BALANCES ON REACTIVE PROCESSES

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BALANCES ON REACTIVE PROCESSES

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Title: BALANCES ON REACTIVE PROCESSES

1
CHAPTER 9 BALANCES ON REACTIVE PROCESSES
2

Consider the familiar reaction in which water is
formed
from hydrogen and oxygen

On the molecular level, the reaction might be
depicted
as follows

H2
?
O2
Each time this reaction takes place, three
chemical bonds are broken (two between hydrogen
atoms and one between oxygen atoms).
3
?

Four bonds are formed among the atoms of the two
water molecules.
As it happens, more energy is released when the
water
molecule bonds form than it takes to break the
hydrogen
and oxygen molecules bonds.
For the reactor temperature to remain constant,
the net
energy released must be transferred away from
the
reactor, otherwise it can raise the reactor
temperature
by several thousand degrees.

In any reaction between stable molecules, energy
is
required to break the reactant chemical bonds
and
energy is released when the product bonds form.

Exothermic reactions if the first process
absorbs less
energy than the second process releases the
product
molecules at a given T and P have lower internal
ener-
gies (and hence lower enthalpies) than the
reactant
molecules at the same T and P.
For an exothermic reaction, the net energy
released
the heat of reaction must be transferred from
the
reactor as heat or work, or else the system
temperature
increases.

Endothermic reactions if less energy is
released when
the product bonds form than it took to break the
reactant
bonds.
For an endothermic reaction, energy must be added
to
the reactor as heat or work to keep the
temperature from
decreasing.
An energy balance on a reactor tells the process
engineer
how much heating or cooling the reactor requires
in order
to operate at the desired conditions.

In this chapter we show how enthalpy changes that
accompany chemical reactions are determined from
tabu-
lated physical properties of the reactants and
products and
how calculated enthalpies of reaction are
incorporated in
energy balances on reactive processes.

7
9.1 HEATS OF REACTION

Consider the reaction between solid calcium
carbide and
liquid water to form solid calcium hydroxide and
gaseous
acetylene

The expression stoichiometric quantities of
reactants means molar amounts of the reactants
numerically equal to their stoichiometric
coefficients.
8

The heat of reaction (or enthalpy of reaction),
, is the enthalpy change for a
process in
which stoichiometric quantities of reactants at
T and
P react completely in a single reaction to form
products at the same T and P.
For example, the heat of calcium carbide
reaction
at 25? and 1atm is

These two equations signify that if 1 mol of
solid CaC2
reacts completely with 2 mol of liquid H2O to
form 1 mol
of Ca(OH)2 and 1 mol of C2H2, and the initial
and final
temperatures are both 25oC and the initial and
final
pressures are both at 1 atm, then

If the reaction is run under conditions such that
the
energy balance reduces to Q?H, then 125.4kJ of
heat
must be transferred from the reactor in the
course of the
reaction.

The units of often cause confusion.
For example,
if the heat of a reaction is reported to be -50
kJ/mol, you
might ask per mol of what? This difficulty is
avoided if
you recall that the given applies
to stoichiometric
quantities of each species. For example,

means that the enthalpy change for the given
reaction is
11
If you knew, say, that 150 mol of C/s was
generated in the given reaction at 100oC and 1
atm, you could calculate the associated enthalpy
change as
12

More generally, if ??A is the stoichiometric
coefficient of
a reactant or reaction product A (positive if A
is a product,
negative if it is a reactant) and nA,r moles of
A are con-
sumed or generated at TT0 and PP0, then the
asso-
ciated enthalpy change is

In Chapter 4, we defined the extent of reaction,
??, as a
measure of how far a reaction has proceeded.
This
quantity is

From the preceding two equations, it follows that
if a
reaction takes place at a temperature T0 and
pressure
P0 and the extent of reaction is ?, the
associated
enthalpy change is

Following are several important terms and
observations
related to heats of reaction.
If is negative the reaction is
exothermic at T
and P, and if is positive the
reaction is endo-
thermic at T and P.
2. At low and moderate pressure is
nearly inde-
pendent of pressure.
3. The value of depends on how the
stoichiome-
tric equation is written. For example

