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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 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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 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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=" parent" style="padding-left: 0px"><i class="expander fa fa-caret-right "></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 "><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=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></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 "><li class="" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../28032/111-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 "></i><a 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</div><section id="main-content"><p>Students often use mathematical formulas to solve chemical problems in exams and sometimes arrive at the wrong answer. This page looks at why this is so and encourages you to work always from first principles rather than mindlessly 'plug' values into a formula that you are unable to derive for yourself. It gives worked examples and provides some further practice questions with worked answers.</p><p style="text-align: center;"><img alt="" class="noborder" src="../../../ib/chemistry/images/2014%20Exams/m1v1%3Dm2v2.png" style="width: 234px; height: 88px;"></p><div class="blueBg"><h1>Introduction</h1><p>Both mathematics and science make much use of formulas to solve problems. There is nothing inherently wrong in using a formula. In fact in many cases it can save a considerable amount of time. For example, Einstein is reputed to have said that compound interest is the eighth wonder of the world – “He who understands it earns it… he who doesn’t… pays it.”. A person who 30 years ago put $1000 dollars in an investment account that paid 7% interest per year ($0.07 per dollar) would have gained 30 x $70 in interest if the interest had been withdrawn at the end of each year giving a total sum of $3100 if the original investment is also included. However if the interest had been left in the account the formula A = P (1 + r)<sup>t</sup> (where A = the future value, P = the principal investment amount, r = the interest rate and t = time) shows that the $1000 initial investment would have grown to $7612 after 30 years. If it had been left for 50 years the figures would have been $4500 and $29460 respectively. Clearly using this particular formula saves all the tedious work of working out the increase and compounding it for each year etc.</p><hr class="hidden"><p>Unfortunately some chemistry students who make considerable use of formulas in exams often arrive at the wrong answer because they have either misused a formula or have been unable to apply the correct formula to solve the problem.</p><hr class="hidden"><p>There are several reasons why this may be so.</p><hr class="hidden"></div><hr class="hidden"><div class="yellowBg"><h1>Reasons for errors using formulas</h1><h4>1. The formula is remembered wrongly.