// Numbas version: finer_feedback_settings
{"name": "Chemical Thermodynamics: Van't Hoff Equation 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Chemical Thermodynamics: Van't Hoff Equation 4", "tags": [], "metadata": {"description": "<p>Public</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "", "advice": "<p>The Van't Hoff equation is used to relate the equilibrium constant of a reaction at one temperature with that at another temperature, as well as to the enthalpy of the reaction:</p>\n<p>$\\mathrm{ln(K_2)-ln(K_1)=\\frac{\\Delta H^\\circ}{R}[(\\frac{1}{T_1})-(\\frac{1}{T_2})]}$ ,</p>\n<p>where $\\mathrm{T_1}$ and $\\mathrm{T_2}$ are the initial and final temperatures, in $\\mathrm{K}$ ;&nbsp; &nbsp;$\\mathrm{K_1}$ and $\\mathrm{K_2}$ are the corresponding initial and final equilibrium constants;&nbsp; $\\mathrm{\\Delta H^\\circ}$ is the standard enthalpy of the reaction; 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 constant $\\mathrm{K_1 = \\var{scientificnumberlatex(siground(k,3))}}$ at a temperature of $\\mathrm{T_1=298 \\space K}$, as well as a new equilibrium constant, $\\mathrm{K_2 = \\var{scientificnumberlatex(siground(k,3))}}$, at temperature $\\mathrm{T_2=\\var{temp} \\space K}$. We are asked to use these values to calculate the enthalpy of the reaction, $\\mathrm{\\Delta H^\\circ}$.</p>\n<p></p>\n<p>To calculate $\\mathrm{\\Delta H^\\circ}$, we must first rearrange the Van't Hoff equation appropriately:</p>\n<p>$\\mathrm{ln(K_2)-ln(K_1)=\\frac{\\Delta H^\\circ}{R}[(\\frac{1}{T_1})-(\\frac{1}{T_2})]}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space \\Delta H^\\circ[(\\frac{1}{T_1})-(\\frac{1}{T_2})]=R[ln(K_2)-ln(K_1)]}$</p>\n<p></p>\n<p>$\\mathrm{\\Rightarrow\\space\\space\\space \\Delta H^\\circ=\\frac{R[ln(K_2)-ln(K_1)]}{[(\\frac{1}{T_1})-(\\frac{1}{T_2})]}}$ .</p>\n<p></p>\n<p>We can now simply substitute in our values to calculate $\\mathrm{\\Delta H^\\circ}$ for the reaction:</p>\n<p></p>\n<p>$\\mathrm{\\Delta H^\\circ=\\frac{8.314\\times[ln(\\var{scientificnumberlatex(siground(k2,3))})-ln(\\var{scientificnumberlatex(siground(k,3))})]}{[(\\frac{1}{298})-(\\frac{1}{\\var{temp}})]}=\\var{enthalpy}\\space J\\space mol^{-1}}$ .</p>\n<p></p>\n<p>Lastly, to quote our answer in the units asked for, we divide by one thousand to obtain:</p>\n<p>$\\mathrm{\\Delta H^\\circ = \\var{siground(h,3)}\\space kJ\\space mol^{-1}}$ .</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"k": {"name": "k", "group": "Ungrouped variables", "definition": "random(0.000001 .. 0.00009#1e - 7)", "description": "", "templateType": "randrange", "can_override": false}, "temp": {"name": "temp", "group": "Ungrouped variables", "definition": "random(1400 .. 1700#1)", "description": "", "templateType": "randrange", "can_override": false}, "k2": {"name": "k2", "group": "Ungrouped variables", "definition": "exp((enthalpy/8.314)*((1/298)-(1/temp))+ln(k))", "description": "", "templateType": "anything", "can_override": false}, "enthalpy": {"name": "enthalpy", "group": "Ungrouped variables", "definition": "random(115500 .. 130500#1000)", "description": "", "templateType": "randrange", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "enthalpy/1000", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "ungrouped_variables": ["k", "temp", "k2", "enthalpy", "h"], "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>For the reaction $\\mathrm{N_2\\space +\\space O_2\\space \\rightleftharpoons\\space 2NO}$ ,&nbsp; the equilibrium constant is $\\mathrm{K = \\var{scientificnumberlatex(siground(k,3))}}$ at $\\mathrm{298 K}$.</p>\n<p>When the temperature is increased to $\\mathrm{\\var{temp} K}$, the equilibrium constant increases to $\\mathrm{K = \\var{scientificnumberlatex(siground(k2,3))}}$.</p>\n<p>Calculate the standard enthalpy change, $\\mathrm{&Delta;H^\\circ}$, for the reaction:</p>\n<p>[[0]] $\\mathrm{kJ\\space mol^{-1}}$</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": "h-(h/200)", "maxValue": "h+(h/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/"}]}