15
4. The value of depends on the
states of aggre- gation (gas, liquid, or
solid) of the reactants and products. For
example, The only difference between the
reactions is that the water formed is a
liquid in the first one and a vapor in the
second. 5. The standard heat of reaction
is the heat of reaction when both the
reactants and products are at a specified
reference T and P, usually 25? and 1atm.
16
Example 9.1-1 Calculation of Heats of Reaction

The standard heat of reaction of the combustion
of
n-butane vapor is

Calculate the rate of enthalpy change,
(kJ/s), if 2400 mol/s of CO2 is produced in this
reaction and the reactants and products are all
at 25?.
Soln
17
2. What is the standard heat of the reaction
Calculate if 2400 mol/s of CO2 is produced
in this reaction and the reactants and products
are all at 25?.
Soln
Since doubling the stoichiometric coefficients of
a reaction must double the heat of reaction,
The enthalpy change associated with the product
of 2400 mol/s of CO2 at 25oC cannot depend on
how the stoichiometric equation is written, and
so must be the value calculated in part(1).
18
Let us do the calculation and prove it.
19
3.The heats of vaporization of n-butane and water
at 25oC are 19.2 kJ/mol and 44.0 kJ/mol,
respectively. What is the standard heat of
reaction
Calculate if 2400 mol/s of CO2 is produced
in this reaction and the reactants and products
are all at 25oC.
Soln Compare the two reactions
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If a reaction takes place in a closed reactor at
constant
volume, the heat released or absorbed is
determined by
the change in internal energy between the
reactants and
products.
The internal energy of reaction, , is
the difference
Uproducts Ureactants if stoichiometric
quantities of reactants
react completely at temperature T.
Suppose a reaction occurs, and??i is the
stoichiometric
coefficient of the ith gaseous reactant or
product. If ideal
gas behavior can be assumed and specific volumes
of
liquid and solid reactants and products are
negligible
compared with those of the gases.

The internal energy of reaction is related to the
heat of
reaction by

For example, for the reaction

the internal energy of reaction is

If there are no gaseous reactants or products,
then to
a good approximation

25
Example 9.1-2 Evaluation of
The standard heat of reaction
is . Calculate
for this reaction.
Soln From the stoichiometric equation
26
9.2 MEASUREMENT AND CALCULATION OF HEATS OF
REACTION HESSS LAW

A heat of reaction may be measured in a
calorimeter
a closed reactor immersed in a fluid contained
in a
well-insulated vessel.
The rise or fall of the fluid temperature can be
measured
and used to determine the energy released or
absorbed
by the reaction, and the values of may
then be cal-
culated from that energy and known reactant and
product
heat capacities.

27
For example, you wish to determine for the
reaction
You can carry out the reactions
1.
2.
and determine their heats of reaction
experimentally. You may then construct a
process path for the reaction
3.
28
Reaction(3)
25oC
25oC
Reaction(1)
Reverse of reaction(2)
25oC
29

This result could have been obtained more
concisely by
treating the stoichiometric equations for
reactions 1 and
2 as algebraic equations. If the equation for
reaction 2 is
subtracted from that for reaction 1, the result
is

?
30
Hesss law
If the stoichiometric equation for reaction 1 can
be obtained by algebraic operations
(multipliation by constants, addition, and
subtraction) on stoichiometric equations for
reactions 2, 3, , then the heat of reaction
can be obtained by performing the same
operations on the heats of reactions ,
,.
31
Example 9.2-1 Hesss Law
The standard heats of the following combustion
reactions have been determined experimentally
Use Hesss law and the given heats of reaction to
deter- mine the standard heat of the reaction
Soln Since (4) 2??(2) 3?(3) - (1)
32
9.3 FORMATION REACTIONS AND HEATS OF FORMATION

A formation reaction of a compound is the
reaction in
which the compound is formed from its elemental
constituents as they normally occur in nature
(e.g. O2
rather than O).
The enthalpy change associated with the formation
of
1 mole of the compound at a reference
temperature
and pressure (usually 25oC and 1 atm) is the
standard
heat of formation of the compound, .

