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href="#" class="mark-page-favorite pull-right" data-pid="890" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../chemistry.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../358/energetics.html">Energetics</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Energy cycles</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 60 minutes"><i class="fa fa-clock-o"></i> 60'</span> </ol> <article id="main-article"> <p><img alt="" src="../../images/test-images/energy-cycle.png" style="float: left; width: 160px; height: 105px;">This section involves more complex energy cycles than those you came across in Section 5.2. Born Haber cycles can be used to determine the lattice enthalpies and enthalpies of solution of ionic compounds. <strong>Use the flash cards to learn the vocabulary thoroughly</strong>, as the definition of an enthalpy changes will determine how the its data in a Born Haber cycle needs to be manipulated. To avoid careless mistakes, always draw a well-spaced and annotated energy cycle – <strong>refer to revision cards 5, 6 and 10 to</strong> <strong>help you organise your thoughts and working</strong>.</p> <p>You should also be able to explain how ionic radius and ionic charge affect the lattice enthalpy of an ionic compound.</p> <hr class="hidden-separator"> <div class="panel panel-has-colored-body panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Key concepts</p> </div> </div> <div class="panel-body"> <div> <div class="panel-body"> <div> <p>Ensure you are confident using the terms below and learn the asterisked* definitions</p> <p><span calibri="" light="" style="font-size:12.0pt;font-family:">lattice enthalpy </span><span calibri="" light="" style="font-size:12.0pt;font-family:">(<em>Δ</em></span><em><sup><s>o</s></sup>H<sub>LE</sub></em>)*, standard enthalpy of atomisation <span calibri="" light="" style="font-size:12.0pt;font-family:">(<em>Δ</em></span><em><sup><s>o</s></sup>H<sub>atm</sub></em>)*, first ionisation enthalpy (<em>1st IE</em>)*, first electron affinity (<em>1st EA</em>)*, enthalpy of solution (<span calibri="" light="" style="font-size:12.0pt;font-family:">Δ</span><em>H</em><sup><s>o</s></sup><em><sub>soln</sub></em>)*, hydration enthalpy <span calibri="" light="" style="font-size:12.0pt;font-family:">(Δ</span><em>H</em><sup><s>o</s></sup><em><sub>soln</sub></em>)*</p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="3" data-mode="" data-topics="636" data-subject-id="7" data-n-flashcards="6" style="text-align:center">Show flashcards</a></div><hr> <div class="panel panel-has-colored-body panel-has-border panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Constructing Born-Haber cycles</p> </div> </div> <div class="panel-body"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/387489220"></iframe></div> </div> <div class="panel-footer"> <div> </div> </div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-yellow panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <p> The revision cards contain all of the essential content:</p> <div id="carousel-141" class="dynamic-gallery carousel slide" data-id="141"><div class="carousel-inner" role="listbox"><div class="item active"><a class="fancy" href="../../../std-galleries/7-141/screenshot-2019-09-05-at-212307.png" data-fancybox="gallery-141" title="" data-caption=""><img alt="" 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src="../../../std-galleries/7-141/screenshot-2019-09-05-at-212517-thumb128.jpg"><li></li></ol> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test yourself</p> </div> </div> <div class="panel-body"> <div> <div class="panel-body"> <div> <div class="tib-quiz" data-stats="7-411-890"><div class="label label-default q-number">1</div><div class="exercise shadow-bottom"><div class="q-question"><p>What is the definition of lattice enthalpy (ΔH<sub>latt</sub>°)?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>The enthalpy change that occurs when elements are formed from 1 mol of ionic solid</span></label> </p><p><label class="radio"> <input type="radio"> <span>The enthalpy change that occurs when 1 mol of ionic solid is formed from its elements in their standard states.</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>The enthalpy change that occurs when 1 mol of ionic solid is dissociated into its gaseous ions</span></label> </p><p><label class="radio"> <input type="radio"> <span>The enthalpy change that occurs when one mole of gaseous ions form an ionic solid</span></label> </p></div><div class="q-explanation"><p>The IB definition of lattice enthalpy is usually a positive value (endothermic as ions are pulled apart and bonds are broken), hence:</p><p><strong>The enthalpy change that occurs when 1 mol of ionic solid is dissociated into its gaseous ions </strong>is the correct answer. e.g. NaCl<sub>(s)</sub> → Na<sup>+</sup><sub>(g)</sub> + Cl<sup>−</sup><sub>(g)</sub></p><p>Be aware that lattice enthalpy is also often defined as the reverse Na<sup>+</sup><sub>(g)</sub> + Cl<sup>−</sup><sub>(g) </sub>→ NaCl<sub>(s) </sub>in certain text books etc. in which case the sign of the lattice energy value will be negative (exothermic as ions come together and bonds are made).