Problem 3 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

An Ellingham diagram provides information about: (a) the conditions of \(\mathrm{pH}\) and potential under which a species is thermodynamically stable. (b) the temperature dependence of the standard Gibbs energies of formation of some metal oxides. (c) the pressure dependence of the standard electrode potentials of reduction reactions involved in the extraction of metals. (d) the kinetics of the reduction process.

Step-by-Step Solution

Answer

(b) The temperature dependence of the standard Gibbs energies of formation of some metal oxides.

Step 1: Understanding the Ellingham Diagram

The Ellingham diagram is a graph that represents the temperature dependence of the Gibbs free energy change for the formation of various compounds, typically oxides, as a function of temperature. It's primarily used in metallurgy for understanding the conditions under which a metal oxide can be reduced by a reducing agent.

Step 2: Analyzing the Options

We analyze each option to determine which one best aligns with the function of an Ellingham diagram: (a) talks about pH and potential which are related to electrochemical reactions, not typical for Ellingham diagrams. (c) involves pressure dependence related to electrode potentials, also not covered by Ellingham diagrams. (d) discusses kinetics, which Ellingham diagrams do not address as they deal purely with thermodynamic considerations. This leaves us with (b) which aligns with the description of the temperature dependence of free energy changes for the formation of metal oxides.

Step 3: Conclusion

Considering the definition and application of the Ellingham diagram, option (b) which mentions 'the temperature dependence of the standard Gibbs energies of formation of some metal oxides,' correctly describes the purpose of an Ellingham diagram.

Key Concepts

Thermodynamics

Thermodynamics is a field of physics that deals with the relationships between heat, work, temperature, and energy. It's essential for understanding how energy is exchanged in chemical processes. The principles of thermodynamics help dictate whether a process is spontaneous or requires external energy input. Understanding thermodynamics is crucial for fields like chemistry and engineering.

• **Laws of Thermodynamics:** These are the rules that guide how energy moves and transforms.
• **First Law:** Energy cannot be created or destroyed, only transformed.
• **Second Law:** Energy transformations are never 100% efficient, leading to increased entropy.

The application of thermodynamics in metallurgical processes, like refining metals using Ellingham diagrams, involves understanding these energy changes to optimize conditions for desired reactions.

Gibbs Free Energy

Gibbs free energy is a thermodynamic property that combines enthalpy and entropy to measure the maximum usable energy from a system that can do work at constant temperature and pressure. It helps predict the favorability of a reaction.
When a reaction occurs under constant conditions, the change in Gibbs free energy \( (\Delta G) \) will provide insight:

• If \( \Delta G < 0 \): The reaction is spontaneous.
• If \( \Delta G > 0 \): The reaction is non-spontaneous.
• If \( \Delta G = 0 \): The system is in equilibrium.

In the context of the Ellingham diagram, Gibbs free energy changes with temperature are plotted to determine the most energy-efficient conditions for reducing metal oxides into pure metals.

Metal Oxides

Metal oxides are compounds formed between metals and oxygen. They're widespread in nature and essential in various industrial processes.
These oxides can be categorized based on metal oxidation states and their properties vary widely:

• **Basic Oxides:** Often react with acids to form salt and water. Example: Sodium oxide (Na₂O).
• **Amphoteric Oxides:** Can react both as acid and base. Example: Aluminum oxide (Al₂O₃).
• **Acidic Oxides:** Typically non-metal oxides that react with bases. Example: Silicon dioxide (SiO₂).

The reduction of metal oxides back to metals is crucial in metallurgy, and the analysis of Gibbs free energy changes in Ellingham diagrams guides this reduction process.

Temperature Dependence

Temperature dependence in chemical reactions is reflected in how temperature impacts Gibbs free energy. The Ellingham diagram exploits this by showing how Gibbs free energy changes with temperature for different metal oxides.
This concept is critical for determining suitable temperatures for reactions:

• **Higher Temperatures:** Often reduce Gibbs free energy, making some reactions more favorable.
• **Plot Analysis:** A downward sloping line on the Ellingham diagram indicates a reaction becomes more feasible at higher temperatures.
• **Intercept Points:** Where lines intersect, it indicates a change in favorability between different reactions or phases.

In metallurgy, understanding temperature dependence helps in effectively setting industrial conditions for metal extraction and refining.