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href="../19287/proteins-enzymes--1.html">Proteins & enzymes </a></li><li><a href="../19291/lipids-1.html">Lipids</a></li><li><a href="../19299/carbohydrates--1.html">Carbohydrates </a></li><li><a href="../19305/vitamins--1.html">Vitamins </a></li><li><a href="../19313/biochemistry-the-environment--1.html">Biochemistry & the environment </a></li><li><a href="../19336/proteins-enzymes-ahl--1.html">Proteins & enzymes (AHL) </a></li><li><a href="../19347/nucleic-acids--1.html">Nucleic acids </a></li><li><a href="../19361/biological-pigments--1.html">Biological pigments </a></li><li><a href="../19366/stereochemistry-in-biomolecules-1.html">Stereochemistry in biomolecules</a></li></ul></li><li><a href="../19390/option-c--1.html" class="father">Option C </a><ul class="level-2"><li><a href="../19391/energy-sources-1.html">Energy sources</a></li><li><a href="../19407/fossil-fuels-1.html">Fossil fuels</a></li><li><a href="../19411/nuclear-fusion-nuclear-fission-reactions-1.html">Nuclear fusion & nuclear fission reactions</a></li><li><a href="../19429/solar-energy-1.html">Solar energy</a></li><li><a href="../19437/environmental-impact-global-warming-1.html">Environmental impact - global warming</a></li><li><a href="../19453/electrochemistry-rechargeable-batteries-fuel-cells-1.html">Electrochemistry, rechargeable batteries & fuel cells</a></li><li><a href="../19458/nuclear-fusion-fission-hl--1.html">Nuclear fusion & fission (HL) </a></li><li><a href="../19470/photovoltaic-cells-and-dsscs-1.html">Photovoltaic cells and DSSCs</a></li></ul></li><li><a href="../19078/option-d-1.html" class="father">Option D</a><ul class="level-2"><li><a href="../19079/pharmaceutical-products-drug-action--1.html">Pharmaceutical products & drug action </a></li><li><a href="../19158/aspirin-penicillin--1.html">Aspirin & penicillin </a></li><li><a href="../19174/opiates-1.html">Opiates</a></li><li><a href="../19184/ph-regulation-of-the-stomach-1.html">pH regulation of the stomach</a></li><li><a href="../19194/antiviral-medications--1.html">Antiviral medications </a></li><li><a href="../19211/environmental-impact-of-some-medications-1.html">Environmental impact of some medications</a></li><li><a href="../19254/taxol-a-chiral-auxiliary-case-study-1.html">Taxol - a chiral auxiliary case study</a></li><li><a href="../19258/nuclear-medicine--1.html">Nuclear medicine </a></li><li><a href="../19273/drug-detection-analysis--1.html">Drug detection & analysis </a></li></ul></li></ul></li><li><a href="../16592/practical-scheme-of-work-ia--1.html">Practical scheme of work & IA </a><ul class="level-1"><li><a href="../16682/internal-assessment-1.html" class="father">Internal Assessment</a><ul class="level-2"><li><a href="../18892/scaffolding-the-investigation-1.html">'Scaffolding' the investigation</a></li><li><a href="../18896/timing-organisation--1.html">Timing & organisation </a></li><li><a href="../18905/choosing-the-research-question-1.html">Choosing the research question</a></li><li><a href="../18946/personal-engagement-1.html">Personal engagement</a></li><li><a href="../18950/exploration-1.html">Exploration</a></li><li><a href="../18957/analysis-1.html">Analysis</a></li><li><a href="../18965/evaluation-1.html">Evaluation</a></li><li><a href="../18966/communication-1.html">Communication</a></li><li><a href="../19882/internal-standardization-of-the-ia-1.html">Internal standardization of the IA</a></li><li><a href="../19901/submitting-the-samples-for-moderation-2.html">Submitting the samples for moderation</a></li><li><a href="../33754/ten-suggestions-for-ias-using-secondary-data-1.html">Ten suggestions for IAs using secondary data</a></li><li><a href="../37544/gaining-full-marks-for-a-databased-ia--1.html">Gaining full marks for a databased IA </a></li><li><a href="../19506/ia-example-marking-exercise--1.html">IA example & marking exercise </a></li><li><a href="../23929/genuine-examples-of-moderated-ia-reports-1.html">Genuine examples of moderated IA reports</a></li><li><a href="../25234/examples-of-teacher-marked-ia-reports--1.html">Examples of teacher-marked IA reports </a></li><li><a href="../37542/history-of-internal-assessment-1.html">History of Internal Assessment</a></li></ul></li><li><a href="../16598/mandatory-laboratory-components-1.html" class="father">Mandatory laboratory components</a><ul class="level-2"><li><a href="../16613/formula-of-magnesium-oxide--1.html">Formula of magnesium oxide </a></li><li><a href="../16612/determining-the-mr-of-an-unknown-gas-1.html">Determining the <i>M</i><sub>r</sub> of an unknown gas</a></li><li><a href="../16615/acid-base-titrations--1.html">Acid-base titrations </a></li><li><a href="../16616/a-green-acid-base-practical-1.html">A green acid-base practical</a></li><li><a href="../16617/analysis-of-aspirin-tablets-1.html">Analysis of aspirin tablets</a></li><li><a href="../16618/caco3-in-egg-shells-1.html">CaCO<sub>3</sub> in egg shells</a></li><li><a href="../16644/enthalpy-changes-1.html">Enthalpy changes</a></li><li><a href="../16631/reaction-rates-1.html">Reaction rates</a></li><li><a href="../16635/rate-dependent-factors-1.html">Rate-dependent factors</a></li><li><a href="../16636/determining-ea-for-a-reaction-1.html">Determining <i>E</i><sub>a</sub> for a reaction</a></li><li><a href="../16637/iodination-of-propanone-1.html">Iodination of propanone</a></li><li><a href="../18144/titrations-with-a-ph-meter-1.html">Titrations with a pH meter</a></li><li><a href="../18355/redox-titration-with-kmno4--1.html">Redox titration with KMnO<sub>4</sub> </a></li><li><a href="../16640/voltaic-cells-1.html">Voltaic cells</a></li><li><a href="../16659/3-d-molecular-modelling--1.html">3-D molecular modelling </a></li></ul></li><li><a href="../17168/other-good-practicals-1.html" class="father">Other good practicals</a><ul class="level-2"><li><a href="../17196/common-chemical-reactions-1.html">Common chemical reactions</a></li><li><a href="../227/elements-oxides-of-the-third-period--1.html">Elements & oxides of the third period </a></li><li><a href="../17239/the-halogens-1.html">The halogens</a></li><li><a href="../17162/boiling-points-of-mixtures-1.html">Boiling points of mixtures</a></li><li><a href="../17170/polarity-of-molecules-1.html">Polarity of molecules</a></li><li><a href="../18083/le-chateliers-principle--1.html">Le Chatelier's principle </a></li><li><a href="../19582/determining-kc-for-an-esterification-reaction-1.html">Determining <i>K</i><sub>c</sub> for an esterification reaction</a></li><li><a href="../18164/redox-reactions-of-vanadium--1.html">Redox reactions of vanadium </a></li><li><a href="../18351/chlorine-in-swimming-pools--1.html">Chlorine in swimming pools </a></li><li><a href="../18178/analysis-of-cuii-ions-in-solution--1.html">Analysis of Cu(II) ions in solution </a></li><li><a href="../18179/percentage-of-copper-in-brass-1.html">Percentage of copper in brass</a></li><li><a href="../18356/electrolytic-cells--1.html">Electrolytic cells </a></li><li><a href="../18598/reactions-of-organic-compounds-1.html">Reactions of organic compounds</a></li><li><a href="../18752/hydrolysis-of-halogenoalkanes-1.html">Hydrolysis of halogenoalkanes</a></li><li><a href="../18784/preparation-of-13-dinitrobenzene--1.html">Preparation of 1,3-dinitrobenzene </a></li><li><a href="../19022/determination-of-an-organic-structure-1.html">Determination of an organic structure</a></li><li><a href="../19887/preparation-of-nylon-66-1.html">Preparation of nylon 6,6</a></li><li><a href="../19343/determination-of-vitamin-c-content--1.html">Determination of vitamin C content </a></li><li><a href="../19342/hydrolysis-of-starch--1.html">Hydrolysis of starch </a></li><li><a href="../19159/preparation-purification-of-aspirin--1.html">Preparation & purification of aspirin </a></li></ul></li><li><a href="../18851/ict-in-practical-work-1.html" class="father">ICT in practical work</a><ul class="level-2"><li><a href="../18852/data-logging--1.html">Data logging </a></li><li><a href="../18853/software-for-graph-plotting--1.html">Software for graph plotting </a></li><li><a href="../18854/spreadsheets-for-data-processing--1.html">Spreadsheets for data processing </a></li><li><a href="../18855/databases-1.html">Databases</a></li><li><a href="../18856/computer-modelling-simulations--1.html">Computer modelling & simulations </a></li></ul></li><li><a href="../16594/group-4-project-1.html" class="father">Group 4 Project</a><ul class="level-2"><li><a href="../16595/practicalities-1.html">Practicalities</a></li><li><a href="../16596/reflective-statement--2.html">Reflective statement </a></li></ul></li><li><a href="../16666/a-new-laboratory-1.html">A new laboratory?</a></li></ul></li><li><a href="../16284/exams-1.html">Exams</a><ul class="level-1"><li><a href="../16286/essential-facts-1.html" class="father">Essential Facts</a><ul class="level-2"><li><a href="../16287/objectives-command-terms-1.html">Objectives & command terms</a></li><li><a href="../16288/grade-descriptors-1.html">Grade descriptors</a></li><li><a href="../16289/grade-boundaries-1.html">Grade boundaries</a></li></ul></li><li><a href="../16302/paper-1-multiple-choice-1.html" class="father">Paper 1 (Multiple Choice)</a><ul class="level-2"><li><a href="../16303/advice-to-students-paper-1-1.html">Advice to students (Paper 1)</a></li><li><a href="../31515/practice-paper-1-exams-1.html">Practice Paper 1 exams</a></li></ul></li><li><a href="../16305/paper-2-1.html" class="father">Paper 2</a><ul class="level-2"><li><a href="../16306/advice-to-students-paper-2-1.html">Advice to students (Paper 2)</a></li><li><a href="../16307/areas-of-difficulty-1.html">Areas of difficulty</a></li></ul></li><li><a href="../16313/paper-3--1.html" class="father">Paper 3 </a><ul class="level-2"><li><a href="../16314/advice-to-students-paper-3-1.html">Advice to students (Paper 3)</a></li><li><a href="../16342/data-response-questions-1.html">Data response questions</a></li><li><a href="../20054/experimental-work-questions-1.html">Experimental work questions</a></li></ul></li><li><a href="../16324/the-examination-process-1.html" class="father">The examination process</a><ul class="level-2"><li><a href="../16316/setting-the-exam-papers-1.html">Setting the exam papers</a></li><li><a href="../16317/predicted-grades-1.html">Predicted grades</a></li><li><a href="../16318/marking-the-papers-1.html">Marking the papers</a></li><li><a href="../16319/commenting-on-the-exams-1.html">Commenting on the exams</a></li><li><a href="../16320/grade-awarding-1.html">Grade Awarding</a></li><li><a href="../16321/enquiry-upon-results-1.html">Enquiry upon results</a></li><li><a href="../16322/chief-examiners-report-1.html">Chief Examiner's report</a></li><li><a href="../16323/retaking-the-exam-1.html">Retaking the exam</a></li></ul></li><li><a href="../16325/faqs-1.html">FAQs</a></li></ul></li><li><a href="../3147/ib-core-1.html">IB Core</a><ul class="level-1"><li><a href="../3149/learner-profile-1.html">Learner Profile</a></li><li><a href="../21735/extended-essays--1.html" class="father">Extended Essays </a><ul class="level-2"><li><a href="../21736/overview--1.html">Overview </a></li><li><a href="../21780/responsibilities-1.html">Responsibilities</a></li><li><a href="../21790/resources-1.html">Resources</a></li><li><a href="../21800/research-1.html">Research</a></li><li><a href="../21804/writing-the-essay-1.html">Writing the essay</a></li><li><a href="../21810/assessment-1.html">Assessment</a></li><li><a href="../22434/summary-of-advice--1.html">Summary of advice </a></li><li><a href="../25272/faqs--1.html">FAQs </a></li></ul></li><li><a href="../307/theory-of-knowledge-tok-1.html" class="father">Theory of Knowledge (TOK)</a><ul class="level-2"><li><a href="../41171/the-12-tok-concepts-1.html">The 12 TOK concepts</a></li><li><a href="../3507/why-tok-chemistry-1.html">Why TOK & Chemistry?</a></li><li><a href="../3505/a-modern-paradigm-1.html">A modern paradigm</a></li></ul></li></ul></li><li><a href="../17783/fast-track-to-tests-questions-1.html">Fast track to tests & questions</a><ul class="level-1"><li><a href="../17784/sl-multiple-choice-tests-on-individual-topics-1.html">SL Multiple choice tests on individual topics</a></li><li><a href="../24351/sl-multiple-choice-quizzes-on-sub-topics-1.html">SL Multiple choice 'quizzes' on sub-topics</a></li><li><a href="../31519/sl-practice-paper-1-exams-1.html">SL Practice Paper 1 exams</a></li><li><a href="../17786/sl-questions-on-each-sub-topic-1.html">SL Questions on each sub-topic</a></li><li><a href="../20431/sl-paper-3-section-a-questions-1.html">SL Paper 3 Section A questions</a></li><li><a href="../17792/sl-questions-on-the-options-1.html">SL Questions on the options</a></li><li><a href="../24897/sl-quizzes-on-option-sub-topics--1.html">SL Quizzes on option sub-topics </a></li><li><a href="../17785/hl-multiple-choice-tests-on-individual-topics-1.html">HL Multiple choice tests on individual topics</a></li><li><a