// Numbas version: finer_feedback_settings
{"name": "Chemical Thermodynamics: Entropy Change from Volume Change", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Chemical Thermodynamics: Entropy Change from Volume Change", "tags": [], "metadata": {"description": "<p>Public</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "", "advice": "<p>The entropy change resulting from a change in volume of a gas is given by the equation:</p>\n<p>$\\mathrm{\\Delta S=nRln(\\frac{V_2}{V_1})}$ ,</p>\n<p>where $\\mathrm{n}$ is the number of moles of the gas; $\\mathrm{R=8.314 J \\space K^{-1} \\space mol^{-1}}$ is the universal gas constant; $\\mathrm{V_1}$ is the initial volume of the gas; and $\\mathrm{V_2}$ is the final volume of the gas. The units of the two volumes do not matter, as long as they are the same unit, e.g. both $\\mathrm{L}$, both $\\mathrm{mL}$, both $\\mathrm{m^3}$, etc.</p>\n<p></p>\n<p>We are told that the volume of our nitrogen gas is doubled. This means that we can express our final volume, $\\mathrm{V_2}$, in terms of our initial volume, $\\mathrm{V_1}$, as:</p>\n<p>$\\mathrm{V_2=2V_1}$ .</p>\n<p></p>\n<p>This will prove very useful in our equation, where we will simplify the fraction $\\mathrm{\\frac{V_2}{V_1}}$ as such:</p>\n<p>$\\mathrm{\\frac{V_2}{V_1}=\\frac{2V_1}{V_1}=2}$ .</p>\n<p></p>\n<p>We are also given the mass of the nitrogen gas, $\\mathrm{m=\\var{mass}\\space g}$ - to use our equation, we must first obtain the number of moles of nitrogen gas, which we can calculate from the mass:</p>\n<p>$\\mathrm{n=\\frac{m}{gFM}=\\frac{\\var{mass}}{\\var{gFM}}=(\\var{sigformat(mol,5)}\\cdots)\\space mol}$ .</p>\n<p></p>\n<p><strong>Note</strong>: We have used the gram formula mass for $\\mathrm{N_2}$, $\\mathrm{gFM=28.02\\space g}$, <strong>not</strong> that of a single $\\mathrm{N}$ atom, which would be&nbsp;half of that value. This is because nitrogen gas exists naturally as diatomic $\\mathrm{N_2}$ molecules; you will likely remember that during the boiling of liquid nitrogen, the intermolecular attractions between $\\mathrm{N_2}$ molecules are overcome <strong>but</strong> the covalent bonds within the molecules remain intact.</p>\n<p></p>\n<p>We can now subsitute our values into our original equation (after a applying our volume trick) to obtain the entropy change:</p>\n<p>$\\mathrm{\\Delta S=nRln(\\frac{V_2}{V_1})=nRln(\\frac{2V_1}{V_1})=nRln(2)}$</p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space \\Delta S=(\\var{sigformat(mol,5)}\\cdots)\\times 8.314\\times ln(2)=\\var{sigformat(entro,3)}\\space J \\space K^{-1}}$ .</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"mass": {"name": "mass", "group": "Ungrouped variables", "definition": "random(0.5 .. 99.5#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "mol": {"name": "mol", "group": "Ungrouped variables", "definition": "mass/gfm", "description": "", "templateType": "anything", "can_override": false}, "entro": {"name": "entro", "group": "Ungrouped variables", "definition": "mol*8.314*ln(2)", "description": "", "templateType": "anything", "can_override": false}, "gfm": {"name": "gfm", "group": "Ungrouped variables", "definition": "28.02", "description": "", "templateType": "number", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["mass", "gfm", "mol", "entro"], "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 the definition of heat capacity?</p>\n<p>[[1]]</p>\n<p></p>\n<p>Calculate the change in entropy of the system when $\\mathrm{\\var{mass}\\space g}$ of nitrogen gas at $\\mathrm{298 \\space K}$ and $\\mathrm{1 \\space bar}$ pressure doubles its volume in an isothermal, reversible expansion.</p>\n<p></p>\n<p>[[0]] $\\mathrm{J\\space K^{-1}}$ .</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "entro-(entro/200)", "maxValue": "entro+(entro/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"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": "1", "showCellAnswerState": true, "choices": ["The ability of a system to absorb heat as a function of temperature.", "The ability of a system to absorb heat as a function of entropy.", "The ability of a system to absorb heat as a function of enthalpy."], "matrix": ["1", 0, 0], "distractors": ["", "", ""]}], "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/"}]}