Chapter 11 Multicomponent Heterogeneous Reacting Systems

1
Chapter 11Multicomponent Heterogeneous Reacting
Systems

• Notes on
• Thermodynamics in Materials Science
• by
• Robert T. DeHoff
• (McGraw-Hill, 1993).

2
Consider a general reaction with N reactants and
M products
Define the affinity, A, as the weighted sum of
the chemical potentials of the M products - the
weighted sum of the chemical potentials of the N
reactants.
At equilibrium the chemical potential of the
products and the chemical potential of the
reactants are equal and A 0.
A0 Equilibrium, no net change in proportions.
Agt0 Products decompose. Proportion of
reactants increases.
Alt0 Products form. Proportion of products
increases.
3
Consider a general reaction with N2 reactants
and M2 products
Write the affinity.
A0 Equilibrium, no net change in proportions.
Agt0 Products decompose. Proportion of
reactants increases.
Alt0 Products form. Proportion of products
increases.
4
Consider a general oxidation reaction with N2
and M1
For one mole of oxide.
For one mole of O2.
Write the affinity.
A0 Equilibrium, no net change in proportions.
Agt0 Oxide decomposes. Atmosphere is reducing
to M.
Alt0 Oxide forms. Atmosphere is oxidizing to M.
5
Write affinity in terms of standard free energy
and activity.
Note relation of chemical potential to free
energy activity.
Substitute for chemical potential in affinity.
Note first two terms on right yield standard free
energy of reaction.
6
Continue to write affinity in terms of DGO
activity.
Note last two terms on right are sums of logs.
The sums of logs are equivalent to products of
the arguments of the logs. Coefficients of logs
become exponents of the arguments.
The proper quotient, Q, is the ratio of the
weighted product of the activities of the
products to the weighted product of the
activities of the reactants.
7
Evaluate affinity at equilibrium.
A0 Equilibrium, no net change in proportions.
Use K in place of Qequil for equilibrium constant
Rewrite affinity
A0, Q/K1 Equilibrium, no net change in
proportions.
Agt0, Q/Kgt1 Products decompose. Reactants
increase.
Alt0, Q/Klt1 Products form. Products increase.
8
Evaluate affinity for general reaction with N2
M2.
_at_ Equilibrium A0 Q/K1
Activity of pure components in reference state 1.
Activity of ideal gases partial pressure, akPk.
Activity of component in solution, akgkXk.
9
Consider a general oxidation reaction, basis 1
mole Mx Oy.
If the metal and oxide are pure
10
Consider a general oxidation reaction, basis 1
mole of O2.
If the metal and oxide are pure
11
A general oxidation reduction reaction, basis 1
mole of O2.
If the oxides are pure and the metals are in
solution
12
Consider the following reactions.
(1)
(2)
(3)
(4)
There are four components
There are two elements
There are two independent reactions
13
Find the standard free energy of the following
reactions at 473 K.
(1)
(2)
(3)
(4)
Find data (in DeHoff) for reactions (2) (3)

App. G
Fig. 11.5
Combine to find DGO for reactions (1) (4)

14
Write expression for affinity of reaction (4) at
473 K.
(4)
15
Find K for reaction (4) at 473 K.
(4)
Find PCO/PCO2 ratio at 473 K.
About 3 ppm of CO exit stack at 200OC.
16
Sieverts Law (applied to hydrogen in aluminum)
Solution of hydrogen takes two steps
Disassociation
Dissolution
Equilibrium constant for overall reaction
Solving for mole fraction of dissolved H
17
Consider units in Sieverts Law
Convert units of CH to mole fraction
Relation between Sieverts Law constant K
18
Relation between Sieverts Law constant XS free
energy
19
Consider the dezincification of brass by steam.
(1)
Combine the following reactions.
(2)
(3)
Subtract (3) from (2).
(4)
Find the standard free energy of reaction.
Based on data from Appendix G of DeHoff
20
Evaluate of reaction at 373 K.
Evaluate the equilibrium constant at 373 K.

Evaluate for XZn0.3 and gZn2.5.
Driving force for reaction at 373 K is high.
21
Consider the dezincification of brass by steam.
(1)
Combine the following reactions.
(2)
(3)
Subtract (3) from (2).
(4)
Find the standard free energy of reaction _at_ 100OC.
Based on data from Figure 11.5 of DeHoff
22
Evaluate of reaction at 373 K.
Evaluate the equilibrium constant at 373 K.

Evaluate for XZn0.3 and gZn2.5.
Driving force for reaction at 373 K is high.