{"title":"Deciphering the physical meaning of Gibbs’s maximum work equation","authors":"Robert T. Hanlon","doi":"10.1007/s10698-024-09503-3","DOIUrl":null,"url":null,"abstract":"<div><p>J. Willard Gibbs derived the following equation to quantify the maximum work possible for a chemical reaction</p><p><span>\\({\\text{Maximum work }} = \\, - \\Delta {\\text{G}}_{{{\\text{rxn}}}} = \\, - \\left( {\\Delta {\\text{H}}_{{{\\text{rxn}}}} {-}{\\text{ T}}\\Delta {\\text{S}}_{{{\\text{rxn}}}} } \\right) {\\text{ constant T}},{\\text{P}}\\)</span></p><p>∆H<sub>rxn</sub> is the enthalpy change of reaction as measured in a reaction calorimeter and ∆G<sub>rxn</sub> the change in Gibbs energy as measured, if feasible, in an electrochemical cell by the voltage across the two half-cells. To Gibbs, reaction spontaneity corresponds to negative values of ∆G<sub>rxn</sub>. But what is T∆S<sub>rxn</sub>, absolute temperature times the change in entropy? Gibbs stated that this term quantifies the heating/cooling required to maintain constant temperature in an electrochemical cell. Seeking a deeper explanation than this, one involving the behaviors of atoms and molecules that cause these thermodynamic phenomena, I employed an “atoms first” approach to decipher the physical underpinning of T∆S<sub>rxn</sub> and, in so doing, developed the hypothesis that this term quantifies the change in “structural energy” of the system during a chemical reaction. This hypothesis now challenges me to similarly explain the physical underpinning of the Gibbs–Helmholtz equation</p><p><span>\\({\\text{d}}\\left( {\\Delta {\\text{G}}_{{{\\text{rxn}}}} } \\right)/{\\text{dT}} = - \\Delta {\\text{S}}_{{{\\text{rxn}}}} \\left( {\\text{constant P}} \\right)\\)</span></p><p>While this equation illustrates a relationship between ∆G<sub>rxn</sub> and ∆S<sub>rxn</sub>, I don’t understand how this is so, especially since orbital electron energies that I hypothesize are responsible for ∆G<sub>rxn</sub> are not directly involved in the entropy determination of atoms and molecules that are responsible for ∆S<sub>rxn</sub>. I write this paper to both share my progress and also to seek help from any who can clarify this for me.</p></div>","PeriodicalId":568,"journal":{"name":"Foundations of Chemistry","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10698-024-09503-3.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10698-024-09503-3","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
J. Willard Gibbs derived the following equation to quantify the maximum work possible for a chemical reaction
∆Hrxn is the enthalpy change of reaction as measured in a reaction calorimeter and ∆Grxn the change in Gibbs energy as measured, if feasible, in an electrochemical cell by the voltage across the two half-cells. To Gibbs, reaction spontaneity corresponds to negative values of ∆Grxn. But what is T∆Srxn, absolute temperature times the change in entropy? Gibbs stated that this term quantifies the heating/cooling required to maintain constant temperature in an electrochemical cell. Seeking a deeper explanation than this, one involving the behaviors of atoms and molecules that cause these thermodynamic phenomena, I employed an “atoms first” approach to decipher the physical underpinning of T∆Srxn and, in so doing, developed the hypothesis that this term quantifies the change in “structural energy” of the system during a chemical reaction. This hypothesis now challenges me to similarly explain the physical underpinning of the Gibbs–Helmholtz equation
While this equation illustrates a relationship between ∆Grxn and ∆Srxn, I don’t understand how this is so, especially since orbital electron energies that I hypothesize are responsible for ∆Grxn are not directly involved in the entropy determination of atoms and molecules that are responsible for ∆Srxn. I write this paper to both share my progress and also to seek help from any who can clarify this for me.
期刊介绍:
Foundations of Chemistry is an international journal which seeks to provide an interdisciplinary forum where chemists, biochemists, philosophers, historians, educators and sociologists with an interest in foundational issues can discuss conceptual and fundamental issues which relate to the `central science'' of chemistry. Such issues include the autonomous role of chemistry between physics and biology and the question of the reduction of chemistry to quantum mechanics. The journal will publish peer-reviewed academic articles on a wide range of subdisciplines, among others: chemical models, chemical language, metaphors, and theoretical terms; chemical evolution and artificial self-replication; industrial application, environmental concern, and the social and ethical aspects of chemistry''s professionalism; the nature of modeling and the role of instrumentation in chemistry; institutional studies and the nature of explanation in the chemical sciences; theoretical chemistry, molecular structure and chaos; the issue of realism; molecular biology, bio-inorganic chemistry; historical studies on ancient chemistry, medieval chemistry and alchemy; philosophical and historical articles; and material of a didactic nature relating to all topics in the chemical sciences. Foundations of Chemistry plans to feature special issues devoted to particular themes, and will contain book reviews and discussion notes. Audience: chemists, biochemists, philosophers, historians, chemical educators, sociologists, and other scientists with an interest in the foundational issues of science.