</h4><p>A simple formula often used to find the concentration of a solution is:</p><p>c = n / V (where c is the concentration, n is ‘number of moles’ (actually amount in mol) and V is the volume).</p><p>I’ve seen several variations of this in exams, e.g. c = V / n or n = c / V. The key to stating formulas correctly is to check the units. Concentration is normally expressed as mol dm<sup>−3</sup>. Once you realise this the formula is redundant as mol dm<sup>−</sup><sup>3</sup> literally means the amount in mol divided by the volume in litres (dm<sup>3</sup>). Another example where the formula is often quoted wrongly is the relationship between the velocity of light (<em>c</em>), the frequency (ν) and the wavelength (λ).</p><p>Looking at the units it is obvious that velocity (m s<sup>−1</sup>) = wavelength (m) x frequency (s<sup>−1</sup>), i.e. <em>c</em> = <em>λν</em>.</p><hr class="hidden"><hr class="hidden"><h4>2. The formula is applied wrongly</h4><p>One of the most common examples of this is the formula M<sub>1</sub>V<sub>1</sub> = M<sub>2</sub>V<sub>2</sub> which students often use to solve titration problems. It does work in the simplest case when one mole of an acid is neutralised by one mole of a base,</p><p>e.g. HCl(aq) + NaOH(aq) → NaCl(aq) + H<sub>2</sub>O(l)</p><p>but certainly does not work when it comes to the neutralisation of diprotic acids,</p><p>e.g. H<sub>2</sub>SO<sub>4</sub>(aq) + 2NaOH(aq) → Na<sub>2</sub>SO<sub>4</sub>(aq) + 2H<sub>2</sub>O(l).</p><p>My advice is to never use it! Instead always work from first principles.</p><h4><span style="color:#FF0000;">Worked example:</span></h4><p>26.80 cm<sup>3</sup> of a solution of sulfuric acid was required to neutralise 25.00 cm<sup>3</sup> of 0.150 mol dm<sup>−3</sup> potassium hydroxide solution. Calculate the concentration of the sulfuric acid solution in mol dm<sup>-3</sup>.</p><p><strong>Step 1: </strong>Write the stoichiometric equation</p><p>H<sub>2</sub>SO<sub>4</sub>(aq) + 2KOH(aq) → K<sub>2</sub>SO<sub>4</sub>(aq) + 2H<sub>2</sub>O(l)</p><hr class="hidden"><p><strong>Step 2: </strong>Calculate the amount (in mol) of potassium hydroxide present.</p><p>1000 cm<sup>3</sup> of 0.150 mol dm<sup>−3</sup> KOH contains 0.150 mol</p><p>so 25.00 cm<sup>3</sup> contains (25.00/1000) x 0.150 = 3.75 x 10<sup>−3</sup> mol.</p><hr class="hidden"><p><strong>Step 3: </strong>Calculate the amount (in mol) of sulfuric acid required to neutralise the potassium hydroxide solution.</p><p>From the equation 1 mol of H<sub>2</sub>SO<sub>4</sub> neutralises 2 mol of KOH so amount of H<sub>2</sub>SO<sub>4</sub> required = ½ x 3.75 x 10<sup>−3</sup> = 1.875 x 10<sup>−3</sup> mol.</p><hr class="hidden"><p><strong>Step 4: </strong>Calculate the concentration of the sulfuric acid in mol dm<sup>−3</sup>.</p><p>26.80 cm<sup>3</sup> of H<sub>2</sub>SO<sub>4</sub> contains 1.875 x 10<sup>−3</sup> mol</p><p>1000 cm<sup>3</sup> of H<sub>2</sub>SO<sub>4</sub> contains (1000/26.80) x 1.875 x 10<sup>−3</sup> = 0.0700 mol</p><p>so the concentration of the sulfuric acid = 0.0700 mol dm<sup>−3</sup> (to 3 significant figures).</p><hr class="hidden"><hr class="hidden"><h4>3. A formula cannot be used at all.