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{"name": "Solutions 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "extensions": [], "variables": {"c": {"description": "", "name": "c", "definition": "random(1..15)", "templateType": "anything", "group": "Ungrouped variables"}, "b": {"description": "", "name": "b", "definition": "random(1..10)", "templateType": "anything", "group": "Ungrouped variables"}, "a": {"description": "", "name": "a", "definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "name": "Solutions 4", "statement": "<p>Answer the following question. Please enter your answer as a decimal, not a fraction. Give your answer to 2 decimal places (only round your final answer, use the exact values on your calculator when working out any intermediate steps).</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>", "tags": ["diluted", "dilution", "moles", "solution", "solutions"], "ungrouped_variables": ["a", "c", "b"], "rulesets": {}, "parts": [{"stepsPenalty": 0, "type": "gapfill", "showFeedbackIcon": true, "prompt": "<p>$\\var{50 * a}$ml of a $\\var{0.25 * b}$M solution is diluted by adding another $\\var{50 * c}$ml of liquid, what is the new concentration?</p>\n<p>[[0]] M</p>", "variableReplacements": [], "steps": [{"correctAnswerStyle": "plain", "showFeedbackIcon": true, "prompt": "<p>1) We started with $\\var{50 * a}$ml of liquid and added another $\\var{50 * c}$ml. Calcluate the new volume of liquid in ml.</p>", "variableReplacements": [], "showCorrectAnswer": true, "mustBeReduced": false, "maxValue": "50 * (a + c)", "allowFractions": false, "type": "numberentry", "correctAnswerFraction": false, "minValue": "50 * (a + c)", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 1}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "prompt": "<p>2) Convert $\\var{50 * a}$ml to a volume in litres.&nbsp;</p>", "variableReplacements": [], "showCorrectAnswer": true, "mustBeReduced": false, "maxValue": "50 * a / 1000", "allowFractions": false, "type": "numberentry", "correctAnswerFraction": false, "minValue": "50 * a / 1000", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 1}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "prompt": "<p>3) Using the value you calculated in step 2, calculate how many moles of the substance we started with. (Because we want to work out our final answer to 2 decimal places, don't round this answer to 2 decimal places, enter it exactly as it appears in your calculator and use the exact number for the rest of the calculations).</p>", "variableReplacements": [], "showCorrectAnswer": true, "mustBeReduced": false, "maxValue": "(50 * a / 1000) * (0.25 * b)", "allowFractions": false, "type": "numberentry", "correctAnswerFraction": false, "minValue": "(50 * a / 1000) * (0.25 * b)", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 1}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "prompt": "<p>4) Convert the volume you found in step 1 to a volume in litres.</p>", "variableReplacements": [], "showCorrectAnswer": true, "mustBeReduced": false, "maxValue": "50 * (a + c) / 1000", "allowFractions": false, "type": "numberentry", "correctAnswerFraction": false, "minValue": "50 * (a + c) / 1000", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 1}, {"correctAnswerStyle": "plain", "showFeedbackIcon": true, "prompt": "<p>5) Using your answers to steps 3 and 4, calculate the new concentration of the solution in mol/L.</p>", "variableReplacements": [], "showCorrectAnswer": true, "mustBeReduced": false, "maxValue": "((50 * a / 1000) * (0.25 * b)) / ((50 * a + 50 * c) / 1000) + 0.005", "allowFractions": false, "type": "numberentry", "correctAnswerFraction": false, "minValue": "((50 * a / 1000) * (0.25 * b)) / ((50 * a + 50 * c) / 1000) - 0.005", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 1}], "showCorrectAnswer": true, "gaps": [{"correctAnswerStyle": "plain", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": false, "marks": 1, "mustBeReduced": false, "maxValue": "((50 * a / 1000) * (0.25 * b)) / ((50 * a + 50 * c) / 1000) + 0.005", "allowFractions": false, "precision": "2", "correctAnswerFraction": false, "minValue": "((50 * a / 1000) * (0.25 * b)) / ((50 * a + 50 * c) / 1000) - 0.005", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "precisionMessage": "You have not given your answer to the correct precision.", "precisionType": "dp", "scripts": {}, "type": "numberentry", "showPrecisionHint": false}], "scripts": {}, "variableReplacementStrategy": "originalfirst", "marks": 0}], "advice": "<p>$\\var{50 * a}$ml of a $\\var{0.25 * b}$M solution is diluted by adding another $\\var{50 * c}$ml of liquid, what is the new concentration?</p>\n<p>Solution:</p>\n<p>We started with $\\var{50 * a}$ml of liquid and added another $\\var{50 * c}$ml so the new volume of liquid is&nbsp;</p>\n<p style=\"text-align: center;\">$\\var{50 * a} + \\var{50 * c} = \\var{50 * (a + c)} \\text{ml.}$</p>\n<p>$\\var{50 * a}$ml is equal to</p>\n<p style=\"text-align: center;\">$\\dfrac{\\var{50 * a}}{1000} = \\var{50 * a / 1000}\\text{L}$</p>\n<p></p>\n<p>so the number of moles we started with is</p>\n<p style=\"text-align: center;\">$\\var{50 * a / 1000}&nbsp;\\times \\var{0.25 * b} = \\var{(50 * a / 1000) * 0.25 * b} \\text{ moles}.$</p>\n<p>We haven't added any more of the substance so we still have $\\var{(50 * a / 1000) * 0.25 * b}$ moles but this is now dissolved in $\\var{50 * (a + c)}$ml of liquid. $\\var{50 * (a + c)}$ml is equal to $\\var{50 * (a + c) / 1000}$L so the new concentration is&nbsp;</p>\n<p style=\"text-align: center;\">$\\begin{align} \\dfrac{\\var{(50 * a / 1000) * 0.25 * b}}{\\var{50 * (a + c) / 1000}} &amp; = \\var{((50 * a / 1000) * 0.25 * b) / (50 * (a + c) / 1000)} \\text{M} \\\\ &amp; = \\var{precround((((50 * a / 1000) * 0.25 * b) / (50 * (a + c) / 1000)), 2)} \\text{M to 2 d.p.} \\end{align}$</p>\n<p>Challenge:</p>\n<p>Can you think of a shorter way of doing this calculation? Don't worry if you can't, just go through the steps one by one.</p>\n<p></p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Calculating the new concentration of a diluted solution.</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/"}]}