href="../24352/hl-multiple-choice-quizzes-on-sub-topics-1.html">HL Multiple choice 'quizzes' on sub-topics</a></li><li><a href="../31520/hl-practice-paper-1-exams--1.html">HL Practice Paper 1 exams </a></li><li><a href="../17787/hl-questions-on-each-sub-topic--1.html">HL Questions on each sub-topic </a></li><li><a href="../20428/hl-paper-3-section-a-questions-1.html">HL Paper 3 Section A questions</a></li><li><a href="../17793/hl-questions-on-the-options-1.html">HL Questions on the options</a></li><li><a href="../24973/hl-quizzes-on-option-sub-topics-1.html">HL Quizzes on option sub-topics</a></li><li><a href="../41573/printable-versions-of-written-tasks--1.html">Printable versions of written tasks </a></li></ul></li><li class="selected"><a href="../41465/complete-course-for-students--2.html">Complete course for students </a><ul class="level-1"><li 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<nav id="sidemenu" class="side-nav"><div class="header"><span style="color: #fff;"><a href="../41465/complete-course-for-students--2.html">Complete course for students </a></span><span id="sidetreecontrol"><a title="Collapse all" rel="collapse" href="#"><i class="fa fa-minus-circle"></i></a> <a title="Expand all" rel="expand" href="#"><i class="fa fa-plus-circle"></i></a></span></div><ul class="level-0 always-expanded"><li class="ancestor parent" style="padding-left: 0px"><i class="expander fa fa-caret-right fa-rotate-90"></i><a href="../27988/full-coverage-of-each-topic-and-sub-topic-2.html" title="Full coverage of each topic and sub-topic">Full coverage of each topic and sub-topic</a></li><ul class="level-1 expanded"><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../27959/topic-1-stoichiometric-relationships-1.html" title="Topic 1 : Stoichiometric relationships">Topic 1 : Stoichiometric relationships</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27947/11-particulate-nature-of-matter-and-chemical-change--1.html" title="1.1 Particulate nature of matter and chemical change ">1.1 Particulate nature of matter and chemical change </a></li><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27954/12-the-mole-concept-1.html" title="1.2 The mole concept">1.2 The mole concept</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41469/comprehending-avogadros-constant-1.html" title="Comprehending Avogadro's constant">Comprehending Avogadro's constant</a></li></ul><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27958/13-reacting-masses-and-volumes--1.html" title="1.3 Reacting masses and volumes ">1.3 Reacting masses and volumes </a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../27960/topics-2-12-atomic-structure-1.html" title="Topics 2 & 12 : Atomic structure">Topics 2 & 12 : Atomic structure</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27961/21-the-nuclear-atom--1.html" title="2.1 The nuclear atom ">2.1 The nuclear atom </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27962/22-electron-configuration--1.html" title="2.2 Electron configuration ">2.2 Electron configuration </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27963/121-electrons-in-atoms--1.html" title="12.1 Electrons in atoms ">12.1 Electrons in atoms </a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../27965/topics-3-13-periodicity-1.html" title="Topics 3 & 13 : Periodicity">Topics 3 & 13 : Periodicity</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27966/31-the-periodic-table-1.html" title="3.1 The periodic table">3.1 The periodic table</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27967/32-periodic-trends--1.html" title="3.2 Periodic trends ">3.2 Periodic trends </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27968/131-first-row-d-block-elements-1.html" title="13.1 First-row d-block elements">13.1 First-row d-block elements</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27970/132-coloured-complexes-1.html" title="13.2 Coloured complexes">13.2 Coloured complexes</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../27971/topics-4-14-chemical-bonding-structure-1.html" title="Topics 4 & 14 : Chemical bonding & structure">Topics 4 & 14 : Chemical bonding & structure</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27972/41-ionic-bonding-structure--1.html" title="4.1 Ionic bonding & structure ">4.1 Ionic bonding & structure </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27973/42-covalent-bonding-1.html" title="4.2 Covalent bonding">4.2 Covalent bonding</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27974/43-covalent-structures-1--1.html" title="4.3 Covalent structures (1) ">4.3 Covalent structures (1) </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27980/43-covalent-structures-2--1.html" title="4.3 Covalent structures (2) ">4.3 Covalent structures (2) </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27981/44-intermolecular-forces--1.html" title="4.4 Intermolecular forces ">4.4 Intermolecular forces </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27982/45-metallic-bonding--1.html" title="4.5 Metallic bonding ">4.5 Metallic bonding </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27983/141-further-aspects-of-covalent-bonding-1.html" title="14.1 Further aspects of covalent bonding">14.1 Further aspects of covalent bonding</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27985/142-hybridization-1.html" title="14.2 Hybridization">14.2 Hybridization</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../27987/topics-5-15-energeticsthermochemistry-1.html" title="Topics 5 & 15 : Energetics/thermochemistry">Topics 5 & 15 : Energetics/thermochemistry</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27989/51-measuring-energy-changes-1.html" title="5.1 Measuring energy changes">5.1 Measuring energy changes</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27991/52-hesss-law-1.html" title="5.2 Hess's Law">5.2 Hess's Law</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27992/53-bond-enthalpies--1.html" title="5.3 Bond enthalpies ">5.3 Bond enthalpies </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27993/151-energy-cycles-1.html" title="15.1 Energy cycles">15.1 Energy cycles</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27994/152-entropy-spontaneity-1.html" title="15.2 Entropy & spontaneity">15.2 Entropy & spontaneity</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../27995/topics-6-16-chemical-kinetics-1.html" title="Topics 6 & 16 : Chemical kinetics">Topics 6 & 16 : Chemical