Standard heats of formation for many compounds
are
listed in Table B.1 of this text and on Perrys
Cemical
Engineers Handbook. For example, for
crystalline
ammonium nitrate is given in Table B.1 as
-365.14kJ/mol,
signifying

Similarly, for liquid benzene
or

The standard heat of formation of an elemental
species
(e.g. O2) is zero.

34
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It may be shown using Hesss law that if ?i is
the
stoichiometric coefficient of the ith species
participating
in a reaction ( for products, - for reactants)
and
is the standard heat of formation of this
species, then
the standard heat of the reaction is

The standard heats of formation of all elemental
species should be set equal to zero in this
formula.
36
(0)
(1)
(2)
(3)
(4)
37
Example 9.3-1 Determination of Heat of Reaction
from Heats of Formation
Determine the standard heat of reaction for the
com- bustion of liquid n-pentane, assuming
H2O(l) is a combustion product.
Soln
? Heats of formation from Table B.1
38
9.4 HEATS OF COMBUSTION

The standard heat of combustion of a substance,
,
is the heat of combustion of that substance with
oxygen
to yield specified products e.g., CO2(g) and
H2O(l), with
both reactants and products at 25oC and 1 atm
(the
arbitrary but conventional reference state).
Table B.1 lists standard heats of combustion for
a
number of substances. The given values are based
on
the following assumptions (a) all carbon in the
fuel forms
CO2(g), (b) all hydrogen forms H2O(l), (c) all
sulfur forms
SO2(g), and (d) all nitrogen forms N2(g).

The standard heat of combustion of liquid
ethanol, for
example, is given in Table B.1 as
which signifies

Additional heats of combustion are given on
Perrys
Chemical Engineers Handbook.

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Standard heats of reactions that involve only
combustible
substances and combustion products can be
calculated
from tabulated standard heats of combustion, in
another
application of Hesss law.
A hypothetical reaction path may be constructed
in which
(a) all combustible reactants are burned with O2
at 25oC
and (b) CO2 and H2O combine to form the reaction
pro-
ducts plus O2. Step (b) involves the reverse of
the com-
bustion reactions of the reaction products.
Since both steps involve only combustion
reactions, the
total enthalpy change which equals the desired
heat of
reaction can be determined entirely from heats
of com-
bustion.

If any of the reactants or products are
themselves com-
bustion products CO2, H2O(l), SO2,, their
terms
in the above equation should be set equal to 0.
Note that this formula is similar to that used to
determine
from heats of formation, except that
in this case
the negative of the sum is taken. The validity
of this for-
mula is illustrated in the next example.

43
(0)
(1)
(2)
(3)
44
Example 9.4-1 Calculation of a Heat of Reaction
from Heats of Combustion
Calculate the standard heat of reaction for the
dehy- dration of ethane
Soln From Table B.1,
??
45

One of the principal applications of

is to determine heats of formation for
combustible substances whose formation reactions
do not occur naturally. For example, the
formation reaction of pentane
cannot be carried out in a laboratory, but
carbon, hydro- gen, and pentane can all be
burned and their standard heats of combustion
determined experimentally. The heat of formation
of pentane may then be calculated from
46
9.5 ENERGY BALANCES ON REACTIVE PROCESSES
9.5a General Procedures

To perform energy balance calculations on a
reactive
system, proceed much as you did for nonreactive
systems
Draw and label a flowchart
Use material balances and phase equilibrium rela-
tionships such as Raoults law to determine
as many
stream amounts or flow rates as possible

47
(c) Choose reference states for specific enthalpy
(or internal energy) calculations and
prepare and fill in inlet-outlet enthalpy
(or internal energy) table and (d) Calculate
(or or ), substitute
the calculated value in the appropriate form
of the energy balance equation, and complete
the required calculation.
48

Two methods are commonly used to choose reference
states for enthalpy calculations and to
calculate specific
enthalpies and .
We outlet the two approaches below, using a
propane
combustion process to illustrate them.
For simplicity, the material balance calculations
for the illustrative process have been performed
and
the results incorporated into the flowchart.

