Problem 51 - A Complete Resource Book in Chemistry for JEE Main

Question

The factor of \(\Delta G\) values is important in metallurgy. The \(\Delta G\) values for the following reactions at \(800^{\circ} \mathrm{C}\) are given as \(\mathrm{S}_{2}(\mathrm{~s})+2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{SO}_{2}(\mathrm{~g}) ; \Delta \mathrm{G}=-544 \mathrm{~kJ}\) \(2 \mathrm{Zn}(\mathrm{s})+\mathrm{S}_{2}(\mathrm{~s}) \longrightarrow 2 \mathrm{ZnS}(\mathrm{s}) ; \Delta \mathrm{G}=-293 \mathrm{~kJ}\) \(2 \mathrm{Zn}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{ZnO}(\mathrm{s}) ; \Delta \mathrm{G}=-480 \mathrm{~kJ}\) the \(\Delta \mathrm{G}\) for the reaction, \(2 \mathrm{ZnS}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{ZnO}(\mathrm{s})+2 \mathrm{SO}_{2}(\mathrm{~g})\) will be (a) \(-357 \mathrm{~kJ}\) (b) \(-731 \mathrm{~kJ}\) (c) \(-773 \mathrm{~kJ}\) (d) \(-229 \mathrm{~kJ}\)

Step-by-Step Solution

Answer

\( \Delta G \) for the reaction is \(-731 \mathrm{~kJ}\).

Step 1: Identify the Given Reactions and Their ΔG

Given the reactions: 1. \( \mathrm{S}_{2}(\mathrm{~s})+2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{SO}_{2}(\mathrm{~g}) \) with \( \Delta \mathrm{G} = -544 \; \mathrm{kJ} \). 2. \( 2 \mathrm{Zn}(\mathrm{s})+\mathrm{S}_{2}(\mathrm{~s}) \longrightarrow 2 \mathrm{ZnS}(\mathrm{s}) \) with \( \Delta \mathrm{G} = -293 \; \mathrm{kJ} \). 3. \( 2 \mathrm{Zn}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{ZnO}(\mathrm{s}) \) with \( \Delta \mathrm{G} = -480 \; \mathrm{kJ} \). The goal is to find \( \Delta \mathrm{G} \) for the reaction: \( 2 \mathrm{ZnS}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{ZnO}(\mathrm{s})+2 \mathrm{SO}_{2}(\mathrm{~g}) \).

Key Concepts

Metallurgy

Metallurgy is the science and technology of extracting metals from their ores and refining them for use. At its core, metallurgy involves a series of chemical reactions, heat treatments, and mechanical processes to produce pure metals and create alloys. It is essential for industries ranging from construction to technology. In these processes, considerations like Gibbs Free Energy (\( \Delta G \)) play a crucial role.

Gibbs Free Energy is used to determine the feasibility of a chemical reaction. In metallurgy, understanding \( \Delta G \) helps identify which reactions can occur efficiently at a given temperature and pressure, indicating how much energy would be absorbed or released. This is critical when designing processes to minimize energy costs and maximize yield. For instance, in the reduction of metal oxides to metals, choosing reactions with negative \( \Delta G \) values ensures that the processes are thermodynamically favorable and spontaneously performed under certain conditions.

In the given exercise, various reactions with specific \( \Delta G \) values at 800°C are part of the calculation to deduce the viability of transforming zinc sulfide to zinc oxide while also producing sulfur dioxide, showcasing real-world metallurgy applications.

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. It helps us understand how energy is transferred and transformed during chemical reactions.

The concept of Gibbs Free Energy (\( \Delta G \)) is central to thermodynamics when evaluating chemical reactions. \( \Delta G \) allows chemists to predict whether a reaction is spontaneous. A reaction is spontaneous if \( \Delta G \) is negative under the conditions of constant temperature and pressure. This is crucial for processes involving the refinement of materials and energy production. In our exercise, \( \Delta G \) of different reactions helps form a comprehension of how energy changes impact the transformation processes in reactions involving zinc sulfide, sulfur dioxide, and zinc oxide.

Considering the reactions given, thermodynamics guides the decision-making process by highlighting how much energy input or output is needed. It shows the path of least resistance in conversion, essential for industrial applications aiming to conserve energy and reduce costs.

Chemical Reactions

Chemical reactions are processes where reactants transform into products through the rearrangement of atoms. Each reaction involves breaking bonds in the reactants and forming new ones in the products, often accompanied by energy changes.

In the context of the exercise, we look at several chemical reactions involving sulfur, oxygen, zinc, and various compounds. Each reaction has an associated Gibbs Free Energy \( \Delta G \), which indicates the reaction's tendency to proceed, impacting product formation efficiency. For example, the reaction involving zinc and sulfur with oxygen to form zinc oxide and sulfur dioxide examines the critical exchange of energies and compounds.

Understanding these reactions is fundamental not only in industrial applications but also in environmental contexts. The production of sulfur dioxide, a component of acid rain, must be carefully managed. Thus, knowing the energy dynamics helps refine the chemical processes to be both economically viable and environmentally considerate. This skill is indispensable for chemists and engineers working to optimize product synthesis and minimize undesirable byproducts.