kinetics</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27996/61-collision-theory-rates-of-reaction-1.html" title="6.1 Collision theory & rates of reaction">6.1 Collision theory & rates of reaction</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27997/161-rate-expression-reaction-mechanism-1.html" title="16.1 Rate expression & reaction mechanism">16.1 Rate expression & reaction mechanism</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27998/162-activation-energy-1.html" title="16.2 Activation energy">16.2 Activation energy</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../28001/topics-7-17-equilibrium--1.html" title="Topics 7 & 17 : Equilibrium ">Topics 7 & 17 : Equilibrium </a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../27999/71-equilibrium-1.html" title="7.1 Equilibrium">7.1 Equilibrium</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28000/171-equilibrium-law-1.html" title="17.1 Equilibrium law">17.1 Equilibrium law</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../28017/topics-8-18-acids-and-bases--1.html" title="Topics 8 & 18 : Acids and bases ">Topics 8 & 18 : Acids and bases </a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28002/81-theories-of-acids-bases-1.html" title="8.1 Theories of acids & bases">8.1 Theories of acids & bases</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28010/82-properties-of-acids-bases-1.html" title="8.2 Properties of acids & bases">8.2 Properties of acids & bases</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28011/83-ph-scale-1.html" title="8.3 pH scale">8.3 pH scale</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28012/84-strong-weak-acids-bases-1.html" title="8.4 Strong & weak acids & bases">8.4 Strong & weak acids & bases</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28013/85-acid-deposition--1.html" title="8.5 Acid deposition ">8.5 Acid deposition </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28014/181-lewis-acids-bases--1.html" title="18.1 Lewis acids & bases ">18.1 Lewis acids & bases </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28015/182-calculations-involving-acids-bases--1.html" title="18.2 Calculations involving acids & bases ">18.2 Calculations involving acids & bases </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28016/183-ph-titration-curves-1.html" title="18.3 pH titration curves">18.3 pH titration curves</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../28031/topics-9-19-redox-process-1.html" title="Topics 9 & 19 : Redox process">Topics 9 & 19 : Redox process</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28021/91-oxidation-reduction-1.html" title="9.1 Oxidation & reduction">9.1 Oxidation & reduction</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28022/92-electrochemical-cells-1.html" title="9.2 Electrochemical cells">9.2 Electrochemical cells</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28023/191-electrochemical-cells-ahl-1.html" title="19.1 Electrochemical cells (AHL)">19.1 Electrochemical cells (AHL)</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../28061/topics-10-20-organic-chemistry-1.html" title="Topics 10 & 20 : Organic chemistry">Topics 10 & 20 : Organic chemistry</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28042/101-fundamentals-of-organic-chemistry-1.html" title="10.1 Fundamentals of organic chemistry">10.1 Fundamentals of organic chemistry</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28043/1021-alkanes-alkenes-addition-polymers-1.html" title="10.2(1) Alkanes, alkenes & addition polymers">10.2(1) Alkanes, alkenes & addition polymers</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28044/1022-alcohols--1.html" title="10.2(2) Alcohols ">10.2(2) Alcohols </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28047/1023-halogenoalkanes-benzene-1.html" title="10.2(3) Halogenoalkanes & benzene">10.2(3) Halogenoalkanes & benzene</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28050/2011-nucleophilic-substitution--1.html" title="20.1(1) Nucleophilic substitution ">20.1(1) Nucleophilic substitution </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28051/2012-electrophilic-addition--1.html" title="20.1(2) Electrophilic addition ">20.1(2) Electrophilic addition </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28053/2013-electrophilic-substitution-1.html" title="20.1(3) Electrophilic substitution">20.1(3) Electrophilic substitution</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28054/2014-reduction-reactions--1.html" title="20.1(4) Reduction reactions ">20.1(4) Reduction reactions </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28056/202-synthetic-routes--1.html" title="20.2 Synthetic routes ">20.2 Synthetic routes </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28059/203-stereoisomerism--1.html" title="20.3 Stereoisomerism ">20.3 Stereoisomerism </a></li></ul><li class="ancestor parent" style="padding-left: 14px"><i class="expander fa fa-caret-right fa-rotate-90"></i><a href="../28038/topics-11-21-measurement-data-processing-analysis-1.html" title="Topics 11 & 21 : Measurement, data processing & analysis">Topics 11 & 21 : Measurement, data processing & analysis</a></li><ul class="level-2 expanded"><li class="current" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="111-uncertainty-errors--1.html" title="11.1 Uncertainty & errors ">11.1 Uncertainty & errors </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28033/112-graphical-techniques-1.html" title="11.2 Graphical techniques">11.2 Graphical techniques</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28034/113-spectroscopic-identification-of-organic-compounds-1.html" title="11.3 Spectroscopic identification of organic compounds">11.3 Spectroscopic identification of organic compounds</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28039/211-spectroscopic-identification-of-organic-compounds-ahl-1.html" title="21.1 Spectroscopic identification of organic compounds (AHL)">21.1 Spectroscopic identification of organic compounds (AHL)</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../28074/option-a-materials--1.html" title="Option A : Materials ">Option A : Materials </a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28062/a1-introduction-to-materials-science--1.html" title="A.1 Introduction to materials science ">A.1 Introduction to materials science </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28063/a2-metals-and-icp-spectroscopy-1.html" title="A.2 Metals and ICP