49
25oC
100 mol O2(g)/s 2256 mol N2(g)/s
100 mol C3H8(g)/s
Furnace
300 mol CO2(g)/s 400 mol H2O(g)/s
600 mol O2(g)/s 2256 mol N2(g)/s
300oC
1000oC
50
Heat of Reaction Method. This method is
generally preferable when there is a single
reaction for which is known.

Complete the material balance calculations on the
reactor to the greatest extent possible.
2. Choose reference states for specific enthalpy
calculations. The best choices are generally
reactant
and product species at 25oC and 1 atm in the
states
for which the heat of reaction is known
C3H8(g), O2(g),
CO2(g), and H2O(l) in the example process,
and non-
reacting species at any convenient
temperature, such
as the reactor inlet or outlet temperature or
the
reference condition used for the species in an
available
enthalpy table N2(g) at 25oC and 1 atm, the
reference
state for Table B.8

51
3. For a single reaction in a continuous process,
calculate the extent of reaction, . When
writing the equation, choose as species A any
reactant or product for which the feed and
the product flow rates are known.
In the example, we may choose any reactant or
product since we know all inlet and outlet
species flow rates and calculate the rate of
consumption or generation of A as
. If A is propane
52
4. Prepare the inlet-outlet enthalpy table,
inserting known molar amounts ( ) or flow
rates ( ) for all inlet and outlet
stream components. If any of the components is
at its reference state, insert 0 for the
corresponding .
ReferencesC3H8(g), O2(g), N2(g), CO2(g), H2O(l)
at 25oC and 1 atm
53
5. Calculate each unknown stream component
enthalpy, , as for the species
going from its reference state to the
process state, and insert the enthalpies in
the table. In the example, from Table B.8
We proceed in the same manner to calculate
54
6. Calculate for the reactor. Use one of
the following formulas
A derivation of these equations is outlined
following the presentation of the heat of
formation method. Substi- tution of the
previously calculated values into the above
equation yields
7. Substitute the calculated value of in
the energy balance and complete the required
calculations.
55
Heat of Formation Method. This method is
generally preferable for multiple reactions and
single reactions for which is not
readily available.

Complete the material balance calculations on the
reactor to the greatest extent possible.
2. Choose reference states for enthalpy
calculations.
(This is the step that distinguishes the
preceding
method from this one.) The choices should be
the
elemental species that constitute the
reactants and
products in the states in which the elements
are found
at 25oC and 1 atm in the states C(s), H2(g),
etc. and
nonreacting species at any convenient
temperature.
In the example, the reference states would be
C(s),
H2(g), and O2(g) at 25oC ( the elemental
species
constituting the reactants and products), and
N2(g) at
25oC the reference temperature for Table B.8

56
3. Prepare the inlet-outlet enthalpy table,
inserting known molar amounts ( ) or flow
rates ( ) for all inlet and outlet
stream components. For the example process,
the table would appear as follows
References C(s), H2(g), O2(g), N2(g) at 25oC
and 1 atm
57
4. Calculate each unknown specific enthalpy. For
a reac- tant or product, start with the
elemental species at 25oC and 1 atm (the
references) and form 1 mol of the pro- cess
species at 25oC and 1 atm (
from Table B.1). Then bring the species from
25oC and 1 atm to its process state,
calculate using the appropriate heat
capacities from Table B.2, specific enthalpies
from Table B.8 or B.9, and latent heats from
Table B.1. The specific enthalpy that goes
in the inlet-outlet table is the sum of the
enthalpy changes for each step in the process
path.
58

In the example, we would first calculate the
specific
enthalpy of the entering propane as
follows

This is the enthalpy of propane at 25oC (the
process
state) relative to C(s) and H2(g) at 25oC (the
reference
state).
If the propane had entered at a temperature T0
other
than 25oC, a term of the form
would be
added to the heat of formation of propane.

Next, we calculate the specific enthalpy of O2 at
300oC
(the process state) relative to O2 at 25oC (the
reference
state) as (from Table
B.8). There is no
heat of formation term, since O2 is an elemental
species.
We proceed in the same manner to calculate
,
,
, and
.
To calculate and , we form the
corresponding
species CO2(g) and H2O(v) at 25oC from their
elements
( ), then heat them from 25oC to
1000oC
( from Table B.8), and add
the formation
and heating terms.