</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following would be correctly included in the definition of <em>first ionisation</em> <em>enthalpy</em>?</p><p><strong>1: </strong>One mole of 1+ ions are formed...</p><p><strong>2: </strong>...from the element...</p><p><strong>3: </strong>...in its standard state.</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>1 only</span></label> </p><p><label class="radio"> <input type="radio"> <span>1, 2 and 3 only</span></label> </p><p><label class="radio"> <input type="radio"> <span>1 and 2 only</span></label> </p><p><label class="radio"> <input type="radio"> <span>2 and 3 only</span></label> </p></div><div class="q-explanation"><p>First ionisation enthalpy is a definition that needs to be learned:</p><p>First ionisation enthalpy is the enthalpy change when <strong>one electron is removed </strong>from <strong>each atom</strong> <strong>in one mole</strong> of <strong>gaseous atoms</strong>.</p><p>Thus <strong>1 only </strong>is the correct answer.</p><p>One mole of 1+ ions are formed, but first ionisation enthalpy involves gaseous atoms (not the element in its standard state)</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">3</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which statement correctly describes the relationship between the lattice enthalpies of sodium chloride (NaCl) and potassium chloride (KCl)?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>KCl has a larger lattice enthalpy than NaCl because the potassium ion is smaller than the sodium ion so there is stronger attraction in the lattice.</span></label> </p><p><label class="radio"> <input type="radio"> <span>NaCl has a larger lattice enthalpy than KCl because the sodium ion is larger than the potassium ion so there is stronger attraction in the lattice.</span></label> </p><p><label class="radio"> <input type="radio"> <span>KCl has a larger lattice enthalpy than NaCl because the potassium ion is larger than the sodium ion so there is stronger attraction in the lattice.</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>NaCl has a larger lattice enthalpy than KCl because the sodium ion is smaller than the potassium ion so there is stronger attraction in the lattice.</span></label> </p></div><div class="q-explanation"><p>Lattice enthalpies increase with increasing ionic charge and decrease with increasing ionic radius.</p><p>Smaller ions can pack in the lattice more tightly (and/or have higher <em>charge density</em>) and therefore tend to generate stronger attraction in the lattice.</p><p>Ions with greater charges tend to generate stonger attraction in the lattice.</p><p>The sodium ion is smaller than the potassium ion (sodium is higher in group 1 on the periodic table) and so: <strong>NaCl has a larger lattice enthalpy than KCl because the sodium ion is smaller than the potassium ion so there is stronger attraction in the lattice</strong> is the correct answer.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">4</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the enthalpy changes given is represented by the letter <strong>C</strong> on the Born Haber cycle diagram below:</p><p><img alt="" height="306" src="../../images/energetics-thermochemistry/bh-kf.png" width="417"></p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>Enthalpy change of formation for potassium fluoride</span></label> </p><p><label class="radio"> <input type="radio"> <span>1st ionisation enthalpy for potassium</span></label> </p><p><label class="radio"> <input type="radio"> <span>1st electron affinity for fluorine</span></label> </p><p><label class="radio"> <input type="radio"> <span>Lattice enthalpy for potassium fluoride</span></label> </p></div><div class="q-explanation"><p>The enthalpy change<strong> C</strong> on the diagram shows the reaction K<sub>(s)</sub> + <span arial="" style="font-size:12.0pt;font-family:">½</span>F<sub>2(g) </sub>→ KF<sub>(s)</sub>. This is the formation of one mole of a compound from its elements in their standard states.</p><p>The correct answer is therefore <strong>Enthalpy change of formation for potassium fluoride</strong>.</p><p>The enthalpy change definitions all need to be learned.