</h4><p>A back to basics stepwise approach is the only way to answer titration questions where a solid, rather than a solution, is being titrated as the formula M<sub>1</sub>V<sub>1</sub> = M<sub>2</sub>V<sub>2</sub> cannot be applied.</p><h4><span style="color:#FF0000;">Example:</span></h4><p>What mass of calcium carbonate will react exactly with 20.00 cm<sup>3</sup> of 0.200 mol dm<sup>−3</sup> hydrochloric acid?</p><p>Equation: 2HCl(aq) + CaCO<sub>3</sub>(s) → CaCl<sub>2</sub>(aq) + CO<sub>2</sub>(g) + H<sub>2</sub>O(l)</p><p>Amount of acid reacting = 20.00/1000 x 0.200 = 4.00 x 10<sup>−3</sup> mol</p><p>Since two mol of HCl react with one mol of CaCO<sub>3</sub></p><p>Amount of CaCO<sub>3</sub> that reacts = ½ x 4.00 x 10<sup>-3</sup> = 2.00 x 10<sup>−3</sup> mol</p><p><em>M</em>(CaCO<sub>3</sub>) = 40.08 + 12.01 + (3 x 16.00) = 100.09 g mol<sup>−1</sup></p><p>Mass of CaCO<sub>3</sub> that reacts with the acid = 100.09 x 2.00 x 10<sup>−3</sup> = 0.200 g ( to 3 significant figures).</p><hr class="hidden"><hr class="hidden"><h4>4.The wrong units are used.</h4><p class="MsoNormal">The classic example of where this often occurs is when students use the equation</p><p class="MsoNormal"><em>ΔG</em> = <em>ΔH </em>– <em>TΔS</em></p><p class="MsoNormal"><em>ΔG</em> and <em>ΔH</em> values are usually quoted in kJ mol<sup>−1</sup> but entropy values are normally quoted in J K<sup>−1</sup> mol<sup>−1.</sup> Constantly remind yourself that you must divide the entropy value by 1000 to convert it into kJ K<sup>−1</sup> mol<sup>−1</sup> when using it in the equation. Of course you also need to ensure that you give the temperature in Kelvin not <sup>o</sup>C.</p><p class="MsoNormal">Other examples of formulas where units must be consistent are the gas equation <em>pV</em> = <em>nRT</em> and rate equations as the units of the rate constant depend upon the overall order of the reaction.</p><hr class="hidden"><hr class="hidden"><h4>5. Problems with the Henderson–Hasselbalch equation.</h4><p>This formula causes particular problems although strictly speaking calculations involving buffer solutions should only appear in Paper 3.</p><p>The theory of buffer solutions is covered at Higher Level in the AHL Topic 18 but buffer calculations only appear in two of the options in Paper 3. However even though buffers are not coved at Standard Level in the core, Option D includes the application of the Henderson–Hasselbalch equation at both SL and HL whereas in option B it is only on the HL syllabus. The use of the Henderson–Hasselbalch equation in Option D can cause real problems for Standard Level students who have not covered either equilibrium calculations or the definitions of <em>K</em><sub>a</sub>, <em>K</em><sub>b</sub>, p<em>K</em><sub>a</sub> and p<em>K</em><sub>b</sub>.</p><p>The Henderson–Hasselbalch equation is given in Section 1 of the IB data booklet but it seems unwise for students to use it if they do not fully understand it. It is easy to use wrongly and I never teach it to my students as I prefer them to be able to work out all buffer calculations from first principles.