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fa-table"></i>&nbsp;&nbsp;Periodic table</button> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i>&nbsp;&nbsp;Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Rate expression and reaction mechanism <a href="#" class="mark-page-favorite pull-right" data-pid="893" 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="../359/kinetics.html">Kinetics</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Rate expression and reaction mechanism</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 60 minutes"><i class="fa fa-clock-o"></i> 60&apos;</span> </ol> <article id="main-article"> <p>&nbsp;<img alt="" src="../../images/test-images/reaction.png" style="width: 160px; height: 146px; float: left;">This section is more straightforward than it at first seems. The important thing is to be comfortable in identifying the order of reaction of a reactant or catalyst from data given, whether that is in the form of a graph or numerical data. Understanding the relationship between the rate equation and the reaction mechanism is the most challenging part of this topic - so focus on that last, once you are confident with everything else.</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>rate determining step*, molecularity*, order of reaction*, reaction mechanism, rate constant, rate equation, intermediate, transition state</p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="3" data-mode="Normal" data-topics="594" data-subject-id="7" data-n-flashcards="8" style="text-align:center">Show flashcards</a></div><hr> &nbsp; <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>Understanding the reaction mechanism</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/392696181"></iframe></div> </div> <div class="panel-footer"> <div>&nbsp;</div> </div> </div> </div> </div> </div> </div> <div class="panel-footer"> <div>&nbsp;</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>&nbsp;&nbsp;&nbsp; The revision cards contain all of the essential content:</p> <div id="carousel-168" 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src="../../images/chemical-kinetics/rate-conc-graphs.png" width="553"></p><p>Which of the following shows the correct order of reaction with respect to [X], [Y] and [Z].?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>[X] second order ; [Y] zero order ; [Z] first order</span></label> </p><p><label class="radio"> <input type="radio"> <span>[X] zero order ; [Y] first order ; [Z] second order</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>[X] first order ; [Y] zero order ; [Z] second order </span></label> </p><p><label class="radio"> <input type="radio"> <span>[X] first order ; [Y] second order ; [Z] zero order</span></label> </p></div><div class="q-explanation"><p>For zero order reactants, changing concentration will have <strong>no effect</strong> on the rate, so [Y] is zero order. For first order reactants, changing concentration will change the rate <strong>proportionally </strong>(double concentration and double rate), so [X] is first order. For second order reactants, changing concentration will change the rate by the <strong>square of the concentration </strong>(double concentration and quadruple rate), so [Z] is second order.</p><p><em>[X] first order ; [Y] zero order ; [Z] second order</em> 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">2</div><div class="exercise shadow-bottom"><div class="q-question"><p>Which of the following statements is true when following the concentration over time of a first order reactant in a chemical reaction?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>The concentration increases with a half-life that is not constant.</span></label> </p><p><label class="radio"> <input type="radio"> <span>The concentration decreases with a half-life that is not constant.</span></label> </p><p><label class="radio"> <input type="radio"> <span>The concentration increases with a constant half-life.</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>The concentration decreases with a constant half-life.</span></label> </p></div><div class="q-explanation"><p>Half-life is the time taken for the concentration of a species to half in value<em>. </em>First order reactants always have <strong>constant </strong>half-lives, and a reactant will be <strong>used up </strong>as a reaction proceeds, so the correct answer is <em>The concentration decreases with a constant half-life</em>.</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>If the stoichiometric equation for a reaction is given thus:</p><p>2NO + H<sub>2</sub> &rarr; N<sub>2</sub> + H<sub>2</sub>O</p><p>What is the rate equation?