// Numbas version: finer_feedback_settings
{"name": "Chemical Thermodynamics: Raoult's Law 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Chemical Thermodynamics: Raoult's Law 1", "tags": [], "metadata": {"description": "<p>Public</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "", "advice": "<p>Raoult's law is used to relate the equilibrium vapour pressure of the <strong>pure form</strong> of a substance to the <strong>partial</strong> vapour pressure of that same substance <strong>in a mixture</strong> (i.e. the substance's <strong>contribution</strong> to the total vapour pressure of the mixture):</p>\n<p></p>\n<p>$\\mathrm{p_i=p_i^*x_i}$ ,</p>\n<p></p>\n<p>where $\\mathrm{p_i}$ is the partial vapour pressure of the $\\mathrm{i^{th}}$ substance in the mixture; $\\mathrm{p_i^*}$ is the equilibrium vapour pressure of the pure form of this substance; and $\\mathrm{x_i}$ is the mole fraction of the $\\mathrm{i^{th}}$ substance in the mixture.</p>\n<p></p>\n<p>We are given the atmospheric pressures at which substances X and Y boil. At a substance's boiling point, its saturated vapour pressure is <strong>equal</strong> to the surrounding atmospheric pressure, so the atmospheric pressures at which substances X and Y boil are simply equal to their equilibrium vapour pressures. Thus, we know from what we are told that $\\mathrm{p_{_{X}}^*=\\var{px} \\space atm}$ and $\\mathrm{p_{_{Y}}^*=\\var{py} \\space atm}$.</p>\n<p>We are also given the number of moles of each of the two substances in the mixture, $\\mathrm{n_{_{X}}=\\var{nx} \\space mol}$ and $\\mathrm{n_{_{Y}}=\\var{ny} \\space mol}$; we will use these to calculate their corresponding mole fractions, $\\mathrm{x_{_{X}}}$ and $\\mathrm{x_{_{Y}}}$, which we will in turn use with Raoult's law to calculate the partial vapour pressure of each substance, $\\mathrm{p_{_{X}}}$ and $\\mathrm{p_{_{Y}}}$.</p>\n<p></p>\n<p>Recall that mole fraction is given by the number of moles of the $\\mathrm{i^{th}}$ substance, divided by the total number of moles of all substances in the mixture:</p>\n<p>$\\mathrm{x_i=\\frac{n_i}{n_{tot}}}$ .</p>\n<p></p>\n<p>Thus:</p>\n<p>$\\mathrm{x_{_{X}}=\\frac{n_{_{X}}}{n_{_{X}}+n_{_{Y}}}=\\frac{\\var{nx}}{\\var{nx}+\\var{ny}}=\\var{siground(xx,3)}}$ ,</p>\n<p>$\\mathrm{x_{_{Y}}=\\frac{n_{_{Y}}}{n_{_{Y}}+n_{_{X}}}=\\frac{\\var{ny}}{\\var{ny}+\\var{nx}}=\\var{siground(xy,3)}}$ .</p>\n<p></p>\n<p>We can now apply Raoult's law to calculate our partial vapour pressures:</p>\n<p>$\\mathrm{p_{_X}=p_{_X}^*x_{_X}=\\var{px}\\times\\var{xx}=\\var{sigformat(partialx,3)}\\space atm}$ ,</p>\n<p>$\\mathrm{p_{_Y}=p_{_Y}^*x_{_Y}=\\var{py}\\times\\var{xy}=\\var{sigformat(partialy,3)}\\space atm}$ .</p>\n<p></p>\n<p>Lastly, to find the <strong>total</strong> vapour pressure of the <strong>mixture</strong>, we simply sum up the partial vapour pressures of the mixture's components:</p>\n<p>$\\mathrm{p_{tot}=p_{_X}+p_{_Y}=\\var{sigformat(partialx,3)}+\\var{sigformat(partialy,3)}=\\var{sigformat(pressure,3)}\\space atm}$ .</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"px": {"name": "px", "group": "Ungrouped variables", "definition": "random(0 .. 2#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "py": {"name": "py", "group": "Ungrouped variables", "definition": "random(0 .. 2#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "nx": {"name": "nx", "group": "Ungrouped variables", "definition": "random(1.1 .. 5#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "ny": {"name": "ny", "group": "Ungrouped variables", "definition": "random(1.1 .. 5#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "xx": {"name": "xx", "group": "Ungrouped variables", "definition": "nx/(nx+ny)", "description": "", "templateType": "anything", "can_override": false}, "xy": {"name": "xy", "group": "Ungrouped variables", "definition": "ny/(nx+ny)", "description": "", "templateType": "anything", "can_override": false}, "partialx": {"name": "partialx", "group": "Ungrouped variables", "definition": "px*xx", "description": "", "templateType": "anything", "can_override": false}, "partialy": {"name": "partialy", "group": "Ungrouped variables", "definition": "py*xy", "description": "", "templateType": "anything", "can_override": false}, "pressure": {"name": "pressure", "group": "Ungrouped variables", "definition": "partialx+partialy", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["px", "py", "nx", "ny", "xx", "xy", "partialx", "partialy", "pressure"], "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>Substances $\\mathrm{X}$ and $\\mathrm{Y}$ have similar molecular masses and structures. At $\\mathrm{100^\\circ C}$, pure $\\mathrm{X}$ boils at $\\mathrm{\\var{px}\\space&nbsp; atm}$, pure $\\mathrm{Y}$ at $\\mathrm{\\var{py}\\space atm}$. If $\\mathrm{\\var{nx}}$ moles of $\\mathrm{X}$ are mixed with $\\mathrm{\\var{ny}}$ moles of $\\mathrm{Y}$ at $\\mathrm{100^\\circ C}$, what is the vapour pressure of this mixture?</p>\n<p>[[0]] $\\mathrm{atm}$</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": "pressure-(pressure/200)", "maxValue": "pressure+(pressure/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/"}]}