spectroscopy">A.2 Metals and ICP spectroscopy</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28065/a3-catalysts--1.html" title="A.3 Catalysts ">A.3 Catalysts </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28066/a4-liquid-crystals-1.html" title="A.4 Liquid crystals">A.4 Liquid crystals</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28067/a5-polymers-1.html" title="A.5 Polymers">A.5 Polymers</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28069/a6-nanotechnology-1.html" title="A.6 Nanotechnology">A.6 Nanotechnology</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28070/a7-environmental-impact-plastics-1.html" title="A.7 Environmental impact - plastics">A.7 Environmental impact - plastics</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28071/a8-superconducting-metals-x-ray-crystallography--1.html" title="A.8 Superconducting metals & X-ray crystallography ">A.8 Superconducting metals & X-ray crystallography </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28072/a9-condensation-polymers-1.html" title="A.9 Condensation polymers">A.9 Condensation polymers</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28073/a10-environmental-impact-heavy-metals-1.html" title="A.10 Environmental impact - heavy metals">A.10 Environmental impact - heavy metals</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../28087/option-b-biochemistry-1.html" title="Option B : Biochemistry">Option B : Biochemistry</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28076/b1-introduction-to-biochemistry--1.html" title="B.1 Introduction to biochemistry ">B.1 Introduction to biochemistry </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28078/b2-proteins-enzymes-1.html" title="B.2 Proteins & enzymes">B.2 Proteins & enzymes</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28079/b3-lipids-1.html" title="B.3 Lipids">B.3 Lipids</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28080/b4-carbohydrates-1.html" title="B.4 Carbohydrates">B.4 Carbohydrates</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28081/b5-vitamins-1.html" title="B.5 Vitamins">B.5 Vitamins</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28082/b6-biochemistry-the-environment-1.html" title="B.6 Biochemistry & the environment">B.6 Biochemistry & the environment</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28083/b7-proteins-enzymes-ahl--1.html" title="B.7 Proteins & enzymes (AHL) ">B.7 Proteins & enzymes (AHL) </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28084/b8-nucleic-acids-1.html" title="B.8 Nucleic acids">B.8 Nucleic acids</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28085/b9-biological-pigments-1.html" title="B.9 Biological pigments">B.9 Biological pigments</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28086/b10-stereochemistry-in-biomolecules-1.html" title="B.10 Stereochemistry in biomolecules">B.10 Stereochemistry in biomolecules</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../28098/option-c-energy--1.html" title="Option C : Energy ">Option C : Energy </a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28088/c1-energy-sources--1.html" title="C.1 Energy sources ">C.1 Energy sources </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28089/c2-fossil-fuels-1.html" title="C.2 Fossil fuels">C.2 Fossil fuels</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28090/c3-nuclear-fusion-nuclear-fission-reactions-1.html" title="C.3 Nuclear fusion & nuclear fission reactions">C.3 Nuclear fusion & nuclear fission reactions</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28091/c4-solar-energy--1.html" title="C.4 Solar energy ">C.4 Solar energy </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28094/c5-environmental-impact-global-warming--1.html" title="C.5 Environmental impact - global warming ">C.5 Environmental impact - global warming </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28095/c6-electrochemistry-rechargeable-batteries-fuel-cells-1.html" title="C.6 Electrochemistry, rechargeable batteries & fuel cells">C.6 Electrochemistry, rechargeable batteries & fuel cells</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28096/c7-nuclear-fusion-fission-hl--1.html" title="C.7 Nuclear fusion & fission (HL) ">C.7 Nuclear fusion & fission (HL) </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28097/c8-photovoltaic-cells-and-dsscs-1.html" title="C.8 Photovoltaic cells and DSSCs">C.8 Photovoltaic cells and DSSCs</a></li></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../28109/option-d-medicinal-chemistry-1.html" title="Option D : Medicinal chemistry">Option D : Medicinal chemistry</a></li><ul class="level-2 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28099/d1-pharmaceutical-products-drug-action--1.html" title="D.1 Pharmaceutical products & drug action ">D.1 Pharmaceutical products & drug action </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28100/d2-aspirin-penicillin-1.html" title="D.2 Aspirin & penicillin">D.2 Aspirin & penicillin</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28101/d3-opiates-1.html" title="D.3 Opiates">D.3 Opiates</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28103/d4-ph-regulation-of-the-stomach-1.html" title="D.4 pH regulation of the stomach">D.4 pH regulation of the stomach</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28102/d5-antiviral-medications-1.html" title="D.5 Antiviral medications">D.5 Antiviral medications</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28104/d6-environmental-impact-of-some-medications-1.html" title="D.6 Environmental impact of some medications">D.6 Environmental impact of some medications</a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28105/d7-taxol-a-chiral-auxiliary-case-study--1.html" title="D.7 Taxol - a chiral auxiliary case study ">D.7 Taxol - a chiral auxiliary case study </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28107/d8-nuclear-medicine--1.html" title="D.8 Nuclear medicine ">D.8 Nuclear medicine </a></li><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28108/d9-drug-detection-analysis-1.html" title="D.9 Drug detection & analysis">D.9 Drug detection & analysis</a></li></ul></ul><li class=" parent" style="padding-left: 0px"><i class="expander fa fa-caret-right 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</div><section id="main-content"><div id="toc-1672969278" class="toc"><a href="#" class="toc-switcher" title="Show table of contents"><small><i class="fa fa-reorder"></i> Table of contents <span class="pull-right"><i class="fa fa-chevron-down"></i></span></small></a></div><p>Written specifically for students to provide help and support for the IB Diploma chemistry <span data-scayt-word="programme" data-wsc-lang="en_US">programme</span> this page provides full coverage of the syllabus content of Topic 11.1 Uncertainty & errors. It encourages you to think critically and provides many questions with full worked answers so that you can monitor and improve your knowledge and understanding.