Ellingham Diagram Thermodynamic 

The Ellingham diagram is a powerful thermodynamic tool used in metallurgy to predict the spontaneity of a reduction reaction and to select a suitable reducing agent for a given metal oxide. It plots the standard Gibbs free energy change (ΔG^o) for the formation of various oxides as a function of temperature. Understanding this diagram is crucial for JEE-level chemistry, as it provides a clear visual representation of the principles governing pyrometallurgy.

1.0What is an Ellingham Diagram?

An Ellingham diagram is a graph that plots the standard Gibbs free energy change (ΔG^o) for the formation of metal oxides against temperature. Each line on the diagram represents a specific metal's oxidation reaction:

$2xM(s)+O_2(g)\to 2M_{x}O(s)$

The Gibbs free energy equation is given by:

$\Delta G^o=\Delta H^o-T\Delta S^o$

where:

• ΔG^o is the standard Gibbs free energy change.
• ΔH^o is the standard enthalpy change.
• ΔS^o is the standard entropy change.
• T is the absolute temperature in Kelvin.

2.0Basic Principles

The Ellingham diagram is based on the second law of thermodynamics, which states that a reaction is spontaneous if the total entropy of the system and its surroundings increases. For a process at a constant temperature and pressure, spontaneity is determined by the sign of ΔG∘.

• If ΔG^o<0, the reaction is spontaneous.
• If ΔG^o>0, the reaction is non-spontaneous.
• If ΔG^o=0, the reaction is at equilibrium.

Key Features of the Diagram 

• Upward Slope: Most lines on the Ellingham diagram have a positive slope. This is because the entropy change (ΔS^o) for the formation of a metal oxide is generally negative. This is due to the consumption of a gas (O2) to form a solid, which leads to a decrease in randomness. Since the slope of the ΔG^o vs. T plot is -ΔS^o, a negative ΔS^o results in a positive slope.
• Sudden Upward Jumps: The slope of a line can change abruptly at a specific temperature. This indicates a phase transition (melting or boiling) of the metal or its oxide. For example, if a solid metal melts, its entropy increases, leading to a steeper positive slope.
• Line for Carbon Oxidation: The diagram also includes lines for the oxidation of carbon to carbon monoxide $(C+\frac{1}{2}{O}_2\to CO)$ and carbon dioxide $(C+O_2\to C{O}_2)$. The line for the formation of CO has a negative slope because it involves an increase in the number of moles of gas (1 mole of gas produced from 0.5 moles of gas), making ΔS^o positive.

3.0Interpreting the Ellingham Diagram

The true power of the Ellingham diagram lies in its ability to predict the feasibility of a reduction process.

Spontaneity of Reactions

A reaction is spontaneous in the direction that has a more negative ΔG^o. When two lines on the diagram are compared, the reaction represented by the lower line is more spontaneous and can reduce the oxide represented by the upper line.

Predicting the Feasibility of Reduction

To determine if a substance 'A' can reduce the oxide of a metal 'B', we look at the positions of their respective lines on the diagram.

Consider the reaction:

$B_{x}O(s)+yA(s)\to xB(s)+y{A}_{x}O(s)$

This reaction can be broken down into two half-reactions:

1. Formation of metal oxide $B_{x}O:xB(s)+\frac{1}{2}y{O}_2(g)\to B_{x}O(s)$

• $\Delta G_1^o$ (represented by the line for B_x​O)

2. Formation of reducing agent oxide $A_{x}O:yA(s)+\frac{1}{2}y{O}_2(g)\to y{A}_{x}O(s)$

• $\Delta G_2^{\circ }$​ (represented by the line for A_x​O)

To find the ΔG∘ for the overall reduction reaction, we subtract the ΔG^o₁ from the ΔS^o2:

$\Delta G_{overall}^o=\Delta G_2^o-\Delta G_1^o$

For the reduction to be spontaneous, $\Delta G_{overall}^o$ must be negative. This happens when $\Delta G_2^o$ is more negative than $\Delta G_1^o$, meaning the line for the reducing agent's oxidation must be below the line for the metal oxide's formation at a given temperature.

Effect of Temperature

The Ellingham diagram clearly shows the influence of temperature on the spontaneity of a reaction. As temperature increases, the ΔG^o value for most oxide formations becomes less negative. However, for the oxidation of carbon to carbon monoxide, the value becomes more negative at higher temperatures, which is why carbon becomes a more effective reducing agent at high temperatures.

The point where two lines intersect is the temperature at which the ΔG^o for both reactions is equal. Above this intersection point, the line for the reducing agent is lower, and therefore, the reducing agent is effective.

4.0Limitations of the Ellingham Diagram

While the Ellingham diagram is a powerful tool, it has some limitations:

• Thermodynamic, Not Kinetic: The diagram only predicts the thermodynamic feasibility of a reaction (whether it will happen spontaneously), not the reaction rate (how fast it will happen). A reaction with a negative ΔG^o may still be very slow and require a catalyst.
• Standard Conditions: The diagram is based on standard Gibbs free energy changes (ΔG^o), which assumes reactants and products are in their standard states. The actual reaction conditions (pressure, concentration) can affect the spontaneity.
• Assumptions: It assumes that the reactants and products are in equilibrium. It does not account for non-equilibrium conditions or the formation of intermediate compounds.

5.0Specific Case Studies

Reduction of Iron Oxide

The reduction of iron oxide ($F{e}_2{O}_3$​) using carbon (as coke) is a classic example of pyrometallurgy carried out in a blast furnace.

• On the Ellingham diagram, the line for $2Fe+\frac{3}{2}{O}_2\to F{e}_2{O}_3$​ is located above the line for $C+\frac{1}{2}{O}_2\to CO$ at temperatures above approximately 983 K.
• This means that at high temperatures, the reaction $F{e}_2{O}_3+3CO\to 2Fe+3C{O}_2$​ is thermodynamically favorable.
• The reduction can also be done with solid carbon: $F{e}_2{O}_3+3C\to 2Fe+3CO$. This reaction becomes feasible at even higher temperatures.

Reduction of Zinc Oxide

The reduction of zinc oxide (ZnO) to zinc metal also uses carbon.

• The line for the formation of ZnO is higher than the line for the formation of CO from carbon at temperatures above 1273 K.
• This indicates that zinc oxide can be reduced by carbon at temperatures greater than 1273 K. The zinc produced is volatile and is distilled off.

Reduction of Alumina

The reduction of aluminum oxide ($A{l}_2{O}_3$) is a special case.

• The line for the formation of is very low on the Ellingham diagram, well below the lines for both carbon and carbon monoxide.
• This shows that the reduction of alumina by carbon is not feasible at any practical temperature.
• Therefore, aluminum is extracted using electrolytic reduction (the Hall–Héroult process), not pyrometallurgy. The diagram beautifully explains why this alternative method is necessary.