1. Balances on Reactive Processes
Shamsuzzoha, PhD
Department of Chemical Engineering, KFUPM

2. Energy Balances on Reactive Processes
Objectives:
Explain the concepts of heat of reaction (exothermic & endothermic), Hess’s Law, heat of formation, heat of combustion
Explain the concepts of combustion related knowledge; heating value, adiabatic flame temperature, flammability limit, flash point and flame properties
Calculate the enthalpy (and internal energy) change due to reaction using Hess’s and from tabulated data of the standard heat of formation and the standard heat of combustion.
Write and solve an energy balance on a chemical reactor using either the heat of reaction method or the heat of formation method
Write and solve a reactive-energy system for the heat transfer for specified inlet / outlet conditions, the outlet temperature for a specified heat input and product composition for a specified outlet temperature
Solve energy problems for processes involving solutions for which heats of solution are significant
Convert a higher heating value of a fuel to a lower heating value vice versa

3. Energy Balance involving Chemical Reaction
DHr = -ve (exothermic)
DHr = +ve (endothermic)
Tout, Pout, Hprod
Tin, Pin, Hreac
Qin/Qout
Tin, Pin = Tout, Pout
2A + B C
Hprod Hreac
(heat/enthalpy of reaction) : DĤr = ∑Ĥproduct – ∑Ĥreactant

4. 9.1 Heat of Reaction (or Enthalpy of Reaction)
Heat of reaction, , is the enthalpy change when stoichiometric quantities of reactants at temperature T and pressure P are consumed completely to form products at the same temperature and pressure
The standard heat of reaction, , is the heat of reaction at a specified reference temperature and pressure (e.g. 25oC & 1 atm)
Example 1
1 g-mole of gaseous methane and 2 g-moles of gaseous oxygen at 25oC and 1 atm react completely to form 1 g-mole of gaseous carbon dioxide and 2 g-moles of liquid water and the products are brought back to 25oC and 1 atm and the net enthalpy would be – kJ. Q = DH , KJ of heat would have to be transferred away from the reactor to keep the products at 25oC.

5. Example 2
6 g-moles of solid carbon and 3 g-moles of gaseous hydrogen at 25oC and 1 atm react completely to form 1 g-mole of liquid benzene the product is brought back to 25oC and 1 atm the specific enthalpy would be kJ. Q = DH , KJ of heat would have to be added into the reactor to keep the product at 25oC.
Note : At low and moderate pressures is nearly independent of pressure. Hence the heat of reaction may be written as

6. Types of Heat of Reaction
If (T,P) < 0 => the reaction is exothermic .. Example 1
less energy is required to break the reactant bonds than is released when the product bonds form, resulting in a net heat release as the reaction proceeds (i.e. Enthalpy of Reactants > Enthalpy of Products).
This energy may be transferred from the reactor or else may serve to raise the temperature of the reaction mixture
Recall Example 1;
If (T,P) > 0 => the reaction endothermic .. Example 2
more energy is required to break the reactant bonds than is released when the product bonds form, resulting in a net absorption of energy as the reaction proceeds (i.e. Enthalpy of Reactants < Enthalpy of Products)
Unless this energy is supplied to the reactor as heat, the temperature decreases
Recall Example 2;

7. Total enthalpy change due to reaction
Recall Example 1;
The standard (T=25oC, P=1 atm) heat of reaction is kJ per ? mol of WHAT?
and if for example, 2 mols /s of CH4 was reacted, the associated enthalpy change is

8. and if for example, 4 mols /s of O2 was reacted the associated enthalpy change is
and if for example, 2 mols /s of CO2 was generated, the associated enthalpy change is
and if for example, 4 mols /s of H2O was generated, the associated enthalpy change is

9. In general, if vA is the stoichiometric coefficient of a reactant or reaction product A ( negative if it is a reactant, positive if it is a product) and nA,r moles of A are consumed / reacted or generated at T=To and P=Po, the associated enthalpy change is
Recall Chapter 4, the extent of reaction, ξ ;
Then the associated enthalpy change is

10. The value of the heat of a reaction depends on how stoichiometric equation is written
1 g-mole of gaseous methane and 2 g-moles of gaseous oxygen at 25oC and 1 atm react completely to form 1 g-mole of gaseous carbon dioxide and 2 g-moles of liquid water and the products are brought back to 25oC and 1 atm and the net enthalpy would be – kJ. Q = DH , KJ of heat would have to be transferred away from the reactor to keep the products at 25oC.
2g-moles of gaseous methane and 4 g-moles of gaseous oxygen at 25oC and 1 atm react completely to form 2 g-moles of gaseous carbon dioxide and 4 g-moles of liquid water and the products are brought back to 25oC and 1 atm and the net enthalpy would be – kJ. Q = DH , KJ of heat would have to be transferred away from the reactor to keep the products at 25oC.