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Rate = k[NO]</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>Unknown</span></label> </p><p><label class="radio"> <input type="radio"> <span>Rate = k[NO][H<sub>2</sub>]</span></label> </p><p><label class="radio"> <input type="radio"> <span>Rate = k[NO]<sup>2</sup>[H<sub>2</sub>]</span></label> </p></div><div class="q-explanation"><p>The rate equation can <strong>only</strong> be determined experimentally. It cannot be deduced from the stoichiometric equation. Thus the correct answer is &#39;unknown&#39;. Although it is possible that any of the other answers given <em>may</em> be correct, we cannot know the answer without further information.</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>The following data was obtained for the chemical reaction: Y + Z &rarr; <em>Products</em></p><table border="0" cellpadding="0" cellspacing="0" style="width: 100%;"><tbody><tr><td style="text-align: center;">[Y] (mol dm<sup>&ndash;3</sup>)</td><td style="text-align: center;">[Z] (mol dm<sup>&ndash;3 </sup>)</td><td style="text-align: center;">Initial Rate (mol dm<sup>&ndash;3 </sup>s<sup>&ndash;1</sup>)</td></tr><tr><td style="text-align: center;">0.10</td><td style="text-align: center;">0.10</td><td style="text-align: center;">0.20</td></tr><tr><td style="text-align: center;">0.20</td><td style="text-align: center;">0.10</td><td style="text-align: center;">0.80</td></tr><tr><td style="text-align: center;">0.20</td><td style="text-align: center;">0.20</td><td style="text-align: center;">0.80</td></tr></tbody></table><p>What is the order of reaction with respect to [Y] and the order of reaction with respect to [Z]?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> 1st and 1st<span></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>2nd and zero</span></label> </p><p><label class="radio"> <input type="radio"> <span>2nd and 2nd</span></label> </p><p><label class="radio"> <input type="radio"> <span>2nd and 1st</span></label> </p></div><div class="q-explanation"><p>The correct answer is that [Y] is 2nd order and [Z] is zero order. When the concentration of only Y is doubled (experiments 1 to 2) the rate quadruples. [Y] &times; 2 causes rate &times; 4, so [Y] is second order. When the concentration of only Z is doubled (experiments 2 to 3) the rate doesn&#39;t change, so [Z] is zero order.</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>The following data was obtained for the chemical reaction: X + Y &rarr; <em>Products</em></p><table border="0" cellpadding="0" cellspacing="0" style="width: 100%;"><tbody><tr><td style="text-align: center;">[X] (mol dm<sup>&ndash;3</sup>)</td><td style="text-align: center;">[Y] (mol dm<sup>&ndash;3 </sup>)</td><td style="text-align: center;">Initial Rate (mol dm<sup>&ndash;3 </sup>s<sup>&ndash;1</sup>)</td></tr><tr><td style="text-align: center;">0.20</td><td style="text-align: center;">0.20</td><td style="text-align: center;">4.0 &times; 10<sup>&ndash;3</sup></td></tr><tr><td style="text-align: center;">0.20</td><td style="text-align: center;">0.60</td><td style="text-align: center;">3.6 &times; 10<sup>&ndash;2</sup></td></tr><tr><td style="text-align: center;">0.30</td><td style="text-align: center;">0.20</td><td style="text-align: center;">6.0 &times; 10<sup>&ndash;3</sup></td></tr></tbody></table><p>What is the order of reaction with respect to X and the order of reaction with respect to Y?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>zero and 2nd</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>1st and 2nd</span></label> </p><p><label class="radio"> <input type="radio"> 1st and 1st<span></span></label> </p><p><label class="radio"> <input type="radio"> <span>2nd and 2nd</span></label> </p></div><div class="q-explanation"><p>The correct answer is that [X] is 1st order and [Y] is 2nd. When the concentration of Y is tripled (experiments 1 to 2) the rate increases nine fold (0.004 to 0.036 &ndash; make sure you understand <em>standard form</em>; to a positive power of ten moves the decimal place that many places to the right, negative power to the left). [Y] &times; 3 causes rate &times; 9, and 3<sup>2</sup>=9, so [Y] is second order. When the concentration of X is multiplied by 1.5 (experiments 1 to 3) the rate also increases by 1.5 times (0.004 to 0.006). [X] &times; 1.5 causes rate &times; 1.5, and 1.5<sup>1</sup>=1.5, so [X] is first order.</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>The following data was obtained for the chemical reaction: X + Y &rarr; <em>Products</em></p><table border="0" cellpadding="0" cellspacing="0" style="width: 100%;"><tbody><tr><td style="text-align: center;">[X] (mol dm<sup>&ndash;3</sup>)</td><td style="text-align: center;">[Y] (mol dm<sup>&ndash;3 </sup>)</td><td style="text-align: center;">Initial Rate (mol dm<sup>&ndash;3 </sup>s<sup>&ndash;1</sup>)</td></tr><tr><td style="text-align: center;">0.30</td><td style="text-align: center;">0.20</td><td style="text-align: center;">6.0 &times; 10<sup>&ndash;3</sup></td></tr></tbody></table><p>Given that the rate equation is:</p><p>Rate = k[X][Y]<sup>2</sup></p><p>What is the numerical value of the rate constant?