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

reactantsproducts),(ˆ HHPTH r

Heat of Reaction : Per mole of what ?

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

Meaning that:

If 150 mol C/s is generated, enthalpy change is

produced C mol 3

50

reacted B mol 1

50

reactedA mol 2

50ˆ kJkJkJH r

-50 kJ 150 mol C generated =3 mol C generated s

ΔH= -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 reactionnA,r - moles of A consumed or generated

A

A

A

inAoutA

v

rn

v

nn ,)( ,,

rnv

PTHH A

A

r ,),(ˆ

),(ˆ PTHH r

Properties of Heat of Reaction1. 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

Example for the reactionC6H14 (l) + 19/2 O2 (g) 6 CO (g) + 7 H2O (v)

reactantsgaseous

productsgaseous

)(ˆ)(ˆiirr vvRTTHTU

reactantproductsr UU(T)UΔ

RTTH

RTTHTU

r

rr

2/7)(ˆ

)2/1976()(ˆ)(ˆ

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 methodC + O2 CO2 ΔHr1 = -393.51 kJ/mol

CO + ½ O2 CO2 ΔHr2 = -282.99 kJ/mol

C + ½ O2 (+ ½ O2) CO (+ ½ O2)

CO2

30ˆ rH

10ˆ rHH

20ˆ rHH

molkJ

HHH rrr

/52.110

99.28251.393

)ˆ(ˆˆ 20

10

30

Class Discussion

Example 9.1-1Example 9.1-2Example 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

fitreacifi

productsifi

iir HvHvHvH ˆˆˆˆ

tan

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

ciproducts

icitsreacici

iir HvHvHvH ˆˆˆˆ

tan

Example 9.4-1

Calculate the standard heat of reaction for the dehydrogenation of ethane

C2H6 C2H4 + H2

Energy Balance on Reactive Processes

Method 1: Heat of Reaction Methodpreferable when there is a single reaction for which ΔĤ°r is known

Reactants

Tin

Products

Tout

Reactants

T=25 oC

Products

T=25 oC

ΔHro

ΔH

ΔH1 ΔH2

Method 1: Heat of Reaction Method

1. Complete the material balance2. 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 outlet3. 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

4. Prepare inlet-outlet enthalpy table5. Calculate each unknown stream component enthalpy6. Calculate for the reactor ; use following eq.

7. Substitute calculated value in the energy balance equation and complete the required calculations.

A

inAoutA

v

nn )( ,,

reactions) (multiple ˆˆˆ

reaction) (single ˆˆˆ

ininoutoutreaction

orjj

ininoutoutor

HnHnHH

HnHnHH

H

H

Energy Balance on Reactive Processes

Method 2: Heat of Formation Methodpreferable when there is a multiple reaction and single reaction for which ΔĤ°r is unknown

Reactants

Tin

Products

Tout

ΔH

Elements

25 oC

ΔH1 ΔH2

Method 2: Heat of Formation Method

1. Complete the material balance2. 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 table4. Calculate each unknown stream component enthalpy5. Calculate 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.

6. Substitute calculated value in the energy balance equation and complete the required calculations.

H

ininoutout HnHnH ˆˆ

H

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 9.5-2Example 9.5.3Example 9.5.4

GOOD LUCK FOR YOUR

FINAL EXAM