11. The value of the heat of a reaction depends the states of aggregation (solid, liquid or gas) of the reactants and products
The only difference between the reactions is that the water formed as a liquid in the first reaction and as a vapor in the second reaction
hence the difference between the two heats of reaction must be the enthalpy change associated with the vaporization of 2 mols of water at 25oC
i.e.

12. The only difference between the reactions is that propane exists as a liquid in the first reaction and as a vapor in the second reaction
hence the difference between the two heats of reaction must be the enthalpy change associated with the vaporization of 1 mol of propane at 25oC
i.e.

13. The only difference between the reactions is that the water formed as a liquid in the first reaction and as a vapor in the second reaction
hence the difference between the two heats of reaction must be the enthalpy change associated with the vaporization of 4 mols of water at 25oC
i.e.

14. The only difference between the reactions is that the water formed as a liquid in the first reaction and as a vapor in the second reaction
hence the difference between the two heats of reaction must be the enthalpy change associated with the vaporization of 4 mols of water at 25oC
i.e.

15. Working session 1
The standard heat of the combustion reaction of liquid n-Hexane to form CO2(g) and H2O(l) with all reactants and products at 25oC and 1 atm, is kJ/mol. The heat of vaporization of hexane and water at 25oC is kJ/mol and 44 kJ/mol, respectively.
Use the given data to calculate the standard heat of reaction at 25oC for the combustion of n-hexane vapor to form CO2(g) and H2O(g).
At what rate in kJ/s is heat absorbed or released (state which) if 54.5 kg/s of O2 is consumed in the combustion of n-hexane vapor , water vapor is the products, and the reactants and products are all at 25oC.

16. Working session 1 - Problem 9.3
Use the given data to calculate the standard heat of reaction at 25oC for the combustion of n-hexane vapor to form CO2(g) and H2O(g).
(Hypothetical reaction steps)
C6H14 (g), 25oC
O2 (g), 25oC
C6H14 (l), 25oC
H2 O (l), 25oC
CO2 (g), 25oC
H2 O (g), 25oC,

17. Working session 1 - Problem 9.3

18. Working session 1 - Problem 9.3
If Q=DH, at what rate in kJ/s is heat absorbed or released (state which) if 54.5 kg/s of O2 is consumed in the combustion of n-hexane vapor , water vapor is the products, and the reactants and products are all at 77oF.
Negative enthalpy indicates
an exothermic process
(i.e. heat is released )

19. The heat of a reaction at constant volume
Determined by the change on internal energy (DU) between reactants and products
Note: This last relation assumes that the gases behave as ideal gases, and that the molar volumes of the liquid or solid components are small. If there are no gaseous species involved in the reaction,
Example :

20. 9.2 Measurement and Calculation of Heats of Reaction: Hess’s Law

21. 9.2 Measurement and Calculation of Heats of Reaction: Hess’s Law

24. 9.2 Hess’s Law A + B + E -->D + F
Just as the species in a chemical reaction can be treated as algebraic quantities, so can the heats of reaction (and other thermodynamic properties). Example:
A + B + E -->D + F
Rxn 1: A + B ---> C + D ∆Horxn,1
Rxn 2: C + E ---> F ∆Horxn,2
Rxn 3 : Rxn 1 + Rxn 2 ∆Horxn,3
∆Horxn,3= ∆Horxn,1 + ∆Horxn,2

25. HESS’s law :- If the stoichiometric equation for a reaction can be derived from other reaction equations (by multiplication by constants, addition and subtraction) then the heat of reaction for the first reaction can be derived by performing the same algebraic operations on the heats of reaction for the other reactions.
Example :

26. Example 3 – Problem 9.6
Formaldehyde may be produced in the reaction between methanol and oxygen
2CH3OH (l) + O2(g)  2HCHO (g) + 2H2O(l) DHor = kJ/mol
The standard heat of combustion of hydrogen is
H2(g) + ½ O2(g)  H2O (l) DHor = kJ/mol
Use these heats of reaction and Hess’s law to estimate the standard heat of direct decomposition of methanol to form formaldehyde
CH3OH (l)  HCHO (g) + H2 (g)

27. Example 3 – Problem 9.6
Rxn 1 : 2CH3OH (l) + O2(g)  2HCHO (g) + 2H2O(l) DHorxn1 = kJ/mol
Rxn 2 : H2(g) + ½ O2(g)  H2O (l) DHorxn2 = kJ/mol
Rxn 3 : CH3OH (l)  HCHO (g) + H2 (g) DHorxn3 = ? kJ/mol
________________________________________________________________
According to Hess’s law
Rxn 3 = ½ Rxn 1 – Rxn2
DHorxn3 = ½ DHorxn DHorxn2
DHorxn3 = ½ (-326.2)- (-285.8) = kJ/mol

