thermo_BM_4 (1)

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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 .

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