</p><div class="box"><h2><img alt="" src="../../../ib/chemistry/images/student-learning/pipette-uncertainty(1).png" style="width: 1px; height: 1px;">Learning outcomes</h2><p>After studying this topic you should be able to:</p><p><strong><strong><img alt="" class="noborder" src="../../../ib/chemistry/images/student-learning/pipette-uncertainty(1).png" style="float: right; width: 334px; height: 407px;">Understand:</strong></strong></p><ul><li>Qualitative data are not obtained from measurement but include all non-numerical information obtained from observations.</li><li>Quantitative data are obtained from measurements. They are affected by human limitations such as reaction times and are always associated with random errors/uncertainties, determined by the apparatus used to measure them.</li><li>The impact of the uncertainties on the final result is shown by the propagation of random errors in data processing.</li><li>Systematic errors in measurement are caused by experimental design and procedure and normally lead to a deviation in a particular direction.</li><li>Random errors, but not systematic errors, will be reduced by repeated trials and measurements.</li></ul><p><strong>Apply your knowledge to:</strong></p><ul><li>Distinguish between random errors and systematic errors.</li><li>Record all measurements together with their associated uncertainties as a range (±) to an appropriate precision.</li><li>Discuss ways to reduce uncertainties in an experiment.</li><li>Propagate uncertainties in processed data, including the use of percentage uncertainties.</li><li>Discuss the impact of systematic errors on the results obtained in all experimental work and how they can be reduced.</li><li>Estimate whether particular sources of error are likely to have a major or minor effect on the final result.</li><li>Calculate the percentage error by comparing the experimental result with a theoretical or accepted result whenever possible.</li><li>Distinguish between accuracy and precision when evaluating results.<hr class="hidden"></li></ul></div><hr class="hidden"><div class="blueBg"><h2>Relationships & vocabulary</h2><h4>Nature of science</h4><p>Replication of quantitative measurements is crucial to ensure reliability—precision, accuracy, systematic, and random errors can only be interpreted properly through replication.</p><hr class="hidden"><h4>International-mindedness</h4><p>The International Standards Organization (ISO) published the Guide to the Expression of Uncertainty in Measurement in 1995. This was a result of seven international organizations, including IUPAC, collaborating together. It has been translated into several different languages and has been widely adopted in most countries.</p><hr class="hidden"><p>For more examples and links to <em>International mindedness, Theory of knowledge, utilization etc. </em>see <a href="../17269/topics-11-21--1.html" title="Core & AHL » Incorporating IM, TOK, 'Utilization' etc. » Topics 4 & 14 ">separate page</a> which covers all of Topics 11 & 21 : Measurement, data processing and analysis.</p><hr class="hidden"><h4>Vocabulary</h4><table><tbody><tr><td>quantitative data</td><td>error</td><td>random error</td><td>systematic error</td></tr><tr><td>uncertainty</td><td>percentage uncertainty</td><td>qualitative data</td><td></td></tr></tbody></table><hr class="hidden"></div><hr class="hidden"><div class="greenBg"><h2 id="header-6">Learning slides</h2><p>You can use this slide gallery for learning or for reviewing concepts and information. It covers all the key points in the syllabus for this sub-topic.</p><div id="myCarousel-9" class="carousel slide" data-id="351"><!-- Carousel items --><div class="carousel-inner"><div class="active item"><a class="fancy" href="../../../tib-galleries/3-351/1111.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1111.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1112.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1112.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1113.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1113.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1114.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1114.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="/files/tib-galleries/3-351/changed-.png" rel="gallery-351" title=""><img alt="" src="/files/tib-galleries/3-351/changed-.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1116.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1116.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1117.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1117.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1118.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1118.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1119.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1119.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="/files/tib-galleries/3-351/new-10.png" rel="gallery-351" title=""><img alt="" src="/files/tib-galleries/3-351/new-10.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/111-111.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/111-111.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/11112.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/11112.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div></div><!