</p><hr class="hidden"><h4><span style="color:#FF0000;">Example using first principles</span></h4><p>Calculate the pH of a buffer solution made by adding 20.0 cm<sup>3</sup> of 1.00 mol dm<sup>−3</sup> sodium hydroxide solution to 40.0 cm<sup>3</sup> of 1.00 mol dm<sup>-3</sup> ethanoic acid solution. Section 21 of the IB data booklet gives the p<em>K</em><sub>a</sub> of ethanoic acid = 4.76</p><p>(Standard level students need to understand that <em>K</em><sub>a</sub> is the equilibrium constant (acid dissociation constant) for a weak acid and that p<em>K</em><sub>a</sub> = − log<sub>10</sub><em>K</em><sub>a</sub> (this is rather similar to pH = − log<sub>10</sub>[H<sup>+</sup>(aq)]). The relationship <em>K</em><sub>a</sub> = 10<sup>−p<em>K</em>a</sup> is also helpful as the data booklet only lists p<em>K</em><sub>a</sub> values, not <em>K</em><sub>a</sub> values.)</p><hr class="hidden"><h4><span style="color:#FF0000;">Worked solution:</span></h4><p><strong>Step 1: </strong>Write the equation for the reaction.</p><p>CH<sub>3</sub>COOH(aq) + NaOH(aq) → CH<sub>3</sub>COONa(aq) + H<sub>2</sub>O(l)</p><p>After the reaction all the sodium hydroxide solution will have been neutralised to form sodium ethanoate and the excess ethanoic acid remains.</p><hr class="hidden"><p><strong>Step 2: </strong>Calculate the amounts of the sodium ethanoate and the excess ethanoic acid in the resulting solution.</p><p>Initial amount of NaOH = 20.0/1000 x 1.00 = 2.00 x 10<sup>−2</sup> mol</p><p>Initial amount of CH<sub>3</sub>COOH = 40.0/1000 x 1.00 = 4.00 x 10<sup>−2</sup> mol</p><p>Since all the NaOH reacts to form CH<sub>3</sub>COONa</p><p>Final amount of CH<sub>3</sub>COONa = 2.00 x 10<sup>−2</sup> mol</p><p>Final amount of CH<sub>3</sub>COOH = 4.00 x 10<sup>−2</sup> − 2.00 x 10<sup>−2</sup> = 2.00 x 10<sup>−2</sup> mol.</p><hr class="hidden"><p><strong>Step 3:</strong> Calculate the concentrations of the sodium ethanoate and the excess ethanoic acid in the resulting solution.</p><p>Final volume = 20.0 + 40.0 = 60.0 cm<sup>3 </sup> (assuming the volumes are exactly additive).</p><p>[CH<sub>3</sub>COONa(aq)] = 1000 / 60.0 x 2.00 x 10<sup>−2</sup> = 0.333 mol dm<sup>−3</sup></p><p>[CH<sub>3</sub>COOH(aq)] = 1000 / 60.0 x 2.00 x 10<sup>−2</sup> = 0.333 mol dm<sup>−3</sup></p><hr class="hidden"><p><strong>Step 4:</strong> Write the equilibrium expression for the dissociation of ethanoic acid.</p><p>CH<sub>3</sub>COOH(aq) ⇌ CH<sub>3</sub>COO<sup>−</sup>(aq) + H<sup>+</sup>(aq)</p><p><em>K</em><sub>a</sub> = [H<sup>+</sup>(aq)] x [CH<sub>3</sub>COO<sup>−</sup>(aq)] / [CH<sub>3</sub>COOH(aq)]</p><hr class="hidden"><p><strong>Step 5: </strong>Substitute the values for the concentration of the acid and the salt into the equilibrium expression to find [H<sup>+</sup>(aq)].</p><p><em>K</em><sub>a </sub>= [H<sup>+</sup>(aq)] x [CH<sub>3</sub>COO<sup>−</sup>(aq)] / [CH<sub>3</sub>COOH(aq)] = [H<sup>+</sup>(aq)] x 0.333 / 0.333 = [H<sup>+</sup>(aq)]</p><p><em>K</em><sub>a </sub>= 10<sup>−4.7</sup> so</p><p>[H<sup>+</sup>(aq)] = 10<sup>−4.76</sup> mol dm<sup>−3</sup></p><hr class="hidden"><p><strong>Step 6: </strong>Convert the hydrogen ion concentration into its pH value</p><p>pH = − log<sub>10</sub>[H<sup>+</sup>(aq)]</p><p>so pH = − log<sub>10</sub>10<sup>−4.76</sup> = 4.76</p><hr class="hidden"><p>Note that this example shows that at the half-equivalence point (i.e. when exactly half of the excess weak acid has been neutralised by the base, so that [acid] = [salt]) the pH = p<em>K</em><sub>a</sub>.