// Numbas version: exam_results_page_options {"name": "Calculate concentration of solution", "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 7, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/7/edit"}, "name": "Quantity with units", "short_name": "quantity", "description": "

The student enters a quantity with units.

", "help_url": "https://github.com/numbas/numbas-extension-quantities", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings[\"correctAnswer\"])", "hint": {"static": false, "value": "switch(\n settings[\"hint\"]=\"remind units\",\n \"Include units in your answer.\",\n settings[\"hint\"]=\"show units\",\n \"Give your answer in \"+units_string(settings[\"correctAnswer\"])\n ,\n \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)\n\ninterpreted_answer:\nstudent_quantity\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_number:\nmatch_student_number[1]\n\nraw_student_units:\ntry(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\nstudent_units:\nif(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)\n\nstudent_quantity:\napply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\ncompatible:\nif(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)\n\ncorrect_units:\nunits(correct_quantity)\n\nsame_units:\nassert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)\n\nhas_units:\nassert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)\n\ncan_compare:\ncompatible or settings[\"incompatible_units_action\"]=\"convert\"\n\nclose_enough:\nif(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)\n\nwiggle:\nunits(correct_quantity)*abs(eval(settings[\"wiggle\"]))\n\nvalid_number:\nif(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "apply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_quantity"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_number", "description": "

The scalar part of the student's quantity

", "definition": "match_student_number[1]"}, {"name": "raw_student_units", "description": "

The units of the student's quantity, before converting.

", "definition": "try(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "student_units", "description": "

The units of the student's quantity.

\n

If the student used units incompatible with the units in the expected answer, and the \"what to do if incompatible units used\" option is set to \"mark as if correct units used\", the student's units are ignored and the expected units are used instead.

", "definition": "if(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)"}, {"name": "student_quantity", "description": "

The student's answer, interpreted as a quantity.

\n

Marking fails if the student does not enter a valid quantity.

", "definition": "apply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]"}, {"name": "compatible", "description": "

Are the units of the student's quantity compatible with the units of the expected quantity?

", "definition": "if(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "same_units", "description": "

/Are the student's quantity and the expected quantity in exactly the same units?

", "definition": "assert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)"}, {"name": "has_units", "description": "", "definition": "assert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)"}, {"name": "can_compare", "description": "

Can the student's answer be compared with the correct answer? True if compatible units used, or \"mark as if correct units used\" selected.

", "definition": "compatible or settings[\"incompatible_units_action\"]=\"convert\""}, {"name": "close_enough", "description": "

Is the student's quantity within the allowed tolerance of the expected answer?

", "definition": "if(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)"}, {"name": "wiggle", "description": "", "definition": "units(correct_quantity)*abs(eval(settings[\"wiggle\"]))"}, {"name": "valid_number", "description": "

Is the scalar part of the student's answer a valid number?

", "definition": "if(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )\n"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The expected quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "hint", "label": "Input hint", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "remind units", "choices": [{"value": "none", "label": "None"}, {"value": "remind units", "label": "Remind to include units"}, {"value": "show units", "label": "Show required units"}]}, {"name": "allow_unitless", "label": "Allow unitless answer?", "help_url": "", "hint": "If not ticked, the student is prevented from submitting an answer without specifying units.", "input_type": "checkbox", "default_value": true}, {"name": "incompatible_units_action", "label": "What to do if incompatible units used", "help_url": "", "hint": "If the student's answer is given in units incompatible with the correct answer's units:
\n", "input_type": "dropdown", "default_value": "incorrect", "choices": [{"value": "incorrect", "label": "Mark as incorrect"}, {"value": "prevent", "label": "Prevent submission"}, {"value": "convert", "label": "Mark as if correct units used"}]}, {"name": "different_units_action", "label": "What to do if different units used", "help_url": "", "hint": "If the student's answer is given in different units to the expected answer:
\n", "input_type": "dropdown", "default_value": "convert", "choices": [{"value": "convert", "label": "Convert"}, {"value": "warn", "label": "Warn and convert"}, {"value": "prevent", "label": "Prevent submission"}, {"value": "incorrect", "label": "Mark incorrect"}]}, {"name": "different_units_penalty", "label": "Penalty if different units used", "help_url": "", "hint": "This penalty is applied if the student gives their answer in different units to the expected answer. The selected percentage of the student's score is taken away.", "input_type": "percent", "default_value": "100"}, {"name": "wiggle", "label": "Margin of error", "help_url": "", "hint": "The student's answer is marked correct if the difference between it and the correct answer is at most this value, measured in the same units as the correct answer.", "input_type": "mathematical_expression", "default_value": "10^-12", "subvars": true}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"settings": {"different_units_action": "convert", "correctAnswer": "concentration_acid", "allow_unitless": false, "different_units_penalty": "100", "wiggle": "10^-12", "hint": "show units"}, "showFeedbackIcon": true, "useCustomName": false, "variableReplacements": [], "steps": [{"settings": {"different_units_action": "incorrect", "correctAnswer": "amount_alkali in \"dm^3\"", "allow_unitless": false, "different_units_penalty": "100", "wiggle": "10^-12", "hint": "show units"}, "showFeedbackIcon": true, "useCustomName": false, "prompt": "

First, convert the amount of sodium hydroxide to {units_string(qty(\"dm^3\"))}.

