// Numbas version: finer_feedback_settings
{"name": "Chemical Thermodynamics: Clausius-Clapeyron Equation 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Chemical Thermodynamics: Clausius-Clapeyron Equation 1", "tags": [], "metadata": {"description": "<p>Public</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "", "advice": "<p>The Clausius-Clapeyron equation is used to relate the equilibrium vapour pressure of a substance at one temperature with that at another temperature:</p>\n<p>$\\mathrm{ln(p_2)-ln(p_1)=\\frac{{\\Delta H^\\circ}_{vap}}{R}[(\\frac{1}{T_1})-(\\frac{1}{T_2})]}$ ,</p>\n<p>where $\\mathrm{T_1}$ and $\\mathrm{T_2}$ are the initial and final temperatures, in $\\mathrm{K}$ ;&nbsp; &nbsp;$\\mathrm{p_1}$ and $\\mathrm{p_2}$ are the corresponding initial and final equilibrium vapour pressures (they must have the same units as eachother);&nbsp; $\\mathrm{{\\Delta H^\\circ}_{vap}}$ is the standard enthalpy of vaporisation of benzene; and $\\mathrm{R=8.314\\space J\\space K^{-1}\\space mol^{-1}}$ is the universal gas constant.</p>\n<p></p>\n<p>We are given an initial equilibrium vapour pressure $\\mathrm{p_1 = \\var{p1}\\space bar}$ at a temperature of $\\mathrm{T_1=\\var{tc1} \\space ^\\circ C}$, and asked to find the new equilibrium vapour pressure, $\\mathrm{p_2}$, at temperature $\\mathrm{T_2=\\var{tc2} \\space ^\\circ C}$.</p>\n<p>We must remember to convert both of our temperatures to Kelvin for use in the equation, by adding $\\mathrm{273.15}$:</p>\n<p>$\\mathrm{T_1=\\var{tc1} \\space ^\\circ C=\\var{temp1}\\space K}$ ,</p>\n<p>$\\mathrm{T_2=\\var{tc2} \\space ^\\circ C=\\var{temp2}\\space K}$ .</p>\n<p></p>\n<p>We are also given the standard enthalpy of vaporisation, $\\mathrm{{\\Delta H^\\circ}_{vap}=\\var{h}\\space kJ\\space mol^{-1}}$, which we convert by multiplying by one thousand, to $\\mathrm{{\\Delta H^\\circ}_{vap} =\\var{enthalpy} \\space J \\space mol^{-1}}$. Enthalpy changes are relatively independent of temperature, and so for these types of questions we can consider $\\mathrm{{\\Delta H^\\circ}_{vap}}$ to be constant over the given temperature change.</p>\n<p></p>\n<p>To calculate $\\mathrm{p_2}$, we must rearrange our equation appropriately, then simply substitute in the values we know:</p>\n<p>$\\mathrm{ln(p_2)-ln(p_1)=\\frac{{\\Delta H^\\circ}_{vap}}{R}([\\frac{1}{T_1}]-[\\frac{1}{T_2}])}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space ln(p_2)=\\frac{{\\Delta H^\\circ}_{vap}}{R}([\\frac{1}{T_1}]-[\\frac{1}{T_2}])+ln(p_1)}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space p_2=exp[\\frac{{\\Delta H^\\circ}_{vap}}{R}([\\frac{1}{T_1}]-[\\frac{1}{T_2}])+ln(p_1)]}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space p_2=exp[\\frac{\\var{enthalpy}}{8.314}\\times([\\frac{1}{\\var{temp1}}]-[\\frac{1}{\\var{temp2}}])+ln(\\var{p1})]=\\var{scientificnumberlatex(siground(p2,3))}\\space bar}$ .</p>\n<p></p>\n<p><strong>Note</strong>: Our answer is in $\\mathrm{bar}$, as this is the same unit as that of the initial pressure we were provided. If the initial pressure provided to us was in $\\mathrm{torr}$, our answer would also be in $\\mathrm{torr}$, for instance.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"p1": {"name": "p1", "group": "Ungrouped variables", "definition": "random(0.8 .. 1.2#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "temp2": {"name": "temp2", "group": "Ungrouped variables", "definition": "random(278.15 .. 303.15#1)", "description": "", "templateType": "randrange", "can_override": false}, "p2": {"name": "p2", "group": "Ungrouped variables", "definition": "exp((enthalpy/8.314)*((1/temp1)-(1/temp2))+ln(p1))", "description": "", "templateType": "anything", "can_override": false}, "enthalpy": {"name": "enthalpy", "group": "Ungrouped variables", "definition": "random(29000 .. 32000#100)", "description": "", "templateType": "randrange", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "enthalpy/1000", "description": "", "templateType": "anything", "can_override": false}, "tc1": {"name": "tc1", "group": "Ungrouped variables", "definition": "temp1-273.15", "description": "", "templateType": "anything", "can_override": false}, "tc2": {"name": "tc2", "group": "Ungrouped variables", "definition": "temp2-273.15", "description": "", "templateType": "anything", "can_override": false}, "temp1": {"name": "temp1", "group": "Ungrouped variables", "definition": "353.15", "description": "", "templateType": "number", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "ungrouped_variables": ["p1", "temp1", "temp2", "p2", "enthalpy", "h", "tc1", "tc2"], "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 equilibrium vapour pressure of benzene at $\\mathrm{\\var{tc1}^\\circ C}$ is $\\mathrm{\\var{p1} \\space bar}$.</p>\n<p>Given that $\\mathrm{{&Delta;H^\\circ}_{vap} = \\var{h} \\space kJ \\space mol^{-1}}$ for benzene, calculate the equilibrium vapour pressure at $\\mathrm{\\var{tc2}^\\circ C}$:</p>\n<p>[[0]] $\\mathrm{bar}$</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": "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/"}]}