// Numbas version: exam_results_page_options
{"name": "Solutions 6", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "ungrouped_variables": ["final_volume", "stock_volume_used", "stock_molarity", "final_molarity", "final_concentration"], "metadata": {"description": "<p>Working backwards from the concentration of a diluted solution to find the concentration of \"stock\" solution.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "variables": {"stock_molarity": {"definition": "final_molarity * final_volume / stock_volume_used", "description": "<p>Moalrity of \"stock\" solution.</p>", "name": "stock_molarity", "group": "Ungrouped variables", "templateType": "anything"}, "final_molarity": {"definition": "final_concentration / 1000", "description": "<p>Molarity of diluted solution.</p>", "name": "final_molarity", "group": "Ungrouped variables", "templateType": "anything"}, "final_volume": {"definition": "100 * random(2..5)", "description": "<p>Volume of solution after dilution.</p>", "name": "final_volume", "group": "Ungrouped variables", "templateType": "anything"}, "stock_volume_used": {"definition": "25 * random(1..4)", "description": "<p>Volume of \"stock\" solution which was diluted</p>", "name": "stock_volume_used", "group": "Ungrouped variables", "templateType": "anything"}, "final_concentration": {"definition": "12.5 * random(1..8)", "description": "<p>Concentration of diluted solution in mM.</p>", "name": "final_concentration", "group": "Ungrouped variables", "templateType": "anything"}}, "advice": "<p>A solution of glucose was prepared by diluting $\\var{stock_volume_used}$ml of the \"stock\" glucose solution to $\\var{final_volume}$ml. The concentration of glucose in the final solution was $\\var{final_concentration}$mM. What was the concentration of glucose in the \"stock\" solution in M (mol/L)?</p>\n<p>Solution:</p>\n<p>First, we convert $\\var{final_volume}$ml to a volume in litres. There are 1000ml in 1L so $\\var{final_volume}$ml is equal to&nbsp;</p>\n<p style=\"text-align: center;\">$\\dfrac{\\var{final_volume}}{1000} = \\var{final_volume / 1000} \\text{ L.}$</p>\n<p style=\"text-align: left;\">Next, we can calculate how many mmol of glucose there are in the final solution. The formula for this is&nbsp;</p>\n<p style=\"text-align: center;\">$\\text{volume of liquid (in litres)} \\times \\text{concentration (in mmol/L)} = \\text{number of millimoles of substance}$.</p>\n<p style=\"text-align: left;\">[Note: This is slightly different to the formula on the wiki page for molar calculations. This is because we are currently working with mmol and mM as opposed to mol and M. If you prefer, you can first convert all values in mmol and mM to values in mol and M respectively and use the formulas as given on the wiki page. If you would like to read a little more about converting between units, see the wiki page on dimensions in the animal science section.]</p>\n<p style=\"text-align: left;\">Putting in our numbers we find that there are&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{final_volume / 1000} \\times \\var{final_concentration} = \\var{(final_volume / 1000) * final_concentration} \\text{ mmol}$</p>\n<p style=\"text-align: left;\">of glucose in the final solution.</p>\n<p style=\"text-align: left;\">We also need to convert $\\var{stock_volume_used}$ml to a volume in litres. $\\var{stock_volume_used}$ml is equal to&nbsp;</p>\n<p style=\"text-align: center;\">$\\dfrac{\\var{stock_volume_used}}{1000} = \\var{stock_volume_used / 1000} \\text{ L}.$</p>\n<p style=\"text-align: left;\">We didn't add any more glucose when diluting the \"stock\" solution so the \"stock\" solution also contained $\\var{(final_volume / 1000) * final_concentration}$mmol of glucose in $\\var{stock_volume_used / 1000}$L of solution. We calculate the concentration of the \"stock\" solution in mM (mmol/L) using the formula</p>\n<p style=\"text-align: center;\">$\\dfrac{\\text{number of millimoles of substance}}{\\text{volume of liquid (in litres)}} = \\text{concentration (in mmol/L)}$.</p>\n<p style=\"text-align: left;\">[Again, if you prefer, you can convert the amount of substance in mmol to an amount in mol before doing the calculation and use the formulas as given on the wiki page.]