</p><hr class="hidden"></div><hr class="hidden"><div class="pinkBg"><h1>Practice questions</h1><p class="MsoNormal"><span style="font-family:Arial">Answer the following questions from first principles (i.e. without using any mathematical formulas). The worked answers can be accessed by clicking on the ‘hidden’ symbol.</span></p><hr class="hidden"><p class="MsoNormal"><span style="font-family:Arial"></span></p><p class="MsoNormal"><strong>1.</strong><span style="font-family:Arial"> Calculate the concentration of an aqueous solution of sodium nitrate containing 1.70 g of sodium nitrate dissolved in 30.0 cm<sup>3</sup> of the solution. </span></p><section class="tib-hiddenbox"><p>M(NaNO<sub>3</sub>) = 22.99 + 14.01 + (3 x 16.00) = 85.00 g mol<sup>−1</sup></p><p>Amount of NaNO<sub>3</sub> in 30.00 cm<sup>3</sup> = 1.70 ÷ 85.00 = 0.0200 mol</p><p>Amount of NaNO<sub>3</sub> in 1000 cm<sup>3</sup> (1 dm<sup>3</sup>) = 1000 / 30.00 x 0.0200 = 0.667 mol</p><p>Concentration of NaNO<sub>3</sub>(aq) = 0.667 mol dm<sup>−3</sup>.</p></section><hr class="hidden"><hr class="hidden"><p><strong>2.</strong> Three separate solutions, 40.0 cm<sup>3</sup> of 2.00 mol dm<sup>−3</sup> HCl(aq), 50.0 cm<sup>3</sup> of 1.60 mol dm<sup>-3</sup> HCl(aq) and 30.0 cm<sup>3</sup> of 1.8 mol dm<sup>−3</sup> HCl(aq) are combined to make one solution. What is the concentration of this new solution?</p><section class="tib-hiddenbox"><p>Amount of HCl in 40.0 cm<sup>3</sup> of 2.00 mol dm<sup>−</sup><sup>3</sup> HCl(aq) = (40.0 / 1000) x 2.00 = 8.00 x 10<sup>−2 </sup>mol.</p><p>Amount of HCl in 50.0 cm<sup>3</sup> of 1.60 mol dm<sup>−</sup><sup>3</sup> HCl(aq) = (50.0 / 1000) x 1.60 = 8.00 x 10<sup>−2 </sup> mol.</p><p>Amount of HCl in 30.0 cm<sup>3</sup> of 1.8 mol dm<sup>−</sup><sup>3</sup> HCl(aq) = (30.0 / 1000) x 1.80 = 5.40 x 10<sup>−2 </sup> mol.</p><p>Total amount of HCl present = (8.00 + 8.00 + 5.40) x 10<sup>−2</sup> = 0.214 mol</p><p>Total volume = 40.0 + 50.0 + 30.0 = 120 cm<sup>3</sup></p><p>Concentration = 0.214 x 1000/120 = 1.78 mol dm<sup>−</sup><sup>3</sup>.</p></section><hr class="hidden"><hr class="hidden"><p><strong>3. </strong>What volume of 0.250 mol dm<sup>−3</sup> sulfuric acid is required to neutralise exactly 15.0 cm<sup>3</sup> of 0.150 mol dm<sup>−3</sup> barium hydroxide solution?</p><section class="tib-hiddenbox"><p>H<sub>2</sub>SO<sub>4</sub>(aq) + Ba(OH)<sub>2</sub> → BaSO4(aq) + 2H<sub>2</sub>O(l)</p><p>Amount of Ba(OH)<sub>2</sub> in 15.0 cm<sup>3</sup> = (15.0 / 1000) x 0.150 = 2.25 x 10<sup>−3</sup> mol</p><p>1 mol of H<sub>2</sub>SO<sub>4</sub> reacts with 1 mol of Ba(OH)<sub>2</sub></p><p>Amount of H<sub>2</sub>SO<sub>4</sub> required = 2.25 x 10<sup>−3</sup> mol</p><p>Volume of 0.250 mol dm<sup>−3</sup> H<sub>2</sub>SO<sub>4</sub> required = (1000 / 0.250) x 2.25 x 10<sup>−3</sup> = 9.00 cm<sup>3</sup>.</p></section><hr class="hidden"><hr class="hidden"><p><strong>4. </strong>What volume of carbon dioxide measured at STP will be evolved when 2.10 g of sodium hydrogen carbonate, NaHCO<sub>3</sub> is reacted with excess hydrochloric acid?