Energy Balances with Reaction

In any chemical reaction, energy is required to break the reactant bonds and energy is released when the product bonds are formed

The large changes in enthalpy and internal energy during a chemical reaction necessitates substantial heat transfer (heating or cooling) from the reactor in order to maintain the reactor at its desired operating temperature

The net change of enthalpy is called the heat of reaction, and is the energy that must either be transferred to or from the reactor to maintain the desired reactor temperature

Heats of Reaction

By definition, the heat of reaction, r (T,P), is the enthalpy change for a process in which stoichiometric quantities of reactants at temperature Tand pressure P react completely to form products at the same temperature and pressure.

For the following reaction,

r is calculated as the difference between the product and reactant enthalpies (at constant T,P) which are weighted by their stoichiometric coefficients. Therefore,

),(),(),(),(),(

),(

PTH

PTHbPTHaPTHdPTHc

HHPTH

ii

BADC

reactantsproductsr

=+=

=

[kJ/mol]

dDcCbBaA ++

Heats of Reaction

The units of r are kJ/mol but, per mole of what?? Recall that the reported r applies to stoichiometric quantities of each species. For example,

2A + B 3C r (100C, 1 atm) = -50 kJ/mol

the enthalpy change for the given reaction is

If 150 mol of C/s was generated at 100C and 1 atm, generated C mol 3

kJ 50consumed B mol 1

kJ 50consumed A mol 2

kJ 50 ==

kJ/s 2500sgenerated C mol 150

generated C mol 3kJ 50 =

=H&

Heats of Reaction Extent of Reaction

In general, if nA,r moles of A are generated or consumed by reaction at a temperature T and pressure P and A is the stoichiometric coefficient of the reactant or product, the associated enthalpy change is:

Recall that the extent of reaction, , is a measure of how far a reaction has proceeded.

( ) ( )||||

|||| ,

A

rA

A

inAoutA nnn =

= &&&

),(||

),(, PTHn

PTHH rrAA

r == &&

Notes on Heats of Reaction

1. If r (T,P) is negative, the reaction is exothermic energy must be removed from the reactor to keep the temperature from increasing

2. If r (T,P) is positive, the reaction is endothermic energy must be added to the reactor to keep the temperature from decreasing

3. At low and moderate pressure, r (T,P) is nearly independent of pressure. Therefore, r (T,P) r (T)

4. The value of the heat of reaction depends on how the stoichiometric equation is written. For example:

CH4(g) + 2 O2(g) CO2(g) + 2 H2O(l): r1 (25C) = -890.3 kJ/mol2 CH4(g) + 4 O2(g) 2 CO2(g) + 4 H2O(l): r2 (25C) = -1780.6 kJ/mol

Notes on Heats of Reaction

5. The value of the heat of reaction depends on the phase of the reactants and products. For example:

CH4(g) + 2 O2(g) CO2(g) + 2 H2O(l) : r1 (25C) = -890.3 kJ/molCH4(g) + 2 O2(g) CO2(g) + 2 H2O(g) : r2 (25C) = -802.3 kJ/mol

6. The standard heat of reaction, r, is the heat of reaction when both reactants and products are at standard conditions, 25C and 1 atm.

The symbol denotes standard conditions (i.e., 25C and 1 atm).

Example

1. The standard heat of the combustion on n-butane vapour is

Calculate the rate of enthalpy change, if 2400 mol/s of CO2 is produced in this reaction and the reactants and products are all at 25C.

2. The heats of vapourization of n-butane and water at 25C are 19.2 kJ/mol and 44.0 kJ/mol, respectively. 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 25C.

kJ/mol 2878 O(l)H 5(g)CO 4(g)O 2

13(g)HC 222104 =++ orH

(kJ/s) H&

O(v)H 5(g)CO 4(g)O 2

13(l)HC 222104 ++

H&

Closed System Reactions

What if the reaction takes place in a closed system of constant volume?

Energy balance: U + Ek + Ep = Q WThe internal energy of reaction, r (T), is calculated as the difference between the product and reactant internal energies if stoichiometric quantities of reactants react completely at temperature T.

Assuming ideal gas behaviour, the internal energy is related to the heat of reaction by

where I is the stoichiometric coefficient of the ith gaseous reactant or product. (See F&R Ex. 9.1-2)

=

tsreacgaseous

i

productsgaseous

irr vvRTTHTU

tan

||||)()(

reactantsproductsr UUTU = )(

Measurement of Heats of Reaction

Heats of reaction are measured in a calorimeter. A calorimeter is a closed reactor that is submersed in a fluid and enclosed in an insulated vessel. The increase or decrease in fluid temperature determines the amount of energy released or absorbed and using the heat capacities of the reactants and products, can be determined.

