place in a closed reactor at constant
volume, the heat released/absorbed is determined by the
change in internal energy between reactants and
products, not enthalpy.
The internal energy of reaction, ∆Ûr(T) is the difference
Uproducts – Ureactants if stoichiometric quantities of reactants
react completely at temperature T.
In general, for any reaction in which stoichiometric
quantities of reactants react completely (which is what is
involved when dealing with standard heats of reaction)
and the stoichiometric coefficient of species i is υi


ˆ
ˆ
U r T   H r  RT   vi   vi
gaseous
 gaseous
products
reactants






Internal Energy of Reaction: Example
Suppose the reaction in which ethylene is chlorinated to
form trichloroethylene
C2 H 4 g   2Cl2 g   C2 HCl3 l   H 2 g HCl g 
Hˆ   420.8 kJ/mol
r
takes place in a batch (closed) reactor at constant volume.
What is the internal energy change when 1 mol of ethylene
and 2 mol of chlorine react completely, with both reactants
and products at 25°C and 1atm?
Internal Energy of Reaction: Example

For any system, H = U + PV , and for any change in the
system state (including reaction),
H  U  PV 

or solving for ΔU and applying the result to our reaction
process
ΔUˆ r  ΔHˆ r  ΔPV 

 420.8 kJ/mol - PV products  PV reactants

Internal Energy of Reaction: Example

The products of the reaction are 1 mol of liquid
trichloroethylene, 1 mol of gaseous hydrogen, and 1 mol
of gaseous hydrogen chloride at 25°C and 1 atm. The
volume of the liquid can be determined from the specific
gravity of trichloroethylene (1.465, which translates to a
specific volume of 0.090 L/mol) and that of the two gases
can be found from the ideal gas equation of state.
If any of the reactants had been liquids, their volumes would have been
neglected.
Class Discussion
EXAMPLE 9.1-2
Hess’s Law
General statement of Hess’s Law:
If the stoichiometric equation for reaction 1 can be obtained by
algebraic operations (multiplication by constants, addition, and
substraction) on stoichiometric equations for reaction 2,3,…,
then the heat of reaction ∆Ĥr1 can be obtained by performing
the same operations on the heat of reactions ∆Ĥr2, ∆Ĥr3,…
In the other words:
Hess’s law states that if you can obtain a stoichiometric equation
as a linear combination of the stoichiometric equations for other
reactions, you can determine its heat of reaction by performing
the same operations on the heats of the other reactions.

For example, suppose we experimentally determine the
following two standard heats of reaction:

We want to determine the heat of the reaction A → B +
2D but can’t carry out that reaction experimentally. We
observe, however, that we can obtain that stoichiometric
reaction as [1] + 2x[2]:
Class Discussion
EXAMPLE 9.2-1
Formation Reactions and Heats of
Formation
Formation reaction:
A reaction in which a compound is formed from its elemental
constituents as they occur in nature [e.g., O2(g), and not O].
The standard heat of formation, Ĥ f , is the standard heat of
such a reaction. Standard heats of formation of many species are
given in Table B.1.
The standard heat of formation of an elemental species is zero
[C(s), H2(g), O2(g),...] is zero.
Formation Reactions and Heats of
Formation
We can use Hess’s law to show that for any reaction a
hypothetical process path can be drawn from reactants to
elements to products:
Formation Reactions and Heats of
Formation
It may shown using Hess’s Law that:
if vi is the stoichiometric coefficient of the ith species participating
in a reaction (+ for products, - for reactants) and Ĥ fi is the
standard heat of formation of this species
and since enthalpy is a state function,
standard heat of reaction is:
,
the
Class Discussion
EXAMPLE 9.3-1
Heat of Combustion
Standard Heat of Combustion:
Standard heat of the complete combustion of a fuel to form
CO2(g) and H2O(l) (+ S in fuel → SO2, N in fuel → N2), with
reactants and products at 25°C and 1 atm.
The standard heats of combustion can be found in Table B-1.
Heat of Combustion
If a reaction only involves combustible reactants and
products, then we can calculate the standard heat of the
reaction from tabulated standard heats of combustion. The
formula is:
where vi is the stoichiometric coefficient of the ith reactant
or product species and Ĥ ci is the standard heat of
combustion of that species. The formula looks like the one
involving heats of formation, except that summations are
reversed (reactants - products).
Heat of Combustion
This formula is derived from Hess’s law in the same way
that the heat of formation formula was derived:
Class Discussion
EXAMPLE 9.4-1
Energy Balances on Reactive Processes
Energy balance equation for heat of reaction method:
Closed system:
Open system:
Energy Balances on Reactive Processes
The process path that leads to this expression for H
(recalling that the reference states are the reactants and
products at 25°C and 1 atm) is

Writing
and substituting for each
of the three enthalpy changes on the right leads to the
given expression for H
Energy Balances for Heat of Formation
Method
Energy balance equation for heat of formation method:
Closed system:
Open system:
Energy Balances for Heat of Formation
Method
The process path (recalling that the reference states are the
elemental species at 25°C and 1 atm) is
Writing
and substituting for each of the
three enthalpy changes on the right leads to the given
expression for H
Class Discussion
EXAMPLE 9.5-1
EXAMPLE 9.5-2