Calculation of Enthalpy Changes in Chemical Engineering, Study notes of Engineering

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Calculation of Enthalpy Changes

Manolito E. Bambase Jr Assistant Professor, Department of Chemical Engineering CEAT, University of the Philippines, Los Banos, Laguna, Philippines

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14. 1 Heat Capacity Equations

As shown previously, the change in enthalpy can be calculated using the heat capacity CP.

H  (^)  CP dT

To give the heat capacity some physical meaning, CP represents the amount of energy required to increase the temperature of a given amount of substance by 1 degree.

Common units for CP:

0

kJ Btu

kmol K lbmol  F

For gas mixtures, the CP of the mixture is the mole weighted average of the heat capacities of the components:

 

N P (^) avg i 1

C



 (^)  x Ci Pi

If CP is not constant for the given temperature range, it may be expressed as a function of temperature in a power series such as:

CP = a + b T + g T^2

where a, b, and g are constants specific to a particular substance ( Appendix E.1 , Basic Principles and Calculations in Chemical Engineering, 6th^ edition, by David M. Himmelblau)

14. 1 Heat Capacity Equations

Example 14 – 1. Calculation of H for a Gas Mixture

An economic feasibility study indicates that solid municipal waste can be burned to a gas of the following composition (on a dry basis):

CO 2 CO O 2 N 2

What is the enthalpy difference for this gas per lbmol between the bottom and the top of the stack if the temperature at the bottom of the stack is 550^0 F and the temperature at the top is 2000 F.

Basis: 1.00 lbmol of gas mixture

The enthalpy difference (H) is calculated as:

Example 14 – 1. Calculation of H for a Gas Mixture

H  (^)  CP dT

The CP of the gas mixture is determined from the equation:

 

  (^) N 2 O 2 CO 2 CO

N P (^) avg i 1

P (^) avg N2 P O2 P CO2 P CO P

C

C x C x C x C x C

x C i Pi





Example 14 – 1. Calculation of H for a Gas Mixture

  

  

  

  

N 2

O 2

CO 2

CO

N2 P

O2 P

CO2 P

CO P

x C 0.82 6. ....

x C 0.073 7. ....

x C 0.092 8. ....

x C 0.015 6. ....

Obtaining S xiCPi :

 

3 7 2 P (^) avg 10 3

C 7.053 1.2242 10 T 2.6124 10 T

0.2814 10 T

 



14. 2 Tables of Enthalpy Values

Enthalpies at various temperatures can also be obtained from tables.

From Basic Principles and Calculations in Chemical Engineering by David M. Himmelblau (6th^ edition):

Table D.2 Enthalpies of Paraffinic Hydrocarbons (C 1 – C 6 )

Table D.3 Enthalpies of Other Hydrocarbons (ethylene, propylene, butene, acetylene, benzene)

Table D.4 Enthalpies of Nitrogen and Some of its Oxides

Table D.5 Enthalpies of Sulfur Compounds

Table D.6 Enthalpies of Combustion Gases

14. 3 Enthalpy Calculations from Standard Heat of Formation

The enthalpy from a standard reference state is given by

R

T

H  H f  T CP dT

where Hfo^ is the standard heat of formation and TR is the reference temperature.

For a mixture,

 R 

N (^) T f (^) T i 1

H mixture H C P dT



Consider an open system with no chemical reaction:

14. 3 Enthalpy Calculations from Standard Heat of Formation

Open System (No Reaction)

Input, T 1 Output, T 2 A: HA B: HB

A: HA B: HB

The enthalpy difference between inlet and outlet will be

H = Hout – Hin = (HA2 + HB2) – (HA1 + HB1)

Calculating the enthalpies from standard heat of formation

14. 3 Enthalpy Calculations from Standard Heat of Formation

   

   

2 2 R R

1 1 R R

T T fA (^) T fB T

T T fA (^) T fB T

H H H

H H

PA PB

PA PB

C dT C dT

C dT C dT

  ^    

 

 

Simplifying,

2 2 1 1

T T T T

 H  (^)  CPA dT   C (^) PB dT

Calculating the enthalpies from standard heat of formation

14. 3 Enthalpy Calculations from Standard Heat of Formation

   

   

2 2 R R

1 1 R R

T T fC (^) T fD T

T T fA (^) T fB T

H H H

H H

PC PD

PA PB

C dT C dT

C dT C dT

  ^    

 

 

Rearranging the terms,

   

2 R 2 1 1 R R R

T fC fD fA fB (^) T

T T T T T T

H H H H H PC

PD PA PB

C dT

C dT C dT C dT

  ^     



  

The group of terms involving the standard heats of formation is called the standard heat of reaction, HoR.

In general,

14. 3 Enthalpy Calculations from Standard Heat of Formation

H (^) R  nH (^) f   nHf  products (^) i reactants (^) i

  (^)   

The n in the equation is the stoichiometric coefficient of species i in the chemical reaction.

The standard heat of reaction is the difference between the heats of formation of the products and that of the reactants.