-- Carousel nav --><a class="carousel-control left" href="#myCarousel-9" data-slide="prev">‹</a><a class="carousel-control right" href="#myCarousel-9" data-slide="next">›</a><div class="tib-indicators"><img class="" title="Click to view" style="margin: 10px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1111-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1112-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1113-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1114-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="/files/tib-galleries/3-351/changed--thumb128.png"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1116-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1117-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1118-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1119-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="/files/tib-galleries/3-351/new-10-thumb128.png"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/111-111-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/11112-thumb128.jpg"></div></div><p> </p></div><hr class="hidden"><div class="pinkBg"><div><h2>Something to think about</h2><p><strong>1. Accuracy and precision</strong></p><p>When marking titration results it is not unusual to come across something like this:</p><p>Titration of 25.00 cm<sup>3</sup> of <em>x</em> mol dm<sup>-3</sup> hydrochloric acid with a standardized solution of 1.00 mol dm<sup>-3</sup> sodium hydroxide solution.</p><p align="center"><img alt="" class="noborder" height="87" src="../../../ib/chemistry/images/Core and AHL/Topic 11 uncertainty/Titration table.png" width="640"><br>Average volume of 1.00 mol dm<sup>-3</sup> NaOH(aq) required to titrate 25.00 cm<sup>3</sup> of <em>x</em> mol dm<sup>-3</sup> HCl(aq) = 25.00 cm<sup>3</sup></p><p>The student then proceeds to calculate the unknown concentration of the hydrochloric acid as 1.00 mol dm<sup>-3</sup> and work out the associated uncertainty by summing up the percentage uncertainties of the apparatus used to give an answer something like 1.00 ± 0.02 mol dm<sup>-3</sup>. They then think that they have listed all their uncertainties and applied them as they are supposed to do.<br><br>There is no awareness that the results achieved by the experimenter are poor and not precise. Titration is a reproducible procedure. If the burette and pipette are accurate to ± 0.10 cm<sup>3</sup> and 0.05 cm<sup>3</sup> respectively then the ‘accurate readings’ on the burette should be in agreement within ± 0.15 cm<sup>3</sup>. A difference of more than 0.15 cm<sup>3</sup> in the accurate results suggests that the experimenter was not carrying out the procedure correctly. They should, in fact continue to repeat the titration until they do get agreement to within ± 0.15 cm<sup>3</sup> for their ‘accurate’ results. Too often when evaluating an experiment students blindly follow the instructions on how to calculate uncertainties without applying or understanding the real assumptions made. Even if you do get reproducible accurate titration results you should also question whether the concentration of the ‘standardized’ sodium hydroxide solution made up by the teacher/technician (and therefore beyond your control) was exactly 1.00 mol dm<sup>-3</sup>. An example like this can be used to illustrate the importance of distinguishing between random errors and systematic errors. Repeating the titration several times will help to reduce random errors although none of the values should differ by more than ± 0.15 cm<sup>3</sup>. If the concentration of the sodium hydroxide solution was in fact 1.10 mol dm<sup>-3</sup> then a systematic error of 10% will apply no matter how many titrations are completed or at least until the correct concentration of the standardized solution is used.</p><hr class="hidden"><p><strong>2. Determining the uncertainty associated with a reading</strong></p><p>Consider using a 1 metre ruler with an uncertainty of ± 0.01 metre to measure a 2 metre length. Because the ruler would be needed to be used twice the length would be expressed as 2.00 ± 0.02 metres as the uncertainties are simply added. This is quite logical as the first measured value would lie between 0.99 and 1.01 m. The second value would be the same so when adding them together the value would lie between 1.98 and 2.02 m, i.e. 2.00 ± 0.02 m. Similarly if a thermometer accurate to ± 0.5 <sup>o</sup>C is used to measure a temperature difference then if the two readings were 19.1 <sup>o</sup>C and 26.9 <sup>o</sup>C the temperature difference should be recorded as 7.8 ± 1.0 <sup>o</sup>C as uncertainties are also added when the measured values are subtracted.<br>In fact, although seemingly logical and accepted by the IB, this is a simplified approach. A more sophisticated treatment uses the relationship:</p><hr class="hidden"><p style="text-align: center;">The cumulative (or total) uncertainty = the square root of the sum of the squares of the absolute uncertainties.</p><hr class="hidden"><p>If this is applied to the metre ruler data above the cumulative uncertainty = √[(0.01)<sup>2</sup> + (0.01)<sup>2</sup>] = 0.014 = 0.01 to one significant figure.</p><hr class="hidden"><p>The IB generally wants to see an awareness of uncertainties rather than insisting on a particular approach and accepts any recognised method of calculation of cumulative uncertainties.</p><hr class="hidden"><p><img alt="" class="left noborder" height="400" src="../../../ib/chemistry/images/Core%20and%20AHL/Topic%2011%20uncertainty/VEE%20GEE%2020114-Series%20Burets-500x500.jpg" title="If the burette says + or - 0.05 cm3 should the uncertainty for thevolume actually used be + or - 0.05 cm3 or 0.10 cm3? or " width="400">It is not quite so obvious when certain instruments are used even though technically two readings are taken. Consider measuring the mass of something using a balance accurate to ± 0.001 g. If the balance is reading zero and say an empty weighing bottle is placed on the balance then the mass of the weighing bottle might be recorded as 20.034 ± 0.001 g. If about ten grams of magnesium are placed in the weighing bottle and the new mass is 30.456 g then it would be usual to record the accurate mass of the magnesium as 10.422 ± 0.002 g. But is this really correct? When the balance was reading zero it is actually accurate to ± 0.001 g i.e. zero is a mass between - 0.001 and + 0.001 g so the mass of the weighing bottle should really be recorded as 20.034 ± 0.002 g and the mass of the magnesium, which is now the result of three separate readings, 10.422 ± 0.003 g. A sensible person will question whether this sort of pedantic attention to detail is really necessary. It isn't, but because of both studnets' and teacher's insecurity with how their IA marks are moderated it has almost become so. In fact instruments that rely on two readings for any measurement e.g. a balance or a burette state on them their uncertainty. A burette for example might say 50 cm<sup>3</sup> accurate to 0.05 cm<sup>3</sup><sup> </sup>(see image on left - although it gives the units as ml rather than cm<sup>3</sup>). What many people take this to mean is that the uncertainty for the actual volume measured can be taken as ± 0.05 cm<sup>3</sup> even though it has been arrived at by taking the difference between the final and initial readings so arguably should actually be quoted as ± 0.10 cm<sup>3</sup>. Luckily the IA moderators are told to accept <strong>either</strong> the actual uncertainty stated on the instrument (or the estimated uncertainty if no value is given) <strong>or</strong> double the uncertainty when moderating student's internal assessment work if the student reports it in their Individual Scientific Investigation.