</p><section class="tib-hiddenbox"><p>NaHCO<sub>3</sub>(s) + HCl(aq) → NaCl(aq) + CO<sub>2</sub>(g) + H<sub>2</sub>O(l)</p><p>M(NaHCO<sub>3</sub>) = 22.99 + 1.01 + 12.01 + (3 x 16.00) = 84.01 g mol<sup>−1</sup></p><p>Amount of NaHCO<sub>3</sub> = 2.10 ÷ 84.01 = 0.0250 mol</p><p>1 mol of NaHCO<sub>3</sub> reacts to produce 1 mol of CO<sub>2</sub></p><p>Amount of CO<sub>2</sub> evolved = 0.0250 mol</p><p>1 mol of any gas occupies 22.7 dm<sup>3</sup> at STP (from Section 2 of the IB data booklet)</p><p>Volume of CO<sub>2</sub> evolved = 0.568 dm<sup>3</sup> = 568 cm<sup>3</sup></p></section><hr class="hidden"><hr class="hidden"><p><strong>5. (a) </strong>What will be the pH of the buffer solution prepared by adding 25.00 cm<sup>3</sup> of 1.25 mol dm<sup>−3</sup> NaOH(aq) to 60.00 cm<sup>3</sup> of 1.20 mol dm<sup>−3</sup> CH<sub>3</sub>COOH(aq). (<em>K</em><sub>a</sub> of CH<sub>3</sub>COOH = 1.74 x 10<sup>−5 </sup>at 298 K)</p><section class="tib-hiddenbox"><p>CH<sub>3</sub>COOH(aq) + NaOH(aq) → CH<sub>3</sub>COONa(aq) + H<sub>2</sub>O(l)</p><p>Initial amount of NaOH = 25.0/1000 x 1.25 = 3.125 x 10<sup>−2</sup> mol</p><p>Initial amount of CH<sub>3</sub>COOH = 60.0/1000 x 1.20 = 7.200 x 10<sup>−2</sup> mol</p><p>Since all the NaOH reacts to form CH<sub>3</sub>COONa</p><p>Final amount of CH<sub>3</sub>COONa = 3.125 x 10<sup>−2</sup> mol</p><p>Final amount of CH<sub>3</sub>COOH = 7.200 x 10<sup>−2</sup> − 3.125 x 10<sup>−2</sup> = 4.075 x 10<sup>−2</sup> mol</p><p>Final volume = 25.0 + 60.0 = 85.0 cm<sup>3 </sup> (assuming the volumes are exactly additive).</p><p>[CH<sub>3</sub>COONa(aq)] = 1000 / 85.0 x 3.125 x 10<sup>−2</sup> = 0.3676 mol dm<sup>−3</sup></p><p>[CH<sub>3</sub>COOH(aq)] = 1000 / 85.0 x 4.075 x 10<sup>−2</sup> = 0.4794 mol dm<sup>−3</sup></p><p><em>K</em><sub>a </sub>= [H<sup>+</sup>(aq)] x [CH<sub>3</sub>COO<sup>−</sup>(aq)] / [CH<sub>3</sub>COOH(aq)] = [H<sup>+</sup>(aq)] x 0.3676 / 0.4794 = 0.767 x [H<sup>+</sup>(aq)]</p><p><em>K</em><sub>a</sub> of CH<sub>3</sub>COOH = 1.74 x 10<sup>−5</sup></p><p>[H<sup>+</sup>(aq)] = 1.74 x 10<sup>−5</sup> / 0.767 = 2.27 x 10<sup>−5</sup></p><p>pH = − log<sub>10</sub>[H<sup>+</sup>(aq)] = 4.64</p></section><p><strong>5.(b) </strong>The same buffer solution can be prepared by dissolving solid sodium ethanoate in a solution of ethanoic acid. What mass of sodium ethanoate would need to be dissolved in 50.0 cm<sup>3</sup> of 1.20 mol dm<sup>−3</sup> CH<sub>3</sub>COOH(aq) to give a buffer solution with a pH of 4.64? Assume that when the salt is dissolved it does not affect the volume of the solution.</p><section class="tib-hiddenbox"><p>CH<sub>3</sub>COOH(aq) ⇌ CH<sub>3</sub>COO<sup>−</sup>(aq) + H<sup>+</sup>(aq)</p><p><em>K</em><sub>a</sub> = [H<sup>+</sup>(aq)] x [CH<sub>3</sub>COO<sup>−</sup>(aq)] / [CH<sub>3</sub>COOH(aq)]</p><p>CH<sub>3</sub>COOH(aq) = 1.20 mol dm<sup>−3</sup> and since the pH must be 4.64, [H<sup>+</sup>(aq)] = 10<sup>−4.64</sup> and the value of <em>K</em><sub>a</sub> is given in <strong>5.(a)</strong>.