</p><p><img alt="" height="268" src="../../images/energetics-thermochemistry/bh-kf-full.png" width="629"></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">5</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the changes given is represented by the letter <strong>Y</strong> on the Born Haber cycle diagram below:</p><p><img alt="" height="336" src="../../images/energetics-thermochemistry/bh-mgf2-blank.png" width="429"></p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>1st electron affinity for fluorine</span></label> </p><p><label class="radio"> <input type="radio"> Enthalpy change of atomisation for fluorine<span></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>1st electron affinity for fluorine × 2</span></label> </p><p><label class="radio"> <input type="radio"> <span>2nd electron affinity for fluorine</span></label> </p></div><div class="q-explanation"><p>The enthalpy change<strong> Y</strong> on the diagram shows the reaction Mg<sup>2+</sup><sub>(g)</sub> + <span arial="" style="font-size:12.0pt;font-family:">2</span>F<sub>(g) </sub>+ 2e<sup>−</sup> → Mg<sup>2+</sup><sub>(g)</sub> + 2F<sup>−</sup><sub>(g)</sub>. The magnesium ion does not change. The electrons are gained by the fluorine atoms. so this is<strong> twice </strong>the 1st electron affinity for fluorine (F<sub>(g) </sub>+ e<sup>−</sup> → F<sup>−</sup><sub>(g)</sub>).</p><p>The correct answer is therefore <strong>1st electron affinity for fluorine × 2</strong>.</p><p>The enthalpy change definitions all need to be learned.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">6</div><div class="exercise shadow-bottom"><div class="q-question"><p><em>Calculator question:</em> Given the enthaply changes below, what is the lattice enthalpy (in kJ mol<sup>−1</sup>) for magnesium fluoride, MgF<sub>2</sub>?</p><table border="0" cellpadding="0" cellspacing="0" style="width:100%;"><tbody><tr><td><strong>Enthalpy change</strong></td><td style="text-align: center;"> </td><td style="text-align: center;"><strong>Value (kJ mol<sup>−1</sup>)</strong></td></tr><tr><td>Enthalpy of formation (magnesium fluoride)</td><td style="text-align: center;"> </td><td style="text-align: center;">−1124</td></tr><tr><td>Enthalpy of atomisation (magnesium)</td><td> </td><td style="text-align: center;">+148</td></tr><tr><td>Enthalpy of atomisation (fluorine)</td><td> </td><td style="text-align: center;">+79</td></tr><tr><td>1st ionisation enthalpy (magnesium)</td><td> </td><td style="text-align: center;">+738</td></tr><tr><td>2nd ionisation enthalpy (magnesium)</td><td> </td><td style="text-align: center;">+1450</td></tr><tr><td>1st electron affinity (fluorine)</td><td> </td><td style="text-align: center;">−328</td></tr></tbody></table></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>+3211</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>+2962</span></label> </p><p><label class="radio"> <input type="radio"> <span>+2883</span></label> </p><p><label class="radio"> <input type="radio"> <span>+3290</span></label> </p></div><div class="q-explanation"><p>ΔH<sub>latt</sub>(MgF<sub>2</sub>) = −(−1124) + 148 + (2×79) + 738 + 1450 + (2×−328) = +2962 kJmol<sup>−1</sup></p><p><strong>+2962</strong> is therefore the correct answer.</p><p><strong>Incorrect answers</strong></p><p>+3290 is obtained if −328 is used instead of 2× −328 (not using twice the electron affinity for fluorine).</p><p>+2883 is obtained if +79 is used instead of 2× +79 (not using twice the atomisation energy for fluorine).</p><p>+3211 is obtained if −328 is used instead of 2× −328 and +79 is used instead of 2× +79 (not using twice the electron affinity and twice the atomisation energy for fluorine).</p><p><img alt="" height="346" src="../../images/energetics-thermochemistry/bh-mgf2-full.png" width="526"></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">7</div><div class="exercise shadow-bottom"><div class="q-question"><p><em>Calculator question: </em>Given the enthalpy changes below, what is the enthalpy of solution in water (in kJ mol<sup>−1</sup>) for sodium chloride, NaCl?</p><table border="0" cellpadding="0" cellspacing="0" style="width:100%;"><tbody><tr><td><strong>Enthalpy change</strong></td><td style="text-align: center;"> </td><td style="text-align: center;"><strong>Value (kJ mol<sup>−1</sup>)</strong></td></tr><tr><td>Lattice enthalpy (sodium chloride)</td><td style="text-align: center;"> </td><td style="text-align: center;">+776</td></tr><tr><td>Enthalpy of hydration (sodium ion)</td><td> </td><td style="text-align: center;">−407</td></tr><tr><td>Enthalpy of hydration (chloride ion)</td><td> </td><td style="text-align: center;">−364</td></tr></tbody></table></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>−1547</span></label> </p><p><label class="radio"> <input type="radio"> <span>+1547</span></label> </p><p><label class="radio"> <input type="radio"> <span>−5</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>+5</span></label> </p></div><div class="q-explanation"><p>ΔH<sub>soln</sub>(NaCl) = +776 + (−407) + (−364) = +5 kJmol<sup>−1</sup></p><p><strong>+5 </strong>is therefore the correct answer.</p><p><strong>Incorrect answers</strong></p><p>−5 is obtained if signs are inverted.</p><p>−1547 is obtained if the sign for the lattice enthalpy is inverted (using −776 instead of +776).