60
5. Calculate for the reactor. For both
single and mul- tiple reactions, the formula is

Note that heat of reaction terms are not required
if the
elements are chosen as references.
The heats of reaction are implicitly included
when the
heats of formation of the reactants (included in
the
terms) are subtracted from those of the products
( in
the terms) in the expression for .
Therefore

61
6. Substitute the calculated value of in
the energy balance equation and complete the
required calculations.
The process paths that correspond to the heat of
reaction and heat of formation methods are shown
below.
Reactants Tin
Products Tout
Products 25oC
Reactants 25oC
(a) Process path for heat of reaction method
62
Reactants Tin
Products Tout
Reactants 25oC
Products 25oC
(a) Process path for heat of reaction method
63
Reactants Tin
Products Tout
Elements 25oC
(b) Process path for heat of formation method
64
Example 9.5-1 Energy Balance About an Ammonia
Oxidizer
The standard heat of reaction for the oxidation
of ammonia is given below
One hundred mol NH3/s and 200 mol O2/s at 25oC
are fed into a reactor in which the ammonia is
completely consumed. The product gas emerges at
300oC. Cal- culate the rate at which heat must
be transferred to or from the reactor, assuming
operation at approximately 1 atm.
65
Soln
Basis Given Feed Rates
Since only one reaction takes place and
is known, we will use the heat of reaction
method for the energy balance, choosing as
references the reactant and product species in
the states for which the heat of re- action is
given.
66
The enthalpy table appears as follows
References NH3(g), O2(g) ), NO(g) , H2O(v)at
25oC and 1 atm
67
Calculate Unknown Enthalpies
Calculate and
Since 100 mol NH3/s is consumed in the process
68
From table
69
Energy Balance
For this open system,
Thus, 19,700kW of heat must be transferred from
the reactor to maintain the product temperature
at 300oC. If less heat were transferred, more of
the heat of reac- tion would go into the
reaction mixture and the outlet temperature
would increase.
70
9.5b Processes with Unknown Outlet Conditions
Adiabatic Reactors

In the reactive systems we have looked at so far,
the inlet
and outlet conditions were specified and the
required heat
input could be determined from an energy
balance.
In another important class of problems, the input
condi-
tions, heat input, and product composition are
specified,
and the outlet temperature is to be calculated.
To solve
such problems, you must evaluate the enthalpies
of the
products relative to the chosen reference states
in terms
of the unknown final temperature, and then
substitute the
resulting expressions into the energy balance (
)
to calculate Tout.

71
9.5c Thermochemistry of Solutions
The enthalpy change associated with the formation
of a solution from the solute elements and the
solvent at 25oC is called the standard heat of
formation of the solution. If a solution
contains n moles of solvent per mole of solute,
then
where is the heat of solution at 25oC
(Section 8.5). From the definitions of
and , the dimensions of the heat of
formation of the solution are (energy)/(mole of
solute).
72
The standard heat of a reaction involving
solutions may be calculated from heats of
formation of the solutions. For example, for the
reaction
the standard heat of reaction is
73
The last equation signifies that if a solution
containing 2 mol of HNO3 in 50 mol of H2O(r25)
is neutralized at 25oC with 1 mol of Ca(OH)2
dissolved in enough water so that the addition
of more water would not cause a measurable
enthalpy change (r?), the enthalpy change is
-114.2 kJ.
74
If a standard heat of formation is tabulated for
a solution involved in a reaction, the tabulated
value may be sub- stituted directly into the
expression for , otherwise,
must first be calculated by adding the standard
heat of formation of the pure solute to the
standard heat of solution.
75
9.4 FUEL AND COMBUSTION

The use of heat generated by a combustion
reaction to
produce steam, which drives turbines to produce
electri-
city, may be the single most important
commercial appli-
cation of chemical reactions.
The analysis of fuels and combustion reactions
and
reactors has always been an important activity
for che-
mical engineers. In this section, we review the
properties
of the fuels most often used for power
generation and
outline techniques for energy balances on
combustion
reactors.

