[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-657116-105":3,"detail-sidebar-cat-0-en-105":84,"doc-detail-657116-en":134},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":77,"head_meta":79,"extra_data":81,"updated_unix":83},105,"en","pourbaix-diagram-notes-by-mit-student-and-mzb","Pourbaix Diagram - Notes by MIT Student (and MZB)","","These lecture-style notes derive electrode equilibrium using the Nernst equation and show how electrode potential separates oxidized and reduced phases on a phase diagram. The notes define pH from H+ activity, then analyze water stability by comparing anode and cathode water electrolysis reactions. They introduce the electrochemical window concept and discuss how Pourbaix diagrams are equilibrium-based, lack kinetics, and require reaction-location interpretation. A worked fruit-battery example (Zn/Cu in lemon acid) illustrates competing equilibria and practical deviations via kinetics and activities.",{"@graph":14,"@context":76},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/pourbaix-diagram-notes-by-mit-student-and-mzb/657116/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/pourbaix-diagram-notes-by-mit-student-and-mzb/657116.png","ImageObject",300,407,{"name":42,"@type":43},"iuabcfuw","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":52,"interactionType":53,"userInteractionCount":30},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68,72],{"name":59,"@type":60,"acceptedAnswer":61},"How is electrode potential related to chemical activities in the notes?","Question",{"text":62,"@type":63},"At equilibrium, the electrode potential follows the Nernst equation, which links E to the activities of oxidized and reduced species. This determines the reaction equilibrium constant from the measured potential relative to a standard electrode.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"What defines the electrochemical window for water stability?",{"text":67,"@type":63},"The electrochemical window is the potential range that prevents water electrolysis from being thermodynamically favored. If the anode potential exceeds the upper boundary or the cathode potential falls below the lower boundary, the reactions favor producing O2 and H2 from H2O.",{"name":69,"@type":60,"acceptedAnswer":70},"Why do Pourbaix diagrams not provide kinetic information?",{"text":71,"@type":63},"The notes state Pourbaix diagrams describe only equilibrium information, so they indicate reaction directions thermodynamically. They do not capture kinetic barriers that can prevent the predicted reaction from occurring.",{"name":73,"@type":60,"acceptedAnswer":74},"How does the fruit-battery example explain real deviations from ideal diagram predictions?",{"text":75,"@type":63},"The Zn/Cu-in-lemon example compares multiple competing equilibria at anode and cathode. It highlights that even if a reaction is thermodynamically favored, slow kinetics (e.g., lacking catalyst) can stop it, and local concentrations can shift effective boundaries on the diagram.","https://schema.org",{"og:url":32,"og:type":78,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":80,"canonical":32},"index,follow",{"doc_id":82,"site_id":7},657116,1792974440,{"code":4,"msg":85,"data":86},"success",[87,91,95,99,104,109,114,118,123,126,130],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},"Exam",70,"exam",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},5,"Comic",60,"comic",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},6,"Technology",50,"technology",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},7,"Healthcare",40,"healthcare",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":116,"slug":117},8,30,"research-report",{"id":119,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},9,"Religion & Spirituality",20,"religion-spirituality",{"id":121,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":121,"slug":125},"World Cup","world-cup",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":127,"slug":129},10,"Lifestyle","lifestyle",{"id":131,"doc_module":4,"doc_module_name":25,"category_name":132,"show_sort_weight":100,"slug":133},19,"General","general",{"code":4,"msg":85,"data":135},{"doc_id":82,"user_id":136,"nickname":42,"user_avatar":137,"doc_module":4,"category_id":115,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":138,"file_id":139,"file_url":140,"file_type":141,"file_size":142,"view_count":30,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":110,"language":143,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":144,"faqs":145,"seo_title":146,"seo_description":12,"update_tm":83,"read_time":147},3985747874027,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Pourbaix Diagram  \nNotes by MIT Student (and MZB)  \n1. Battery equilibrium electrochemistry  \nSuppose an electrochemical reaction happening on the electrode/electrolyte interface:  \nR O + ne − (1)  \nAt equilibrium, the electrode potential is related to activities of the reactants by the Nernst equation: E = E0 + kTnelnaOaaRn~~e ~~ (2)  \nwhere E0 is the electrical potential of the electrode measured against a standard hydrogen cell electrode under standard conditions. aO is the chemical activity of the oxidized state, aR the chemical activity of the reduced state. At equilibrium, the reaction constant KO = aOaaRn~~e~~ is thus determined by the electrode potential:  \nKO = exp nekT (E − E0 )  \nGiven the dependence of chemical activities on other thermodynamic parameters, the equilibrium electrode potential will separate the oxidized/reduced phases on a phase diagram. If the electrode potential is raised above the equilibrium potential, oxidization is preferred. If below the equilibrium potential, reduction is preferred.  \n2. Pourbaix diagram  \nOne certain class of phase diagrams is displayed by the equilibrium electrical potential plotted against the pH, when some of the reactants have chemical activities that vary with pH. For instance if H+ is part of the electrode reaction, then under dilute approximation, aH+ ∼ cH+ . The pH of the electrolyte is defined as the negative of the natural log of the H+ ion concentration in the electrolyte:  \npH = −log 10 cH+ (3)  \nUnder room temperature, water as the most common solvant by self-ionization will give pH = 7 which is the neutral pH. For an acidic solution pH \u003C 7, for basic pH > 7.  \n2.1. The electrochemical window for water stability  \nNow consider the water electrolysis reactions: Anode reaction:  \nH2 = 2H+ + 2e − , E0 = 0 (4)  \n1.5  \n1  \n􀁉  \ne  \n0.5  \noxidized  \nstandard  \n0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1  \nc,T,P,   \nFig. 1.—Phase diagram of an electrochemical reaction  \naccording to the Nernst equation:  \nE1 = E0 + k2Telna+Ha22e = −0.06pH(Volts) (5)  \nCathode reaction:  \nH2 O = 2H+ + 2e − + 12O2 , E0 = 1 .229 (6)  \naccording to the Nernst equation:  \nE2 = E0 + k2Telna+Ha22e = 1 .229 − 0.06pH(Volts) (7)  \nAs shown in the Pourbaix diagram of these Fig2, if we impose a potential on the anode higher than E1 , or the potential on the cathode lower than E2 , the reactions will favor the production of O2 and H2 from H2 O , which is the electrolysis of water itself. Thus the maximum open circuit voltage of a Galvanic cell with water as the solvant in the electrolyte must not exceed the voltage differencein the Pourbaix diagram. This limitation on the open circuit voltage is called the ’electrochemical window’ for water stability.  \n2.2. Remarks on the Pourbaix diagrams  \n1. Since Pourbaix diagrams describe only equilibrium information, it can tell the reaction directions from thermodynamics but doesn’t tell any kinetic information.  \n2. Pourbaix diagrams are only one certain class of the phase diagrams, which gives a handy description of electrode potential v.s. pH. There are other dimensions of parameters that are not shown on the Pourbaix diagrams. For example, the activity of reactants other than H+ , temperature, etc. The Pourbaix diagram is a projection of the equilibrium potential surface in a many dimensional parameter space onto the subspace of pH. When other conditions deviate from the standard conditions, the equilibrium potential curve will also move on the Pourbaix diagram.  \n3. To correctly interprete the Pourbaix diagrams, we should first locate the reactions, i.e. , whether the reactions are considered on the anode or cathode. This will as shown in the next section lead to different physics such as electrodeposition or corrosion.  \n3. Example analysis for a fruit battery  \nSuppose we now insert a Zn anode and a Cu cathode into a lemon, which contains acid. There will be 4 electrochemical equilibriums in this system:  \nZn = Zn2+ + 2e − , E01 = −0.76V (8)  \n􀁉  \ne  \n1.4  \n1","cbCaikra917lX1o0","https://ap.wps.com/l/cbCaikra917lX1o0","pdf",309835,"English","# Battery equilibrium electrochemistry\n## Pourbaix diagram\n### The electrochemical window for water stability\n### Remarks on the Pourbaix diagrams\n# Example analysis for a fruit battery","[{\"question\":\"How is electrode potential related to chemical activities in the notes?\",\"answer\":\"At equilibrium, the electrode potential follows the Nernst equation, which links E to the activities of oxidized and reduced species. This determines the reaction equilibrium constant from the measured potential relative to a standard electrode.\"},{\"question\":\"What defines the electrochemical window for water stability?\",\"answer\":\"The electrochemical window is the potential range that prevents water electrolysis from being thermodynamically favored. If the anode potential exceeds the upper boundary or the cathode potential falls below the lower boundary, the reactions favor producing O2 and H2 from H2O.\"},{\"question\":\"Why do Pourbaix diagrams not provide kinetic information?\",\"answer\":\"The notes state Pourbaix diagrams describe only equilibrium information, so they indicate reaction directions thermodynamically. They do not capture kinetic barriers that can prevent the predicted reaction from occurring.\"},{\"question\":\"How does the fruit-battery example explain real deviations from ideal diagram predictions?\",\"answer\":\"The Zn/Cu-in-lemon example compares multiple competing equilibria at anode and cathode. It highlights that even if a reaction is thermodynamically favored, slow kinetics (e.g., lacking catalyst) can stop it, and local concentrations can shift effective boundaries on the diagram.\"}]","Pourbaix Diagram - Notes by MIT Student (and MZB) | PDF",18]