However, this measurement technique will not work for every reaction. For example, consider the following reaction:

- only minimal amounts of CO would form since the rate of reaction at 25C is too low

- higher reaction temperatures (higher reaction rates) would not lead to the formation of pure CO but rather a mixture of CO and CO2

CO(g)(g)O 21C(s) 2 +

rH

?atm) 1 C(25 = ,H r

Measurement of Heats of Reaction

What if we cant measure experimentally for our desired reaction?

However, we can measure these heats of reaction,

rHCOO

21C 2 + ?= 1 rH

22

22

COO 21 OC

COOC

++ kJ/mol 393.51= 2 rH

kJ/mol 282.99= 3 rH

)O21(O

21C 22 ++ )O2

1CO( 2+

2CO

= 2rr HH = 3rr HH

1rH

kJ/mol -110.52(-282.99)-393.51)( =+=+= 321 rrr HHH

Hesss Law

The previous result could be more readily obtained if we treated the stoichiometric equations as algebraic equations. That is,

Hesss Law if a set of reactions can be manipulated through a series algebraic operations to yield the desired reaction, then the desired heat of reaction can be obtained by performing the same algebraic operations on the heats of reaction of the manipulated set of reactions

1) reaction (desired COO21C

3) reaction-2 (reaction COCOO21COOC

2

2222

+

+

kJ/mol -110.52282.99)(393.51 === 321 rrr HHH

Example

The standard heats of the following combustion reactions have been determined experimentally:

Use Hesss Law and the given heats of reaction to determine the standard heat of the reaction

kJ/mol 285.8 OHO21 H

kJ/mol 393.5 COOC

kJ/mol 1559.8 OH 3CO 2O 27HC

222

22

22262

=+=+=++

3

2

1

r

r

r

H

H

H

? HCH 3C 2 622 =+ 4rH

Calculating r from Heats of FormationThe can be calculated using standard heats of formation. A formation reaction of a compound is the reaction in which the compound is formed from its elemental constituents as they would occur in nature (e.g., O2 rather than O).

The enthalpy change associated with the formation of 1 mole of the compound at 25C and 1 atm is the standard heat of formation of the compound. for many compounds are found in Table B.1.

For example, from Table B.1 it can be seen that the of ammonium nitrate (NH4NO3(s)) is -365.14 kJ/mol. This signifies that,

rH

fH fH fH

kJ/mol 365.14 (s)NONH(g)O 23(g)H 2(g)N 34222 =++ rH

Calculating r from Heats of FormationA consequence of Hesss Law is that the of any reaction can be calculated as:

where,

is the stoichiometric coefficient of reactant or product species iis the standard heat of formation of species i

==reactants

ifiproducts

ifiifi

ir HvHvHvH )(||)(||

ifH )(

rH

i

The standard heats of formation of all elemental species (e.g., O2, N2, Zn, etc.) are zero.

Example

Determine the standard heat of reaction for the combustion of liquid n-pentane.

C5H12(l) + 8 O2(g) 5 CO2(g) + 6 H2O(l)

Calculating r from Heats of CombustionThe standard heat of combustion of a species, , is the enthalpy change associated with the complete combustion of mole of a species with oxygen at 25C and 1 atm such that:

all the carbon forms CO2(g) all the hydrogen forms H2O(l) all the sulphur forms SO2(g) all the nitrogen forms N2(g)

values for combustible species (if available) are found in Table B.1.

For example, from Table B.1 it can be seen that the of ethanol is -1366.9 kJ/mol. This signifies that,

cH

cH cH

kJ/mol 1366.9 O(l)H 3(g)CO 2(g)O 3OH(l)HC 22252 =++ rH

Calculating r from Heats of CombustionA consequence of Hesss Law is that the of any reaction involving only oxygen and a combustible species can be calculated as:

where,

is the stoichiometric coefficient of reactant or product species iis the standard heat of formation of species i

rH

==products

icireactants

iciici

ir HvHvHvH )(||)(||)(

iicH )(

Note: this is reverse to determining the heat of reaction from heats of formation

If any reactants or products are combustion products (i.e, CO2, H2O(l), SO2,), their heats of combustion are zero.

Example

Calculate the standard heat of reaction form the dehydrogenation of ethane:

C2H6 C2H4 + H2

Determining f from cFor many substances, it is much easier to measure than

For example, the formation of pentane:

Carbon, hydrogen and pentane can all be burned and their standard heats of combustion determined experimentally. Therefore,

fH cH

? (l)HC(g)H 6C(s) 5 1252 =+ fH

)(-)6()()( (l)HC(g)HC(s)(l)HC 1252125 += cccf HHHH 5

Energy Balances with ReactionHeats of ReactionHeats of ReactionHeats of Reaction Extent of ReactionNotes on Heats of ReactionNotes on Heats of ReactionExampleClosed System ReactionsMeasurement of Heats of ReactionMeasurement of Heats of ReactionHesss LawExampleCalculating r from Heats of FormationCalculating r from Heats of FormationExampleCalculating r from Heats of CombustionCalculating r from Heats of CombustionExampleDetermining f from c