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> 0.1 </label></p><p><label class="radio"> <input class="c" type="radio"> <span>0.5</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.33</span></label> </p><p><label class="radio"> <input type="radio"> 2<span></span></label> </p></div><div class="q-explanation"><p>k = Rate / [X][Y]<sup>2</sup></p><p>k = 6.0 &times; 10<sup>&ndash;3</sup> / 0.30 &times; (0.20)<sup>2</sup></p><p>k = 0.006 / 0.3 &times; 0.04</p><p>k = 0.006 /0.012 = <strong>0.5 is the correct answer</strong></p><p><strong>2: </strong>the fraction is the wrond way around</p><p><strong>0.1</strong>: the square has been left out</p><p><strong>0.33</strong>: 0.30 has been squared instead of 0.20</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>The following data was obtained for the chemical reaction: Y + Z &rarr; <em>Products</em></p><table border="0" cellpadding="0" cellspacing="0" style="width: 100%;"><tbody><tr><td style="text-align: center;">[Y] (mol dm<sup>&ndash;3</sup>)</td><td style="text-align: center;">[Z] (mol dm<sup>&ndash;3 </sup>)</td><td style="text-align: center;">Initial Rate (mol dm<sup>&ndash;3 </sup>s<sup>&ndash;1</sup>)</td></tr><tr><td style="text-align: center;">0.20</td><td style="text-align: center;">0.10</td><td style="text-align: center;">0.80</td></tr></tbody></table><p>Given that the rate equation is:</p><p>Rate = k[Y]<sup>2</sup></p><p>What are the units of the rate constant?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>s<sup>&ndash;1</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>mol<sup>&ndash;3</sup> dm<sup>9</sup> s<sup>&ndash;1</sup></span></label> </p><p><label class="radio"> <input type="radio"> mol<sup>&ndash;2</sup> dm<sup>6</sup> s<sup>&ndash;1</sup><span></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>mol<sup>&ndash;1</sup> dm<sup>3</sup> s<sup>&ndash;1</sup></span></label> </p></div><div class="q-explanation"><p>Units of the rate constant can be worked out by cancelling out in the equation in the same way as calculating the numerical value for the rate constant:</p><p>k = Rate / [Y]<sup>2</sup></p><p>units = mol dm<sup>&ndash;3</sup> s<sup>&ndash;1</sup> / (mol dm<sup>&ndash;3</sup>)(mol dm<sup>&ndash;3</sup>)</p><p>So cancel one <em>moles per decimetre cubed</em> from top and bottom:</p><p>units = s<sup>&ndash;1</sup> / mol dm<sup>&ndash;3</sup></p><p>Move units from bottom to top and therefore invert the sign:</p><p>mol<sup>&ndash;1 </sup>dm<sup>3 </sup>s<sup>&ndash;1</sup> is the correct answer.</p><p>Or they can be learnt:</p><table border="0" cellpadding="0" cellspacing="0" width="650"><colgroup><col><col span="4"></colgroup><tbody><tr height="29"><td height="29" style="height:39px;width:265px;"><p style="text-align: center;">Overall order of reaction</p></td><td style="width:151px;"><p style="text-align: center;">1st</p></td><td style="width:151px;"><p style="text-align: center;">2nd</p></td><td style="width:151px;"><p style="text-align: center;">3rd</p></td><td style="width:151px;"><p style="text-align: center;">4th</p></td></tr><tr height="29"><td height="29" style="height:39px;width:265px;"><p style="text-align: center;">Rate constant units</p></td><td style="width:151px;"><p style="text-align: center;">s<sup>&ndash;1</sup></p></td><td style="width:151px;"><p style="text-align: center;">mol<sup>&ndash;1</sup> dm<sup>3</sup> s<sup>&ndash;1</sup></p></td><td style="width:151px;"><p style="text-align: center;">mol<sup>&ndash;2</sup> dm<sup>6</sup> s<sup>&ndash;1</sup></p></td><td style="width:151px;"><p style="text-align: center;">mol<sup>&ndash;3</sup> dm<sup>9 </sup>s<sup>&ndash;1</sup></p></td></tr></tbody></table></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>The mechanism below represents the S<sub>N</sub>1 reaction between 2-bromo-2-methyl propane and a hydroxide ion:</p><p>Step (i) (slow step): (CH<sub>3</sub>)<sub>3</sub>CBr &rarr; (CH<sub>3</sub>)<sub>3</sub>C<sup>+</sup> + Br<sup>&ndash;</sup></p><p>Step (ii) (fast step): (CH<sub>3</sub>)<sub>3</sub>C<sup>+</sup> + OH<sup>&ndash;</sup> &rarr; (CH<sub>3</sub>)<sub>3</sub>COH</p><p>The hydroxide ion does not take part in step (i) and the bromide ion does not take part in step (ii).</p><p>What is the molecularity of the steps (i) and (ii) respectively?