76
9.6a Fuels and Their Properties
Fuels burned in power-plant furnaces may be
solids, liquids, or gases. Some of the more
common fuels are Solid fuels Principally coal
(a mixture of carbon, water, noncombustible
ash, hydrocarbons, and sulfur), coke( primarily
carbon the solid residue left after coal or
petroleum is heated, driving off volatile
substances and decomposing hydrocarbons), and
to a small extent wood and solid waste
(garbage).
77
Liquid fuels Principally hydrocarbons obtained
by distilling crude oil (petroleum) also coal
tars and shale oil. There is also a strong
worldwide interest in the use of alcohols
obtained by fermenting grains. Gaseous fuels
Principally natural gas (80 to 95 methane,
the balance ethane, propane, and small
quantities of other gases) also light
hydrocarbons obtained from petroleum or coal
treatment, acetylene, and hydrogen (the latter
two are relatively expensive to produce).
78

The heating value of a combustible material is
the
negative of the standard heat of combustion.
The
higher heating value (or total heating value or
gross heating value) is with H2O(l)
as a
combustion product, and the lower heating value
(
or net heating value) is the value based on
H2O(v)
as a product. Since is always negative,
the
heating value is positive.
To calculate a lower heating value of a fuel from
a
higher heating value or vice versa, you must
determine
the moles of water produced when one mole of
the
fuel is burned. If this quantity is designated
n, then

79
The heat of vaporization of water at 25oC is
If a fuel contains a mixture of combustible
substances, its heating value (lower or higher)
is
where (HV)i is the heating value of the ith
combustible substance. If the heating values are
expressed in units of (energy)/(mass), then the
xis are the mass fractions of the fuel
components, while if the dimensions of the
heating values are (energy)/(mole) then the xis
are mole fractions.
80

Higher heating values for common solid, liquid,
and
gaseous fuels are tabulated in Section 27 of
Perrys
Chemical Engineers Handbook. Representative
values
are given in Table 9.6-1. From the standpoint of
heating
value per unit mass, hydrogen is clearly the
best fuel
however, it does not occur naturally in
appreciable
quantities and the current cost of producing it
makes it
less economical than the other fuels in Table
9.6-1.

81
Table 9.6-1 Typical Heating Values of Common Fuels
Higher Heating Value
Fuel
kJ/g Btu/lbm
Wood 17
7700 Soft coal
23 10000 Hard coal
35 15000 Fuel
oil, gasoline 44
19000 Natural gas
54 23000 Hydrogen
143 61000
82
9.6b Adiabatic Flame Temperature

When a fuel is burned, a considerable amount of
energy is released. Some of this energy is
transferred
as heat through the reactor wall, and the
remainder
raises the temperature of the reaction products
the
less heat transferred, the higher the product
temperature.
The highest achievable temperature is reached if
the
reactor is adiabatic and all of the energy
released by
the combustion goes to raise the temperature of
the
combustion products. This temperature is called
the
adiabatic flame temperature, Tad.

The calculation of an adiabatic flame temperature
follows
the general procedure outlined in Section 9.5b.
Unknown stream flow rates are first determined by
ma-
terial balances.
Reference conditions are chosen, specific
enthalpies of
feed components are calculated, and specific
enthalpies
of product components are expressed in terms of
the
product temperature, Tad.
Finally, for the process is evaluated
and substi-
tuted into the energy balance equation,
which is solved for Tad.

Suppose (mol/s) of a fuel species with heat
of com-
bustion is burned completely with pure
oxygen or
air in a continuous adiabatic reactor. If the
reference
states of the molecular feed and product species
are
those used to determine , the enthalpy
change
from inlet to outlet is determined from

Since the reactor is adiabatic, in the
energy balance. If shaft work and kinetic and
potential energy changes
are negligible compared to each of the first two
terms in the expression for , the
85
energy balance simplifies to
which in turn leads to
Once again, the reference states for
determination of the specific enthalpies in
this equation must be those used to determine
the value of .
86
9.6c Flammability and Ignition