// Numbas version: finer_feedback_settings
{"name": "Chemical Thermodynamics:  Non-Standard Chemical Potential 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Chemical Thermodynamics:  Non-Standard Chemical Potential 2", "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 given by the following equation:</p>\n<p>$\\mathrm{\\mu_x={\\mu_x}^\\circ + RTln(a_x)}$ ,</p>\n<p>where $\\mathrm{{\\mu_x}^\\circ}$ is the <strong>standard</strong> chemical potential of the substance, in $\\mathrm{J \\space mol^{-1}}$;&nbsp; $\\mathrm{R=8.314\\space J \\space K^{-1}\\space mol^{-1}}$ is the universal gas constant;&nbsp; $\\mathrm{T}$ is the temperature of the system, in $\\mathrm{K}$; and $\\mathrm{a_x}$ is the activity (effective concentration) of the substance, which is unitless.</p>\n<p></p>\n<p></p>\n<p>We are asked to calculate the activity of sulfur trioxide when its chemical potential is $\\mathrm{\\mu_{_{SO_3}}=\\var{sigformat(p,5)}\\space kJ\\space mol^{-1}}$. We convert the chemical potential by multiplying by one thousand, to $\\mathrm{{\\mu_{_{SO_3}}}=\\var{sigformat(pot,5)} \\space J \\space mol^{-1}}$ .</p>\n<p>We are given the standard chemical potential of sulfur trioxide, $\\mathrm{{\\mu_{_{SO_3}}}^\\circ =\\var{gso3} \\space kJ \\space mol^{-1}}$, which we convert by multiplying by one thousand, to $\\mathrm{{\\mu_{_{SO_3}}}^\\circ =\\var{sigformat(realg,4)} \\space J \\space mol^{-1}}$ .</p>\n<p></p>\n<p>To calculate the activity value, $\\mathrm{a_{_{SO_3}}}$, we must rearrange our original equation appropriately, then simply substitute our values into the equation and evaluate:</p>\n<p>$\\mathrm{\\mu_{_{SO_3}}={\\mu_{_{SO_3}}}^\\circ + RTln(a_{_{SO_3}})}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space ln(a_{_{SO_3}})=\\frac{[\\mu_{_{SO_3}}-{\\mu_{_{SO_3}}}^\\circ]}{RT}}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space a_{_{SO_3}}=exp(\\frac{[\\mu_{_{SO_3}}-{\\mu_{_{SO_3}}}^\\circ]}{RT})}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space a_{_{SO_3}}=exp(\\frac{[\\var{sigformat(pot,5)}-\\var{sigformat(realg,4)}]}{8.314\\times 298 })=\\var{sigformat(a,3)}}$ .</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"gso3": {"name": "gso3", "group": "Ungrouped variables", "definition": "random(-371.4 .. -369.4#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(0.5 .. 2.5#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "pot": {"name": "pot", "group": "Ungrouped variables", "definition": "realg + (8.314*298*ln(a))", "description": "", "templateType": "anything", "can_override": false}, "realg": {"name": "realg", "group": "Ungrouped variables", "definition": "gso3*1000", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "pot/1000", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "ungrouped_variables": ["gso3", "realg", "a", "pot", "p"], "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>The standard chemical potential of sulfur trioxide in a mixture is found to be $\\mathrm{\\var{gso3}\\space kJ\\space mol^{-1}}$ at $\\mathrm{298\\space K}$.</p>\n<p>What must the activity of the sulfur trioxide be when its chemical potential is found to be $\\mathrm{\\var{sigformat(p,5)}\\space kJ\\space mol^{-1}}$?</p>\n<p>[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a-(a/200)", "maxValue": "a+(a/200)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Frances Docherty", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4059/"}, {"name": "Tess Lynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/16608/"}, {"name": "Michael McFadden", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18132/"}], "resources": []}]}], "contributors": [{"name": "Frances Docherty", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4059/"}, {"name": "Tess Lynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/16608/"}, {"name": "Michael McFadden", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18132/"}]}