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>1 and 1</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>1 and 2</span></label> </p><p><label class="radio"> <input type="radio"> <span>2 and 1</span></label> </p><p><label class="radio"> <input type="radio"> <span>1 and 3</span></label> </p></div><div class="q-explanation"><p>Molecularity is the number of particles that react together in a given reaction/step. In step (i) the only reactant is (CH<sub>3</sub>)<sub>3</sub>CBr so the molecularity is 1 (a unimolecular step). In step (ii) the reactants are (CH<sub>3</sub>)<sub>3</sub>C<sup>+</sup> and OH<sup>&ndash;</sup> so the molecularity is 2 (a bimolecular step). &#39;1 and 2&#39; 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">9</div><div class="exercise shadow-bottom"><div class="q-question"><p>Nitrogen dioxide and carbon monoxide react together according to the following stoichiometric equation:</p><p>NO<sub>2(g)</sub> + CO<sub>(g)</sub> &rarr; NO<sub>(g) </sub>+ CO<sub>2(g)</sub></p><p>Experimental data at high temperatures suggests the following mechanism for the reaction:</p><p>Step 1 (slow step): NO<sub>2(g)</sub> + NO<sub>2(g)</sub> &rarr; NO<sub>(g) </sub>+ NO<sub>3(g)</sub></p><p>Step 2 (fast step): NO<sub>3(g)</sub> + CO<sub>(g)</sub> &rarr; NO<sub>2(g) </sub>+ CO<sub>2(g)</sub></p><p>Given the mechanism above, what is the rate equation?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Rate = k[NO<sub>3</sub>][CO]</span></label> </p><p><label class="radio"> <input type="radio"> <span>Rate = k[NO<sub>2</sub>][CO]</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>Rate = k[NO<sub>2</sub>]<sup>2</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>Rate = k[NO<sub>2</sub>]<sup>2</sup>[CO]</span></label> </p></div><div class="q-explanation"><p>Only reactants that are <strong>in </strong>the rate determining step &ndash; slowest step &ndash; (or contribute to <strong>an intermediate that is in</strong> the rate determining step) can appear in the rate equation and therefore have an effect upon rate. NO<sub>2</sub> appears<strong> twice </strong>in the slow/rate determining step and thus [NO<sub>2</sub>] has an order of 2. CO does not appear in slow/rate determining step and thus [CO] has an order of zero.</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>Nitrogen monoxide and oxygen react together according to the following stoichiometric equation:</p><p>2NO<sub>(g)</sub> + O<sub>2(g)</sub> &rarr; 2NO<sub>2(g)</sub></p><p>Experimental data suggests the following mechanism for the reaction:</p><p>Step 1 (fast step): 2NO<sub>(g)</sub> ⇌ N<sub>2</sub>O<sub>2(g)</sub></p><p>Step 2 (slow step): N<sub>2</sub>O<sub>2(g)</sub> + O<sub>2(g)</sub> &rarr; 2NO<sub>2(g)</sub></p><p>Given the mechanism above, what is the rate equation?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>Rate = k[O<sub>2</sub>]</span></label> </p><p><label class="radio"> <input type="radio"> <span>Rate = k[N<sub>2</sub>O<sub>2</sub>][O<sub>2</sub>]</span></label> </p><p><label class="radio"> <input type="radio"> <span>Rate = k[NO]<sup>2</sup></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>Rate = k[NO]<sup>2</sup>[O<sub>2</sub>]</span></label> </p></div><div class="q-explanation"><p>Only reactants that are <strong>in </strong>the rate determining step &ndash; slowest step &ndash; or contribute to <strong>an intermediate that is in</strong> the rate determining step, can appear in the rate equation and therefore have an effect upon rate. O<sub>2</sub> appears<strong> once </strong>in the slow/rate determining step and thus [O<sub>2</sub>] has an order of 1. N<sub>2</sub>O<sub>2</sub> also appears in the slow/rate determining step; it is an intermediate. Intermediates cannot themselves appear in the rate equation (hence Rate = k[N<sub>2</sub>O<sub>2</sub>][O<sub>2</sub>] is incorrect) but the reactants that produce the intermediate <strong>do</strong> appear in the rate equation. And since <strong>two</strong> moles of NO produce the intermediate (N<sub>2</sub>O<sub>2</sub>), this is equivalent to appearing <strong>twice </strong>in the slow/rate determining step and thus [NO] has an order of 2. Rate = k[NO]<sup>2</sup>[O<sub>2</sub>] 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 fa-check-square-o"></i> Check</button></div></div><hr> </div> </div> </div> </div> <div class="panel-footer"> <div>&nbsp;</div> </div> </div> <div class="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam-style questions</p> </div> </div> <div class="panel-body"> <h4>Paper 1</h4> <h5>Core (SL&amp;HL):&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<a href="../2712/kinetics-core-sl-and-hl-paper-1-questions.html" title="Kinetics core (SL and HL) paper 1 questions">Kinetics core (SL and HL) paper 1 questions</a></h5> <h5>AHL (HL only): &nbsp; 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