</p><p>+1547 is obtained if the sign for both hydration enthalpies are inverted (using + instead of −)</p><p><img alt="" height="305" src="../../images/energetics-thermochemistry/solution-nacl.png" width="582"></p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">8</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the equations below represents the <em>standard enthalpy change of hydration</em> for sodium chloride?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Na<sub>(s) </sub>+ ½Cl<sub>2(g)</sub> → NaCl<sub>(aq)</sub></span></label> </p><p><label class="radio"> <input type="radio"> <span>Na<sub>(g) </sub>+ ½Cl<sub>2(g)</sub> → NaCl<sub>(aq)</sub></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>Na<sup>+</sup><sub>(g) </sub>+ Cl<sup>−</sup><sub>(g)</sub> → NaCl<sub>(aq)</sub></span></label> </p><p><label class="radio"> <input type="radio"> <span>NaCl<sub>(s)</sub> → NaCl<sub>(aq)</sub></span></label> </p></div><div class="q-explanation"><p>Standard enthalpy change of hydration is a definition that needs to be learned:</p><p>Standard enthalpy of hydration is the enthalpy change when <strong>one mole of</strong> <strong>aqueous solution</strong> is formed from <strong>ions in the gaseous state</strong>.</p><p>Thus <strong>Na<sup>+</sup><sub>(g) </sub>+ Cl<sup>−</sup><sub>(g)</sub> → NaCl<sub>(aq)</sub></strong> is the correct answer.</p><p>Standard enthalpy change of <em>solution</em> is also definition that needs to be learned (and not confused with hydration):</p><p>Standard enthalpy of solution is the enthalpy change when <strong>one mole </strong>of <strong>aqueous solution</strong> is formed from <strong>one mole of solute in its standard state</strong>. (e.g. NaCl<sub>(s)</sub> → NaCl<sub>(aq) </sub>for sodium chloride)</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the equations below represents the <em>standard enthalpy of atomisation of bromine</em>?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Br<sub>2(g)</sub> → 2Br<sub>(g)</sub></span></label> </p><p><label class="radio"> <input type="radio"> <span>½Br<sub>2(g)</sub> → Br<sub>(g)</sub></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>½Br<sub>2(l)</sub> → Br<sub>(g)</sub></span></label> </p><p><label class="radio"> <input type="radio"> <span>Br<sub>2(l)</sub> → 2Br<sub>(g)</sub></span></label> </p></div><div class="q-explanation"><p>Standard enthalpy of atomisation is a definition that needs to be learned:</p><p>Standard enthalpy of atomisation is the enthalpy change when <strong>one mole </strong>of <strong>gaseous atoms</strong> is formed from the element in its <strong>standard state</strong> (at 100kPa and 298K).</p><p>Thus <strong>½Br<sub>2(l)</sub> → Br<sub>(g) </sub></strong>is the correct answer.</p><p><strong>Incorrect answers:</strong></p><p>Br<sub>2(l)</sub> → 2Br<sub>(g) </sub>shows two moles of bromine atoms (rather than <strong>one mole</strong>).</p><p>½Br<sub>2(g)</sub> → Br<sub>(g) </sub>shows bromine molecules in the gaseous state (rather than liquid; its <strong>standard state</strong>).</p><p>Br<sub>2(g)</sub> → 2Br<sub>(g) </sub>shows bromine molecules in the gaseous state (rather than liquid; its <strong>standard state</strong>) and shows two moles of bromine atoms (rather than <strong>one mole</strong>).</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="label label-default q-number">10</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the equations below represents the <em>second electron affinity </em>of oxygen?</p></div><div class="q-answer"><p><label class="radio"> <input class="c" type="radio"> <span>O<sup>−</sup><sub>(g)</sub> + e<sup>−</sup> → O<sup>2−</sup><sub>(g)</sub></span></label> </p><p><label class="radio"> <input type="radio"> <span>½O<sub>2(g)</sub> + 2e<sup>−</sup> → O<sup>2</sup><sup>−</sup><sub>(g)</sub></span></label> </p><p><label class="radio"> <input type="radio"> <span>O<sub>(g)</sub> + e<sup>−</sup> → O<sup>2−</sup><sub>(g)</sub></span></label> </p><p><label class="radio"> <input type="radio"> <span>½O<sub>2</sub><sup>−</sup><sub>(g)</sub> + e<sup>−</sup> → O<sup>2</sup><sup>−</sup><sub>(g)</sub></span></label> </p></div><div class="q-explanation"><p>First electron affinity and second electron affinity are definitions that need to be learned:</p><p>First electron affinity is the enthalpy change when <strong>one electron is gained </strong>by <strong>each atom</strong> <strong>in one mole</strong> of <strong>gaseous atoms</strong>.</p><p>Second electron affinity is the enthalpy change when <strong>one electron is gained </strong>by <strong>each 1− ion</strong> <strong>in one mole</strong> of <strong>gaseous ions</strong>.</p><p>Thus <strong>O<sup>−</sup><sub>(g)</sub> + e<sup>−</sup> → O<sup>2−</sup><sub>(g) </sub></strong>is the correct answer.</p></div><div class="actions"><span class="score" data-score="0"></span><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="totals"><span class="score"></span><button class="btn btn-success btn-block text-center check-total"><i class="fa 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