// Numbas version: exam_results_page_options {"name": "Rearranging the percentage weight per volume formula", "feedback": {"showtotalmark": true, "advicethreshold": 0, "showanswerstate": true, "showactualmark": true, "allowrevealanswer": true}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "allQuestions": true, "shuffleQuestions": false, "percentPass": 0, "duration": 0, "pickQuestions": 0, "navigation": {"onleave": {"action": "none", "message": ""}, "reverse": true, "allowregen": true, "showresultspage": "oncompletion", "preventleave": true, "browse": true, "showfrontpage": true}, "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "exam", "questions": [], "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": [{"name": "Rearranging concentration formula for mass (symbolic)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "functions": {}, "ungrouped_variables": [], "tags": ["algebra", "balancing equations", "ephlth", "Linear equations", "linear equations", "rearranging equations", "solving equations", "Solving equations", "two step equations"], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "displayColumns": "1", "prompt": "

Given that \\[\\text{percentage concentration (w/v)}=\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100},\\] which of the following is a valid equation for the mass of the solute (g)?

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\n

$\\text{mass of solute (g)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{100}}\\times \\text{volume of solvent (ml)}$

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", "

\n

$\\text{mass of solute (g)}=\\text{percentage concentration (w/v)}\\times \\text{volume of solvent (ml)}\\times {\\text{100}}$

\n

", "

\n

$\\text{mass of solute (g)}=\\text{percentage concentration (w/v)}\\times \\text{volume of solvent (ml)}$

\n

", "

\n

$\\text{mass of solute (g)}=\\dfrac{\\text{100}}{\\text{percentage concentration (w/v)}}\\times \\text{volume of solvent (ml)}$

\n

", "

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$\\text{mass of solute (g)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{volume of solvent (ml)}} $

\n

", "

\n

$\\text{mass of solute (g)}=\\dfrac{\\text{volume of solvent (ml)}}{\\text{percentage concentration (w/v)}}$

\n

", "

\n

$\\text{mass of solute (g)}=\\dfrac{\\text{100}}{\\text{volume of solvent (ml)}}\\times {\\text{percentage concentration (w/v)}}$

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", "

\n

$\\text{mass of solute (g)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{100}\\times \\text{volume of solvent (ml)}}$

\n

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Given that \\[\\text{percentage concentration (w/v)}=\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100},\\]

\n

to find an equation for 'mass of solute (g)', we need to get rid of all the other things on the right hand side of the equation (so that mass is by itself). To do this we divide both sides by 100 and multiply both sides by 'volume of solvent (mL)'.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\text{percentage concentration (w/v)}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100}$
 
$\\dfrac{\\text{percentage concentration (w/v)}}{\\text{100}}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\dfrac{\\text{100}}{\\text{100}}$
 
$\\dfrac{\\text{percentage concentration (w/v)}}{\\text{100}}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}$
 
$\\dfrac{\\text{percentage concentration (w/v)}}{\\text{100}}\\times \\text{volume of solvent (mL)}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{volume of solvent (mL)}$
 
$\\dfrac{\\text{percentage concentration (w/v)}}{\\text{100}}\\times \\text{volume of solvent (mL)}$$=$$\\text{mass of solute (g)}$
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https://en.wikipedia.org/wiki/Mass_concentration_(chemistry)#Usage_in_biology

", "description": "

For Nursing and midwifery

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Given that \\[\\text{percentage concentration (w/v)}=\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100},\\] which of the following is a valid equation for the volume of the solvent (mL)?

", "matrix": ["1", 0, 0, 0, 0, 0, 0], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["

\n

$\\text{volume of solvent (ml)}=\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}\\times \\text{100}$

\n

", "

\n

$\\text{volume of solvent (ml)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{mass of solute (g)}}\\times \\text{100}$

\n

", "

\n

$\\text{volume of solvent (ml)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{mass of solute (g)}}\\div \\text{100}$

\n

", "

\n

$\\text{volume of solvent (ml)}=\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}\\div \\text{100}$

\n

\n

", "

\n

$\\text{volume of solvent (ml)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{mass of solute (g)}}$

\n

", "

\n

$\\text{volume of solvent (ml)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{mass of solute (g)}}$

\n

", "

\n

$\\text{volume of solvent (ml)}=\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}$

\n

"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "distractors": ["", "", "", "", "", "", ""], "steps": [{"prompt": "