28. Working session 2
Calculate DĤ (kJ/mol) for the following reaction using the listed standard enthalpy of reaction data
R4 : 2N2(g) + 5O2(g)  2N2O5(s)
R1 : N2(g) + 3O2(g) + H2(g)  2HNO3(aq) DĤo= -414 kJ/mol
R2: N2O5(s) + H2O(l)  2HNO3(aq) DĤo= -86 kJ/mol
R3 :O2(g) + 2H2(g)  2 H2O(l) DĤo= kJ/mol
R4 = 2R1 – 2R2 – R1

29. 9.3 Heats of Formation
The heat of formation, , for a chemical species is equal to the heat of reaction for the reaction forming 1 mol of this species from its “elements” at standard conditions.
Note: Elements may be monatomic (e.g., C) or diatomic (e.g., H2), and the standard state may be any phase (c, l, or g). In this notation, “c” means crystalline or solid phase.
The standard heat of formation ( ) of the compound the enthalpy change associated with the formation of 1 mole of the compound at a reference temperature and pressure (usually 25oC and 1 atm)
Do not depend on pressure for low and moderate pressure (i.e. < 10 atm)
Depend on the phase (gas, liquid, solid)
The standard heat of formation an elemental species (e.g. O2, N2, H2) is zero.
The standard heat of formation of some substances is given in Table B-1

30. Table B-1 :- Standard Heat of Formation

31. An example - heat of formation for liquid propane:
Note: This value is from Table B.1. Values for the heats of formation for C(c) and H2(g) are listed in Table B.1 as zero, indicating that these are elements. The heat of formation for propane as a gas is different ( kJ/mol).
Heats of reaction from heats of formation (by Hess’s law):

32. Calculation of Heat of Reaction from Heats of Formation
An example - consider the reaction
Write the formula for in terms of the standard heats of formation of the reactants and products

33. Example 4
Calculate the standard heat of reaction for methane using the heats of formation if the water is formed as a liquid:
Read the standard heat of formation of respective species from Table B.1.

34. Example 5
Calculate the standard heat of reaction for methane the heats of formation if the water is formed as a vapor:
Read the standard heat of formation of respective species from Table B.1.

36. Working session 3 - Problem 9.8
Trichloroethylene, C2HCl3 , may be produced in a two-step reaction sequence as follows;
C2H4 (g) + 2Cl2(g)  C2H2Cl4 (l) + H2(g) DHor = kJ/mol
C2H2Cl4(l)  C2HCl3(l) + HCl (g)
The standard heat of formation of liquid trichloroethylene is kJ/mol
a) Calculate the standard heat of formation of tetrachloroethane, C2H2Cl4 (l)
and the standard heat of the second reaction
b) Use Hess’s law to calculate the standard heat of reaction of
C2H4 (g) + 2Cl2(g)  C2HCl3 (l) + H2(g) + HCl(g)
c) If 300 mol/h of C2HCl3 (l) is produced in the reaction of part (b) and the reactants and products are all at 25oC and 1 atm, how much heat is evolved or absorbed in the process?

37. Working session 3 - Problem 9.8
a) Calculate the standard heat of formation of tetrachloroethane, C2H2Cl4 (l)
C2H4 (g) + 2Cl2(g)  C2H2Cl4 (l) + H2(g) DHor = kJ/mol
DHor = (DHof) H2(g) + (DHof) C2H2Cl4(l) - (DHof) C2H4(g) - 2(DHof) Cl2(g)
read the standard heat of formation of ethylene, chlorine and hydrogen from Table B-1
= [0 + (DHof) C2H2Cl4(l) ] - [( (0)]
(DHof) C2H2Cl4(l) = kJ/mol

38. Working session 3 - Problem 9.8
Calculate the standard heat of the second reaction
C2H2Cl4(l)  C2HCl3(l) + HCl (g)
DHor = (DHof) HCl(g) + (DHof) C2HCl3(l) - (DHof) C2H4Cl4(l)
Read the standard heat of formation of hydrochloric acid from Table B-1 & the standard heat of formation of liquid trichloroethylene and tetrachloroethane are kJ/mol and kJ/mol, respectively.
DHor = – ( ) = kJ/mol