</p><p><em>K</em><sub>a</sub> = 1.74 x 10<sup>−5</sup> = 10<sup>−4.64</sup> x [CH<sub>3</sub>COO<sup>−</sup>(aq)] / 1.20</p><p>[CH<sub>3</sub>COO<sup>−</sup>(aq)] = 1.74 x 10<sup>−5</sup> x 1.20 / 10<sup>−4.64</sup> = 0.911 mol dm<sup>−3</sup></p><p><em>M</em>(CH<sub>3</sub>COONa) = (2 x 12.01) + (3 x 1.01) + (2 x 16.00) + 22,99 = 82.04 g mol<sup>∼1</sup></p><p>Mass of CH<sub>3</sub>COONa required in 50.0 cm<sup>3</sup> = 0.911 x 82.04 x 50.0 / 1000 = 3.74 g</p></section><hr class="hidden"></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="41420" 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=%22Misuse+of+formulas+%22+-+via+%40InThinker+%23chemistry%0A&url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F41420%2Fmisuse-of-formulas-"><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%2F41420%2Fmisuse-of-formulas-&t=Misuse+of+formulas+"><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%2F41420%2Fmisuse-of-formulas-"><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%2F41420%2Fmisuse-of-formulas-"><i class="fa fa-google-plus-square"></i><span>Google +</span></a></li><li><a class="" href="mailto:?subject=Misuse of formulas &body=Students often use mathematical formulas to solve chemical problems in exams and sometimes arrive at the wrong answer. 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commentContent=commentEditor.getData(),fatherId=$("#father-comment").val(),ticket=$("#comment-ticket").val(),sectionId=$("#section-id").val();$.post("pages/comment.php",{action:"post",section_id:sectionId,father_id:fatherId,content:commentContent,ticket:ticket},(function(data){if("0"==data.success)alert(data.error);else{commentEditor.setData(""),placeComment(data.html,fatherId),$("form#comment-form #cancel-comment-post").hide();var n=0;$("#n-comments").text().length>0&&(n=parseInt($("#n-comments").text())),$("#n-comments").text(n+1)}}),"json")})),$("section#comments").on("click","a.reply-comment",(function(e){e.preventDefault(),$(".comment .fa-arrow-down").removeClass("fa-arrow-down").addClass("fa-reply"),$(".comment-content").removeClass("marked");var form=$("form#comment-form"),fatherId=$(this).parent().parent(".comment").attr("rel");form.find("#father-comment").val(fatherId),$(this).parent().parent(".comment").find("> 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commentId=$(this).data("comment-id"),isFather=$("#comm-"+commentId).children(".comment").length>0,ticket=$("#comment-ticket").val(),msg="You are going to delete a comment.\n\nThis action cannot be undone.\n\nAre you sure?";isFather&&(msg="You are going to delete a comment and all its replies.\n\nThis action cannot be undone.\n\nAre you sure?"),confirm(msg)&&$.post("pages/comment.php",{action:"delete",comment_id:commentId,is_father:isFather,ticket:ticket},(function(data){if("0"==data.success)alert(data.error);else{$("#comm-"+commentId+".comment").replaceWith(data.text);var n=0;$("#n-comments").text().length&&(n=parseInt($("#n-comments").text())),$("#n-comments").text(n-parseInt(data.deleted))}}),"json"),e.preventDefault(),e.stopPropagation()})),$("section#comments").on("click","a.pull-right",(function(e){e.preventDefault();var 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