</p>\n<p style=\"text-align: left;\">Putting in our numbers, we find that theconcentration of the \"stock\" stock in mM is</p>\n<p style=\"text-align: center;\">$\\dfrac{\\var{(final_volume / 1000) * final_concentration}}{\\var{stock_volume_used / 1000}} = \\var{stock_molarity * 1000} \\text{ mM}.$</p>\n<p style=\"text-align: left;\">Finally, we have been asked to give the answer in M so we have to convert $\\var{stock_molarity * 1000}$mM to a concentration in M. There are 1000mM in 1M so the concentration of the \"stock\" solution in M is</p>\n<p style=\"text-align: center;\">$\\begin{align}\\dfrac{\\var{stock_molarity * 1000}}{1000} &amp; = \\var{stock_molarity}\\text{ M} \\\\ &amp; = \\var{precround(stock_molarity, 3)} \\text{ M to 3 d.p.} \\end{align}$</p>", "functions": {}, "parts": [{"gaps": [{"type": "numberentry", "mustBeReducedPC": 0, "marks": 1, "minValue": "stock_molarity - 0.0005", "variableReplacements": [], "strictPrecision": false, "maxValue": "stock_molarity + 0.0005", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": false, "showPrecisionHint": false, "precision": "3", "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "scripts": {}, "precisionPartialCredit": 0, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "precisionType": "dp"}], "marks": 0, "prompt": "<p>A solution of glucose was prepared by diluting $\\var{stock_volume_used}$ml of the \"stock\" glucose solution to $\\var{final_volume}$ml. The concentration of glucose in the final solution was $\\var{final_concentration}$mM. What was the concentration of glucose in the \"stock\" solution in M (mol/L)?</p>\n<p>[[0]] M</p>", "showCorrectAnswer": true, "variableReplacements": [], "type": "gapfill", "scripts": {}, "showFeedbackIcon": true, "stepsPenalty": 0, "steps": [{"type": "numberentry", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>1) First, convert $\\var{final_volume}$ml to a volume in litres.</p>", "minValue": "final_volume / 1000 - 0.0005", "variableReplacements": [], "maxValue": "final_volume / 1000 + 0.0005", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst"}, {"type": "numberentry", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>2) Then calculate how much glucose there is in the final solution in mmol.</p>", "minValue": "final_concentration * final_volume / 1000 - 0.0005", "variableReplacements": [], "maxValue": "final_concentration * final_volume / 1000 + 0.0005", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst"}, {"type": "numberentry", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>3) The next step is to convert $\\var{stock_volume_used}$ml to a volume in litres.</p>", "minValue": "stock_volume_used / 1000 - 0.0005", "variableReplacements": [], "maxValue": "stock_volume_used / 1000 + 0.0005", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst"}, {"type": "numberentry", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>4) Calculate the concentration of the \"stock\" solution in mM using your answers to parts 2 and 3.</p>", "minValue": "stock_molarity * 1000 - 0.0005", "variableReplacements": [], "maxValue": "stock_molarity * 1000 + 0.0005", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst"}, {"type": "numberentry", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "prompt": "<p>5) Finally, convert the concentration you found in mM (mmol/L) in part 4 to a concentration in M (mol/L).</p>", "minValue": "stock_molarity - 0.0005", "variableReplacements": [], "maxValue": "stock_molarity + 0.0005", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "allowFractions": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "mustBeReduced": false, "variableReplacementStrategy": "originalfirst"}], "variableReplacementStrategy": "originalfirst"}], "tags": ["concentration", "diluted", "dilution", "molarity", "moles", "solution"], "variable_groups": [], "name": "Solutions 6", "extensions": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>Answer the following question. Please enter your answer as a decimal, not a fraction. Give your answer to 3 decimal places.</p>\n<p>Clicking on 'Show steps' will provide you with some prompts to break down the question into smaller parts.</p>\n<p>If you would like to see how to do this question, click on 'Reveal answers' at the bottom of the page.</p>", "type": "question", "contributors": [{"name": "Jamie Antoun", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/266/"}]}]}], "contributors": [{"name": "Jamie Antoun", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/266/"}]}