// Numbas version: finer_feedback_settings
{"name": "Chemical Thermodynamics: Chemical Potential 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Chemical Thermodynamics: Chemical Potential 1", "tags": [], "metadata": {"description": "<p>Public</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "", "advice": "<p>The chemical potential of a substance in a mixture, $\\mathrm{\\mu_x}$, is the contribution of that substance to the total Gibbs free energy, $\\mathrm{G}$, of the mixture. It is effectively the <strong>molar</strong> Gibbs free energy inherent to that substance under a particular set of conditions.</p>\n<p>As a substance is formed, more of its chemical potential is introduced - and as a substance is consumed, its chemical potential is removed - from the total $\\mathrm{G}$ value. Since $\\mathrm{\\mu_x}$ is molar (i.e. it results from one mole of the substance), the change in $\\mathrm{G}$ when a substance is formed or consumed is proportional to the <strong>number of moles</strong> of the substance formed or consumed which we denote $\\mathrm{\\Delta n}$:</p>\n<p>$\\mathrm{\\Delta G=\\Delta n\\cdot \\mu_x}$</p>\n<p></p>\n<p>We are told that $\\mathrm{\\Delta n}$ moles of $\\mathrm{O_2}$ are used up in&nbsp;the reaction:</p>\n<p>$\\mathrm{2SO_2\\space +\\space O_2\\space \\rightleftharpoons\\space 2SO_3}$.</p>\n<p></p>\n<p>Since $\\mathrm{\\Delta n}$ moles are <strong>consumed</strong>, we will re-express the change in moles of $\\mathrm{O_2}$ as $\\mathrm{-\\Delta n}$.</p>\n<p>From the reaction, we can see that twice as much $\\mathrm{SO_2}$ is consumed, so the change in moles of $\\mathrm{SO_2}$ is $\\mathrm{-2\\Delta n}$.</p>\n<p>Similarly, we can see that twice as much $\\mathrm{SO_3}$ is formed than $\\mathrm{O_2}$ consumed, but we must pay attention to the fact that that much $\\mathrm{SO_3}$ is being <strong>formed</strong>, so the change in moles of $\\mathrm{SO_3}$ is $\\mathrm{+2\\Delta n}$.</p>\n<p></p>\n<p>Knowing all this, we can express the net change in the Gibbs free energy of the mixture in terms of the chemical potentials of the three substances:</p>\n<p>$\\mathrm{\\Delta G=-2\\Delta n\\mu_{_{SO_2}}-(1)\\Delta n\\mu_{_{O_2}}+2\\Delta n\\mu_{_{SO_3}}}$ .</p>\n<p></p>\n<p>Additionally, $\\mathrm{\\Delta G_{reaction}}$ is defined as the <strong>molar</strong> Gibbs free energy change (i.e. the change per one mole of specified substance formed or consumed), which we simply divide our previous answer by $\\mathrm{\\Delta n}$ to obtain:</p>\n<p>$\\mathrm{\\Delta G_{reaction}=\\frac{\\Delta G}{\\Delta n}=-2\\mu_{_{SO_2}}-(1)\\mu_{_{O_2}}+2\\mu_{_{SO_3}}}$ .</p>\n<p></p>\n<p></p>\n<p></p>\n<p>Finally, we are told that, for the certain set of conditions we are concerned with:</p>\n<p>$\\mathrm{\\mu_{_{SO_3}}\\var{arrow[rand]}\\space \\mu_{_{SO_2}}+0.5\\mu_{_{O_2}}}$ .</p>\n<p></p>\n<p>We can double this to compare it to our expression for $\\mathrm{\\Delta G_{reaction}}$:</p>\n<p>$\\mathrm{2\\mu_{_{SO_3}}\\var{arrow[rand]}\\space 2\\mu_{_{SO_2}}+\\mu_{_{O_2}}}$ .</p>\n<p></p>\n<p>From this, we can deduce whether our $\\mathrm{\\Delta G_{reaction}}$ will be positive or negative:</p>\n<p>$\\mathrm{\\Delta G_{reaction}=-2\\mu_{_{SO_2}}-\\mu_{_{O_2}}+2\\mu_{_{SO_3}}=2\\mu_{_{SO_3}}-(2\\mu_{_{SO_2}}+\\mu_{_{O_2}})}$ ,</p>\n<p></p>\n<p>$\\mathrm{2\\mu_{_{SO_3}}\\var{arrow[rand]}\\space 2\\mu_{_{SO_2}}+\\mu_{_{O_2}}}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space 2\\mu_{_{SO_3}}-(2\\mu_{_{SO_2}}+\\mu_{_{O_2}})\\space \\var{arrow[rand]}\\space 0}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space \\Delta G_{reaction}\\space \\var{arrow[rand]}\\space 0}$ .</p>\n<p></p>\n<p>Thus, {outcome[rand]}</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"arrow": {"name": "arrow", "group": "Ungrouped variables", "definition": "[ \"<\", \">\" ]", "description": "", "templateType": "list of strings", "can_override": false}, "rand": {"name": "rand", "group": "Ungrouped variables", "definition": "random(0 .. 1#1)", "description": "", "templateType": "randrange", "can_override": false}, "outcome": {"name": "outcome", "group": "Ungrouped variables", "definition": "[ \"the forward reaction is spontaneous and thus the quantity of sulfur trioxide increases.\", \"the reverse reaction is spontaneous and thus the quantity of sulfur trioxide decreases.\" ]", "description": "", "templateType": "list of strings", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["arrow", "rand", "outcome"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is $\\mathrm{\\Delta G_{reaction}}$ for the reaction:</p>\n<p>$\\mathrm{2SO_2\\space +\\space O_2\\space \\rightleftharpoons\\space 2SO_3}$</p>\n<p>when $\\mathrm{\\Delta n}$ moles of $\\mathrm{O_2}$ are used up?</p>\n<p>Express your answer in terms of chemical potentials, $\\mathrm{\\mu_{_X}}$ (your coefficients may be negative).</p>\n<p></p>\n<p>$\\mathrm{\\Delta G_{reaction}=}$ [[0]] $\\mathrm{\\mu_{_{SO_2}}} +$ [[1]] $\\mathrm{\\mu_{_{O_2}}} +$ [[2]] $\\mathrm{\\mu_{_{SO_3}}}$ .</p>\n<p></p>\n<p></p>\n<p>Given that $\\mathrm{\\mu_{_{SO_3}}\\var{arrow[rand]}\\space \\mu_{_{SO_2}}+0.5\\mu_{_{O_2}}}$ at a certain reaction coordinate, will the quantity of $\\mathrm{SO_3}$ increase or decrease?</p>\n<p>[[3]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "-2", "maxValue": "-2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], 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