Given that \\[\\text{percentage concentration (w/v)}=\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100},\\]

\n

to find an equation for volume of the solvent (mL), we need to get 'volume of solvent (mL)' on to the left side of the equation and then get 'percentage concentration (w/v)' on the right hand side of the equation (so that 'volume of solvent (mL)' is by itself). To do this we multiply both sides by 'volume of solvent (mL)' and divide both sides by 'percentage concentration (w/v)' 

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\text{percentage concentration (w/v)}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100}$
 
$\\text{percentage concentration (w/v)}\\times \\text{volume of solvent (mL)}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100}\\times \\text{volume of solvent (mL)}$
 
$\\text{percentage concentration (w/v)}\\times \\text{volume of solvent (mL)}$$=$$\\text{mass of solute (g)}\\times \\text{100}$
 
$\\dfrac{\\text{percentage concentration (w/v)}\\times \\text{volume of solvent (mL)}}{\\text{percentage concentration (w/v)}}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}\\times \\text{100}$
 
$\\text{volume of solvent (mL)}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}\\times \\text{100}$
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https://en.wikipedia.org/wiki/Mass_concentration_(chemistry)#Usage_in_biology

", "description": "

For Nursing and midwifery

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A solution has a percentage concentration of {ansb} % w/v of {chem}. It was made by mixing {millb} mL of solvent and  [[0]] grams of {chem}.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "gramsb", "minValue": "gramsb", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "

Given \\[\\text{percentage concentration (w/v)}=\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100},\\]

\n

we can substitute our values for percentage concentration and volume of solvent and rearrange to get the value of 'mass of solute (g)'. 

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\text{percentage concentration (w/v)}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100}$
 
$\\var{ansb}  \\text{ % (w/v)}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\var{millb} \\text{ mL}}\\times 100$
 
$\\dfrac{\\var{ansb}  \\text{ % (w/v)}}{100}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\var{millb} \\text{ mL}}\\times \\dfrac{100}{100}$
 
$\\dfrac{\\var{ansb}  \\text{ % (w/v)}}{100}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\var{millb} \\text{ mL}}$
 
$\\dfrac{\\var{ansb}  \\text{ % (w/v)}}{100}\\times \\var{millb} \\text{ (mL)}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\var{millb} \\text{ mL}}\\times \\var{millb} \\text{ mL}$
 
$\\var{gramsb} \\text{ (g)}$$=$$\\text{mass of solute (g)}$
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https://en.wikipedia.org/wiki/Mass_concentration_(chemistry)#Usage_in_biology

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A solution is made so it has a percentage concentration of {ansb} % w/v of {chem} by using {gramsb} grams of {chem}. This means that  [[0]] mL of solvent was used.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "millb", "minValue": "millb", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "

Given \\[\\text{percentage concentration (w/v)}=\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100},\\]

\n

we can substitute our values for percentage concentration and mass of solute and rearrange to get the value of 'volume of solvent (mL)'. 

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\text{percentage concentration (w/v)}$$=$$\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times 100$
  
$\\var{ansb} \\text{ (% w/v)}$$=$ $\\dfrac{\\var{gramsb}\\text{ (g)}}{\\text{volume of solvent (mL)}}\\times 100$
 
$\\var{ansb} \\text{ % (w/v)}\\times \\text{volume of solvent (mL)}$$=$$\\dfrac{\\var{gramsb}\\text{ (g)}}{\\text{volume of solvent (mL)}}\\times  100\\times \\text{volume of solvent (mL)}$
 
$\\var{ansb} \\text{ % (w/v)}\\times \\text{volume of solvent (mL)}$$=$$\\var{gramsb}\\text{ (g)}\\times  100$
  
$\\dfrac{\\var{ansb} \\text{ % (w/v)}\\times \\text{volume of solvent (mL)}}{\\var{ansb} \\text{ % (w/v)}}$ $=$$\\dfrac{\\var{gramsb}\\text{ (g)}\\times  100}{\\var{ansb} \\text{ % (w/v)}}$
  
$\\text{volume of solvent (mL)}$ $=$$\\dfrac{\\var{gramsb}\\text{ (g)}\\times  100}{\\var{ansb} \\text{ % (w/v)}}$
 
$\\text{volume of solvent (mL)}$$=$$\\var{millb} \\text{ (mL)}$
\n

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%w/v is annoying
https://en.wikipedia.org/wiki/Mass_concentration_(chemistry)#Usage_in_biology

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