\n

\\[ \\var{qty(1,\"cm^3\")} = \\var{qty(1,\"cm^3\") in \"dm^3\"} \\]

", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "unitTests": [], "type": "quantity", "scripts": {}, "customName": "", "adaptiveMarkingPenalty": 0, "marks": 1, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"settings": {"different_units_action": "convert", "correctAnswer": "moles_alkali", "allow_unitless": false, "different_units_penalty": "100", "wiggle": "10^-12", "hint": "show units"}, "showFeedbackIcon": true, "useCustomName": false, "prompt": "

Next, work out the number of moles of sodium hydroxide:

\n

\\[ \\text{number of moles} = \\text{concentration} \\times \\text{volume} \\]

", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "unitTests": [], "type": "quantity", "scripts": {}, "customName": "", "adaptiveMarkingPenalty": 0, "marks": 1, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"settings": {"different_units_action": "convert", "correctAnswer": "moles_acid in \"mol\"", "allow_unitless": false, "different_units_penalty": "100", "wiggle": "10^-12", "hint": "show units"}, "showFeedbackIcon": true, "useCustomName": false, "prompt": "

Work out the number of moles of acid using the balanced equation

\n

\\[ \\mathrm{HCl_{(aq)} + NaOH_{(aq)} \\rightarrow NaCl_{(aq)} + H_2O_{(l)}} \\]

\n

This is a 1:1 reaction, so how many moles of $\\mathrm{HCl}$ are neutralised by the $\\mathrm{NaOH}$?

", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "unitTests": [], "type": "quantity", "scripts": {}, "customName": "", "adaptiveMarkingPenalty": 0, "marks": 1, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"settings": {"different_units_action": "convert", "correctAnswer": "concentration_acid in \"mol/dm^3\"", "allow_unitless": false, "different_units_penalty": "100", "wiggle": "10^-12", "hint": "show units"}, "showFeedbackIcon": true, "useCustomName": false, "prompt": "

Finally, work out the concentration of the acid:

\n

\\[ \\text{concentration} = \\frac{\\text{number of moles}}{\\text{volume}} \\]

", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "unitTests": [], "type": "quantity", "scripts": {}, "customName": "", "adaptiveMarkingPenalty": 0, "marks": 1, "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "prompt": "

What was the concentration of the hydrochloric acid?

", "extendBaseMarkingAlgorithm": true, "stepsPenalty": 0, "unitTests": [], "type": "quantity", "scripts": {}, "customName": "", "adaptiveMarkingPenalty": 0, "marks": "10", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "variable_groups": [], "ungrouped_variables": ["amount_acid", "amount_alkali", "concentration_alkali", "moles_alkali", "reaction_ratio", "moles_acid", "concentration_acid"], "tags": [], "statement": "

{amount_acid} of dilute hydrochloric acid is neutralised by {amount_alkali} of {concentration_alkali} sodium hydroxide.

", "variables": {"moles_alkali": {"definition": "amount_alkali*concentration_alkali in \"mol\"", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "moles_alkali"}, "concentration_alkali": {"definition": "qty(random(0.2..0.9#0.1), \"mol/dm^3\")", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "concentration_alkali"}, "moles_acid": {"definition": "reaction_ratio * moles_alkali", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "moles_acid"}, "reaction_ratio": {"definition": "1", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "reaction_ratio"}, "amount_alkali": {"definition": "(random(2..3)/random(1,2,5))*amount_acid", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "amount_alkali"}, "amount_acid": {"definition": "qty(random(10..40#5),\"cm^3\")", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "amount_acid"}, "concentration_acid": {"definition": "moles_acid/amount_acid in \"mol/dm^3\"", "description": "", "templateType": "anything", "group": "Ungrouped variables", "name": "concentration_acid"}}, "functions": {}, "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Calculate the concentration of a dilute acid given the amount and concentration of dilute alkali to neutralise it. Cribbed from this Bitesize problem.

\n

There are steps to break down the calculation, and the student must give units at each step.

"}, "preamble": {"css": "", "js": ""}, "advice": "

Since the acid is neutralised, we can conclude that all of it has reacted with the sodium hydroxide.

\n

The equation of the reaction is:

\n

\\[ \\mathrm{HCl_{(aq)} + NaOH_{(aq)} \\rightarrow NaCl_{(aq)} + H_2O_{(l)}} \\]

\n

1 mole of $\\mathrm{HCl}$ reacts with 1 mole of $\\mathrm{NaOH}$, so the number of moles of $\\mathrm{HCl}$ must be the same as the number of moles of $\\mathrm{NaOH}$.

\n

To work out the number of moles of $\\mathrm{NaOH}$, use the formula:

\n

\\[ \\text{number of moles} = \\text{concentration} \\times \\text{volume} \\]

\n

Since the concentration is given in {units_string(concentration_alkali)}, first convert the amount of sodium hydroxide to the same units:

\n

\\[ \\var{amount_alkali} = \\var{amount_alkali in (qty(1,\"mol\")/concentration_alkali)} \\]

\n

Now, the number of moles of $\\mathrm{NaOH}$ is:

\n

\\begin{align}
\\text{number of moles} &= \\text{concentration} \\times \\text{volume}  \\\\
&= \\var{concentration_alkali} \\times \\var{amount_alkali in \"dm^3\"} \\\\
&= \\var{moles_alkali}
\\end{align}

\n

Finally, we can work out the concentration of the hydrochloric acid:

\n

\\begin{align}
\\text{concentration} &= \\frac{\\text{number of moles}}{\\text{volume}} \\\\
&= \\simplify{{moles_acid}/{amount_acid}} \\\\
&= \\simplify{{moles_acid}/{amount_acid}} \\\\
&= \\var{concentration_acid}
\\end{align}

", "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": ["quantities"], "name": "Calculate concentration of solution", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}