</p><hr class="hidden"></div></div><hr class="hidden"><div class="yellowBg"><h2 id="header-8">Test your understanding of this topic</h2><p><em>(Note that your teacher may have restricted your access to some or all of these questions and worked answers if they are going to use them as a class test or set them as an assignment.)</em></p><hr class="hidden"><p>For ten 'quiz' multiple choice questions with the answers explained see <a href="../24818/mc-test-uncertainties-errors-1.html" title="Core & AHL » Teaching each topic & sub-topic » Topics 11 & 21 » Uncertainty & errors » MC test: Uncertainties & errors">MC test: Uncertainties & errors</a>.</p><p style="margin: 0px 0px 1em; padding: 0px; color: rgb(0, 0, 0); font-size: 1em;">For short-answer questions see <a href="../38869/uncertainty-error-questions--1.html" title="Core & AHL » Teaching each topic & sub-topic » Topics 11 & 21 » Uncertainty & errors » Uncertainty & error questions ">Uncertainty & error questions</a>.</p><hr class="hidden"></div><hr class="hidden"><div class="blueBg"><h2><span style="font-weight: bold;">More resources</span></h2><p><strong>1.</strong> Stephanie Bell at the National Physics Laboratory has produced a really good guide entitled,<a href="http://www.npl.co.uk/publications/guides/a-beginners-guide-to-uncertainty-of-measurement"> "Beginners Guide to Uncertainty of Measurement" <img class="ico" src="../../../img/icons/pdf-1.png">.</a> An electronic version can be downloaded free.</p><hr class="hidden"><p><strong>2. </strong>Precision versus accuracy by The Chemistry Solution. It contains some useful information for answering multiple choice questions on this topic.</p><p style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="280" src="//www.youtube.com/embed/TzLnO04uO30?rel=0" width="360"></iframe></p><p style="text-align: center;"><a href="http://youtu.be/TzLnO04uO30">Precision v accuracy <img class="ico" src="../../../img/icons/video-1.png"><span class="anchor" id="video-1" name="video-1"> </span></a></p><hr class="hidden"><p><strong>3.</strong> Uncertainty in measurements by lewischemistry.</p><p style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="280" src="//www.youtube.com/embed/F7YKc4SOZz4?rel=0" width="360"></iframe></p><p style="text-align: center; "><a href="http://youtu.be/F7YKc4SOZz4">Uncertainty in measurements <img class="ico" height="16" src="../../../img/icons/video-1.png" width="16"><span class="anchor" id="video-2" name="video-2"> </span></a></p><p style="text-align: center; "></p><hr class="hidden"><p><strong>4. </strong>Using significant figures by Brightstorm<strong> </strong></p><p style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="280" src="//www.youtube.com/embed/_jZAe9xeTFA?rel=0" width="360"></iframe></p><p style="text-align: center;"><a href="http://youtu.be/_jZAe9xeTFA">Using significant figures <img class="ico" src="../../../img/icons/video-1.png"><span class="anchor" id="video-3" name="video-3"> </span></a></p><hr class="hidden"><p><strong>5. </strong>Calculating overall uncertainties by Richard Thornley</p><p style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="280" src="//www.youtube.com/embed/B7dKWE-0FZY?rel=0" width="360"></iframe></p><div style="text-align: center;"><object height="280" width="360"><param name="movie" value="//www.youtube.com/v/B7dKWE-0FZY?version=3&hl=en_GB&rel=0"><param name="allowFullScreen" value="true"><param name="allowscriptaccess" value="always"></object><a href="http://youtu.be/B7dKWE-0FZY">Calculating overall uncertainties </a><a href="http://youtu.be/_jZAe9xeTFA"><img class="ico" src="../../../img/icons/video-1.png"><span class="anchor" id="video-4" name="video-4"> </span></a><hr class="hidden"></div></div></section></article><section id="media-extras"><div class="page-actions no-print navbar inline hidden-desktop"><div class="navbar-inner"><ul class="nav"><li><a class="presentation" href="#" onclick="return false;"><i class="fa fa-desktop"></i></a></li><li><a class="print-section-blog" href="#" onclick="return false;"><i class="fa fa-print"></i></a></li><li><a class="page-bookmarker" data-ticket="IB Docs (2) Team" data-pid="28032" href="#" onclick="return false;"><i class="fa fa-star"></i></a></li><li><a class="personal-notes" href="#" onclick="return false;"><i class="fa fa-file-text"></i></a></li><li><a class="" data-toggle="modal" href="#modal-feedback" onclick="return false;"><i class="fa fa-envelope-o"></i></a></li><li class="dropdown"><a class="dropdown-toggle" data-toggle="dropdown" data-target="#" href="#"><i class="fa fa-share-alt"></i></a><ul class="dropdown-menu" role="menu"><li><a class="" target="_blank" title="Share on Twitter" href="https://twitter.com/share?text=%2211.1+Uncertainty+%26+errors+%22+-+via+%40InThinker+%23chemistry%0A&url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F28032%2F111-uncertainty-errors-"><i class="fa fa-twitter-square"></i><span>Twitter</span></a></li><li><a class="" target="_blank" title="Share on Facebook" href="https://www.facebook.com/sharer.php?u=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F28032%2F111-uncertainty-errors-&t=11.1+Uncertainty+&+errors+"><i class="fa fa-facebook-square"></i><span>Facebook</span></a></li><li><a class="" href="http://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F28032%2F111-uncertainty-errors-"><i class="fa fa-linkedin-square"></i><span>LinkedIn</span></a></li><li><a class="" href="https://plus.google.com/share?url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F28032%2F111-uncertainty-errors-"><i class="fa fa-google-plus-square"></i><span>Google +</span></a></li><li><a class="" href="mailto:?subject=11.1 Uncertainty & errors &body=Written specifically for students to provide help and support for the IB Diploma chemistry programme this page provides full coverage of the syllabus content of Topic 11.1 Uncertainty & errors. 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