39. Working session 3 - Problem 9.8
b) Use Hess’s law to calculate the standard heat of reaction of
C2H4 (g) + 2Cl2(g)  C2HCl3 (l) + H2(g) + HCl(g)
According to Hess’s law
Rxn 1 : C2H4 (g) + 2Cl2(g)  C2H2Cl4 (l) + H2(g) DHorxn1 = kJ/mol
Rxn 2 : C2H2Cl4(l)  C2HCl3(l) + HCl (g) DHorxn2 = kJ/mol
Rxn 3 : C2H4 (g) + 2Cl2(g)  C2HCl3 (l) + H2(g) + HCl(g) DHorxn3 = ? kJ/mol
_________________________________________________________________
Rxn 3 = Rxn 1 + Rxn 2
DHorxn3 = = kJ/mol

40. Working session 3 - Problem 9.8
c) If 300 mol/h of C2HCl3 (l) is produced in the reaction of part (b) and the reactants and products are all at 25oC and 1 atm, how much heat is evolved or absorbed in the process?
C2H4 (g) + 2Cl2(g)  C2HCl3 (l) + H2(g) + HCl(g) DHor = kJ/mol

41. 9.4 Heats of Combustion
Combustion involves a chemical reaction between combustible species and oxygen (usually from air) to produce heat and combustion products (mainly water and carbon dioxide plus some other by-products such as carbon monoxide, oxides of nitrogen / sulphur , unburned fuels and radicals)
The standard heat of combustion, DH°c, is the heat released when one mole of a substance reacts with oxygen to yield specified products in a specified phase:
CO2 is always gas phase.
H2O can be liquid or vapor with the reactants and products at 25°C, 1 atm.
The standard heat of combustion of some substances is given in Table B-1
Important note : Please read carefully the footnotes in page regarding the use of these and other values provided by the table )

42. Table B-1:- Standard Heat of Combustion
Foot Note (pg. 629): standard states of products CO2(g), H2O(l) SO2(g), HCl(aq) & N2(g)

43. Higher and Lower Heats of Combustion
Heating value (HV) or calorific value (CV) is other common terms used to describe the heat of combustion; However, they are expressed as a negative value of standard heat of combustion (-DHoc) …..hence HV or CV is always positive
Often two heats of combustion are listed for hydrogen containing species: lower and higher.
Lower heating or calorific value (LHV or LCV ): product water is in the gas phase.
Higher heating or calorific value (HHV or HCV): product water is in the liquid phase.
These two metrics differ by the molar heat of vaporization of water times the moles of water produced.
LHV (or LCV) = HHV (or HCV) - nwDHvap
…. where nw = mole of water formed / mole of fuel burned
DHvap = 44 kJ/mol ( at T = 25oC and P = 1 atm)
Lower heating value is usually more relevant for engineering purposes because water leaves practical combustion devices as a vapor.

44. Heat of Reactions from Heat of Combustion
The standard heat of combustion in Table B-1 (Please take note of the assumptions applied)
The 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 Hess’s law
If any of reactants or products are themselves combustion products (CO2, H2O(l), SO2(g)…) their terms in the above equation should be set equal to zero

45. Calculation of Heat of Reaction from Heats of Combustion
An example - consider the reaction
Write the formula for in terms of the standard heats of combustion of the reactants and products

46. Calculation of Heat of Reaction from Heat Formation

47. Working session 4
Calculate the standard heat of the acetylene hydrogenation reaction
C2H2 (g) + 2H2(g)  C2H6 (g) DHor = ? kJ/mol
a) using the standard heat of combustion (Table B-1)

48. Working session 4
b) using the standard heat of formation (Table B-1)

49. Working session 4 c) Standard Heat of Combustion + Hess’s law
Rxn 1 : C2H2 (g) O2(g)  2CO2 (g) + H2O (l) DHoc = kJ/mol
Rxn 2 : H2(g) + 0.5O2(g)  H2O (l) DHoc = kJ/mol
Rnx 3 : C2H6 (g) O2(g)  2CO2 (g) + 3H2O (l) DHoc = kJ/mol
_________________________________________________________________
Rxn 4 : C2H2 (g) + 2H2(g)  C2H6 (g) DHoc = ? kJ/mol
Rxn 4 = Rxn 1 + 2Rxn2 – Rxn3
DHoc = ( ) – ( ) kJ/mol = kJ/mol
Calculate the standard heat of the acetylene hydrogenation reaction using the standard heat of formation and Hess’s law

50. Working session 4 c) Standard Heat of Formation + Hess’s law
Rxn 1 : 2C(s) + H2 (g)  C2H2(g) DHof = kJ/mol
Rxn 2 : H2(g) DHof = 0 kJ/mol
Rnx 3 : 2C2(g) + 3H2(g)  C2H6 (g) DHof = kJ/mol
_________________________________________________________________
Rxn 4 : C2H2 (g) + 2H2(g)  C2H6 (g) DHof = ? kJ/mol
Rxn 4 = Rxn 3 - Rxn2 – Rxn1
DHof = ( – ) kJ/mol = kJ/mol