// Numbas version: finer_feedback_settings
{"name": "Chemical Thermodynamics: Gibbs Free Energy Change from Pressure Change 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Chemical Thermodynamics: Gibbs Free Energy Change from Pressure Change 1", "tags": [], "metadata": {"description": "<p>Public</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "", "advice": "<p>The Gibbs free energy change resulting from a change in pressure at constant temperature is given by the equation:</p>\n<p>$\\mathrm{\\Delta G=RTln(\\frac{p_2}{p_1})}$ ,</p>\n<p>where $\\mathrm{R=8.314 J \\space K^{-1} \\space mol^{-1}}$ is the universal gas constant; $\\mathrm{T}$ is the temperature of the gas, in $\\mathrm{K}$; $\\mathrm{p_1}$ is the initial pressure of the gas; and $\\mathrm{p_2}$ is the final pressure of the gas. The units of the two pressures do not matter, as long as they are the same unit, e.g. both $\\mathrm{Pa}$, both $\\mathrm{torr}$, both $\\mathrm{bar}$, etc.</p>\n<p></p>\n<p>We are given the temperature of the system, $\\mathrm{T=\\var{temp}\\space K}$, as well as the initial gas pressure, $\\mathrm{p_1=\\var{p1}\\space atm}$, and the Gibbs free energy change associated with the process, $\\mathrm{\\Delta G=+\\var{dpformat(gckj,3)}}$, which we convert by multiplying by one thousand, to $\\mathrm{\\Delta G^\\circ =\\var{dpformat(gibbschange,0)} \\space J \\space mol^{-1}}$.&nbsp;</p>\n<p>To calculate the final pressure of the gas, we must rearrange our original equation, then substitute in our values:</p>\n<p>$\\mathrm{\\Delta G=RTln(\\frac{p_2}{p_1})}$</p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space ln(\\frac{p_2}{p_1})=\\frac{\\Delta G}{RT}}$</p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space \\frac{p_2}{p_1}=exp(\\frac{\\Delta G}{RT})}$</p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space {p_2}=p_1exp(\\frac{\\Delta G}{RT})}$</p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space {p_2}=\\var{p1}\\times exp(\\frac{\\var{dpformat(gibbschange,3)}}{8.314\\times \\var{temp}})=\\var{sigformat(p2,3)}\\space atm}$ .</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"p1": {"name": "p1", "group": "Ungrouped variables", "definition": "random(1.5 .. 6.5#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "p2": {"name": "p2", "group": "Ungrouped variables", "definition": "p1+pchange", "description": "", "templateType": "anything", "can_override": false}, "pchange": {"name": "pchange", "group": "Ungrouped variables", "definition": "random(0.3 .. 2.8#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "gibbschange": {"name": "gibbschange", "group": "Ungrouped variables", "definition": "8.314*temp*ln(p2/p1)", "description": "", "templateType": "anything", "can_override": false}, "temp": {"name": "temp", "group": "Ungrouped variables", "definition": "random(250 .. 450#1)", "description": "", "templateType": "randrange", "can_override": false}, "gckj": {"name": "gckj", "group": "Ungrouped variables", "definition": "gibbschange/1000", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "gckj>0", "maxRuns": "1000"}, "ungrouped_variables": ["p1", "pchange", "p2", "temp", "gibbschange", "gckj"], "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>One mole of an unknown gas at $\\mathrm{\\var{temp}\\space K}$ and $\\mathrm{\\var{p1} \\space atm}$ is increased in pressure, undergoing a Gibbs free energy change of $\\mathrm{+\\var{dpformat(gckj,3)}\\space kJ\\space mol^{-1}}$.</p>\n<p>Assuming the temperature remains constant throughout, what is the final pressure of the gas?</p>\n<p>[[0]] $\\mathrm{atm}$</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": "p2-(p2/200)", "maxValue": "p2+(p2/200)", "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", "scientific"], "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": "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": "Michael McFadden", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18132/"}]}