Heterogeneous systems and reaction equilibria
B. Mishra
PART – 4
HETEROGENOUS SYSTEMS & REACTION EQUILIBRIA INVOLVING SOLIDS
Let us consider a mineralogical reaction involving solid phases aA +bB
cC +dD
(1)
For each solid phase, an equation of state of equilibrium can be written for C : GCP ,T = GC0, P ,T + RT ln X C + RT ln γ C for A : G AP ,T = G A0, P ,T + RT ln X A + RT ln γ A
Then we can write the free energy change of the reaction (ΔGrP ,T ) as follows: P ,T P ,T ΔGrP ,T = ∑ G products − ∑ Greac tan ts
(
) (
⇒ ΔGrP ,T = cGcP ,T + dG DP ,T − aG AP ,T + bG BP ,T
) (2)
(X C ) (X D ) ( X A ) A ( X B )B C
⇒ ΔGrP ,T = ΔGr0, P ,T + RT ln
D
(γ C ) (γ D ) (γ A ) A (γ B )B C
+ RT ln
D
(3) where ΔGr0, P ,T is the free energy change of the pure phases at equilibrium P, T and defined by eqn. (24) in part – 1. Now, let’s recall eqn. (16) in part -1.
G P ,T = H P0T0 − TS P0T0
T P ⎡T ⎛ CP ⎞ ⎤ + ⎢ ∫ C P dT − T ∫ ⎜ ⎟dT ⎥ + ∫ V .dP T ⎝ ⎠ ⎥⎦ P0 T0 ⎣⎢T0
If the terms in the square bracket is expressed as Cp* then we can write the following expression from eqn. (3) by replacing G P ,T (for pure phase) with G 0, P ,T .
1