4. CHEMICAL REACTION EQUILIBRIA 4.1. Introduction In materials processing or materials in service, chemical reactions take place. For example, in the production of steel, liquid iron containing impurities are subjected a reaction with gaseous oxygen. When a material is exposed to an atmosphere, it may be capable of reacting with other constituents of the environment. 4.2. Chemical Reaction Equilibrium Consider a general equilibrium, aA + bB = cC + dD ————— ————— Reactants Products Under constant T and P G = 0 (Criteria for equilibrium) G = Gproducts - Greactants = cG C + dG D - aG A - bG B For condensed phases: G i = o i G + R T ln a i For gases, G i = o i G + R T ln P i Therefore, activity is replaced by partial pressure for gases; Then G = c G C o + cRT ln a C + d G D o + dRT ln a D - a G A o - aRT ln a A - b G B o - bRT ln a B G = G+ R T ln b B a A d D c C a a a a
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4. CHEMICAL REACTION EQUILIBRIA
4.1. Introduction
In materials processing or materials in service, chemical reactions take place.
For example, in the production of steel, liquid iron containing impurities are
subjected a reaction with gaseous oxygen. When a material is exposed to an
atmosphere, it may be capable of reacting with other constituents of the
environment.
4.2. Chemical Reaction Equilibrium
Consider a general equilibrium,
aA + bB = cC + dD ————— —————
Reactants Products
Under constant T and P
G = 0 (Criteria for equilibrium)
G = Gproducts - Greactants
= cGC + dGD - aGA - bGB
For condensed phases:
Gi = o
iG + R T ln ai
For gases,
Gi = o
iG + R T ln Pi
Therefore, activity is replaced by partial pressure for gases; Then
G = cGCo + cRT ln aC + dGD
o + dRT ln aD - aGA
o - aRT ln aA - bGB
o - bRT ln aB
G = G + R T ln b
B
a
A
d
D
c
C
aa
aa
Activity can be replaced by partial pressure for gases. For pure condensed
phases activity can be taken as unity.
This equation can be written as: G = G + R T ln Q
Q is called reaction quotient.
G = f(T) tabulated
Since, G = H - T S
at any temperature T
G = Ho298 + Cp dT - T(S o
298 + Cp dT
T)
Cp = a + bT + cT-2
Cp = a + bT + cT-2
where
a = aprod - areact
the same way b and c are differences between b and c constants of the
products and the reactants.
G = Ho298 + (a + b T + c T-2) dT - T(S o
298 + a bT cT
TdT
2
)
G =Ho298 + (
a T
bT c T
T
2
2
298/ - T(S o
298 + (
a T bTc
TT
ln
2
2
298)
Replacement of the upper and the lower limits yields
G = Io + I1 T -
aT Tb
Tc
Tln
2 2
2 1
where, Io = Ho298 - (
a
bc298
2298 2982 / )
I1 = a - S o298 +
a b
cln 298 298
2298 2
4.3. Oxidation of Metals
One important equilibrium; between condensed phases (metals and oxides)
and a gaseous phase (oxygen containing) is oxidation of metals. Consider
the oxidation of copper
4 Cu(s) + O2(g) = 2 Cu2O(s)
Ho298 = -334400 J
S o298 = -152.07 J/K
Cp = 4.18 + 18.39x10-3 T + 1.67x105 T-2 J/K
Using above values
Io = -334400 - 1500
I1 = 4.18 + 152.07 + 28.35
Go, purely from thermochemical data is
Go = -335900 + 184.59 T - 4.18 T ln T - 9.2x10-3 T2 - 0.84x105 T-1 J (a)
If pure Cu reacting with oxygen to form pure Cu2O;
Go = R T ln PO2(eqm')
Experimental variation of Go with T can be calculated from the measured
oxygen partial pressure, PO2(eqm') that is in equilibrium with Cu and Cu2O.
When experimental Go vs. T is fit to
Go = A + B T log T + C T
for oxidation of copper
Go = -338580 - 32.77 T log T + 246.62 T (J) (b)
The comparison of Go calculated from (a) and (b) is shown in Table. The
difference in the temperature range 400 to 1200 K is between 293 to 794 J.
2-term fit
Go = A + B T
Go = -328500 + 137.94 T (J) (c)
The comparison of Go calculated from (c) with (b) is given in Table. The
difference between (b) and (c) in the 400 to 1200 K temperature range is