# Bragram Diagram: The Ellingham Diagram Of Binary Solutions

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1.0) The Ellingham Diagram

1.1) Introduction

The Gibbs free energy (∆G) of a reaction is defined as the measure of the thermodynamic force that drives a reaction to occur. When ∆G is positive, it indicates that a reaction will not occur spontaneously while when ∆G is negative, the reaction is spontaneous. The Gibbs free energy equation is given by :

∆G = ∆H –T∆S

∆H refers to the enthalpy and is a measure of the actual energy that is released when the reaction occurs. A negative value of ∆H means the reaction is exothermic while a positive ∆H is for an endothermic reaction. ∆S refers to the entropy and it is a measure of the degree of disorder in the product compared to reactants. When a solid with an ordered state reacts with
2.2) Construction of Gibbs Free Energy Diagram of Binary Solutions

A binary solution is a system that consists of two components. Consider the Gibbs free energy of one mole of atoms, some of which are atoms A and some of which are atoms B. For research purpose, a partition separates both types of atoms and the relative amounts of A and B are changed as shown in Figure 2.2.

Figure 2.2.1

Therefore, it is deduced that g (pure, combined) = gA•XA + gB•XB

Where gA is the gibbs free energy of A, gB is the gibbs free energy of B, XA is molar fraction of A and XB is molar fraction of B.

When plotted against composition, the gibbs free energy for the combination of pure A and pure B is a straight line connecting gA and gB as shown in Figure 2.2.2

Figure 2.2.2

Now, consider removing the imaginary partition in Figure 2.2.1. This will result in some changes in G due to the mixing of both solutions. This changes is given by the formula