tag:blogger.com,1999:blog-20955840509095653602024-03-17T01:12:35.312-07:00The problem with the aufbau principle for finding electronic configurationsEric Scerrihttp://www.blogger.com/profile/11518257339531938496noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2095584050909565360.post-10838148678895926502015-08-03T04:12:00.001-07:002015-08-03T04:12:42.853-07:00Five ideas in chemical education that must die – part two<a href="http://www.rsc.org/blogs/eic/2015/07/le-ch%C3%A2telier-principle-equilibrium#.Vb9MoQJAxaU.blogger">Five ideas in chemical education that must die – part two</a>Eric Scerrihttp://www.blogger.com/profile/11518257339531938496noreply@blogger.com1tag:blogger.com,1999:blog-2095584050909565360.post-41821276506717345792012-07-19T14:44:00.000-07:002012-07-19T14:58:26.380-07:00more on the 'sloppy aufbau principle'<div style="color: red;">
<span style="font-size: large;">Eric Scerri,</span></div>
<div style="color: red;">
<span style="font-size: large;">UCLA, Department of Chemistry & Biochemistry,</span></div>
<div style="color: red;">
<span style="font-size: large;">Los Angeles.</span></div>
<div style="color: red;">
<span style="font-size: large;"><br /></span></div>
<div style="color: red;">
<span style="font-size: large;">website: http://ericscerri.com</span></div>
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<span style="font-size: large;"><br /></span><br />
<span style="font-size: large;">In a recent posting I mentioned what I called the 'sloppy aufbau', that seems to have taken root in almost all chemistry and physics textbooks which claim to explain how the electronic configurations of atoms develop as one moves through the periodic table.</span><br />
<span style="font-size: large;"><br /></span><br />
<span style="font-size: large;">Although the reception has been encouragingly favorable, a few textbook writers have written to me to say that their book covers the topic adequately and does not fall into the trap that I am trying to highlight. On checking each of these books I find that although a number of them issue cautions when using the n + l rule or the aufbau principle, none of them actually state explicitly that for scandium, and the following atoms in the first transition, the 3d orbitals are occupied before the 4s.</span><br />
<span style="font-size: large;"><br /></span><br />
<span style="font-size: large;">What I want to do here is to emphasize that what I am urging and what has been discussed in recent articles by Schwarz is nothing new. It seems to be a matter of 'having to rediscover the wheel'. In addition to a few old textbooks from the 1940s and 50s that give a full and accurate account, I have found two articles in the <i>Journal of Chemical Education</i> that warn explicitly against the use of the sloppy aufbau even though they don't call it so. </span><br />
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<span style="font-size: large;">For example, exactly 50 years ago, R.N. Keller wrote,</span><br />
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<span style="font-size: large;">In the case of scandium, cited above, the 19th electron
assumes a 3d state rather than a 4s state because the Sc<sup>+1</sup> ion
has lower total energy with a 3d<sup>1</sup>
than with a 4s<sup>1 </sup>configuration.</span></div>
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<span style="font-size: large;"><br /></span></div>
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<span style="font-size: large;">However, the Sc<sup>+</sup> ion is more stable if the 20<sup>th</sup>
electron occupies a 4s orbital rather than a 3d, or, a 3d<sup>1</sup>4s<sup>1</sup> state is more
stable for this ion than a 3d<sup>2</sup> or a 4s<sup>2</sup> state. Similarly the lowest lying state for
neutral scandium, 3d<sup>1</sup>4s<sup>2</sup>, is a more favorable state
energetically than any other state such as 3d<sup>3</sup>, 4s<sup>2</sup>4p<sup>1</sup>,
etc.</span></div>
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<span style="font-size: large;"><br /></span></div>
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<span style="font-size: large;">Or saying this in a slightly different way, the effective
nuclear charge in tri-positive scandium is such as to cause the 19th electron
added (i.e., Sc<sup>+3</sup> + e- </span><span style="font-family: Wingdings; font-size: large;"><b>---></b></span><span style="font-size: large;"><b> </b>Sc<sup>2+</sup>) to occupy the 3d level because this level lies lower
energetically than the 4s. </span></div>
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<span style="font-size: large;">However, once the 19th electron has been added, the whole
electronic energy level system for Sc<sup>+2</sup> is now slightly different
from that for Sc<sup>+3</sup>. The interaction of the nucleus of scandium with the 19
electrons in Sc<sup>+2</sup> produces a field which favors a 4s state for the
20th electron added (i.e., Sc<sup>2+ </sup><b>+ </b>e- </span><span style="font-family: Wingdings; font-size: large;">---></span><span style="font-size: large;"> Sc<sup>1+</sup>). The
resulting field in turn favors a 4s state for the 21<sup>st </sup>electron
added. </span></div>
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<span style="font-size: large;"> R.N. Keller, <span style="font-style: italic;">Journal
of Chemical Education</span>,
39, 289-293, 1962.</span></div>
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<span style="font-size: large;">Even earlier, in an article published in 1950 (62 years ago), also in <i>J Chem. Ed.,</i> the author D.F. Swinehart also complains of the careless use of the aufbau and among other things says,</span><br />
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" /><br />
<style>
<!--
/* Font Definitions */
@font-face
{font-family:"MS 明朝";
mso-font-charset:78;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:-536870145 1791491579 18 0 131231 0;}
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;
mso-font-charset:0;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:-536870145 1107305727 0 0 415 0;}
@font-face
{font-family:Cambria;
panose-1:2 4 5 3 5 4 6 3 2 4;
mso-font-charset:0;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:-536870145 1073743103 0 0 415 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-unhide:no;
mso-style-qformat:yes;
mso-style-parent:"";
margin:0in;
margin-bottom:.0001pt;
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<span style="font-size: 16pt;"><span style="font-family: Times,"Times New Roman",serif;">It is rather odd to see this clear-cut case of a regression in the teaching of chemistry and physics. This is not supposed to happen. So why does it happen? Or is it just part of the overall downgrading in science education, especially in the US, as described in the latest issue of <i>Scientific American</i>? </span></span><br />
<span style="font-size: 16pt;"><span style="font-family: Times,"Times New Roman",serif;"><br /></span></span><br />
<span style="font-size: 16pt;"><span style="font-family: Times,"Times New Roman",serif;"><br /></span></span><br />
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<br /></div>Eric Scerrihttp://www.blogger.com/profile/11518257339531938496noreply@blogger.com4tag:blogger.com,1999:blog-2095584050909565360.post-33354754338813423842012-07-11T10:37:00.001-07:002012-07-11T11:47:25.328-07:00The anomalous configuration of the chromium atom and related issues<div class="WordSection1">
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<span style="font-size: large;">Eric Scerri</span></div>
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<span style="font-size: large;">UCLA</span></div>
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<span style="font-size: large;">Department of Chemistry & Biochemistry</span></div>
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<span style="font-size: large;">Los Angeles, CA</span></div>
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<ul>
<li><span style="font-size: large;">Website: <a href="http://ericscerri.com/">http://ericscerri.com/</a></span><span style="font-size: large;"> </span></li>
</ul>
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<span style="font-size: large;">In this the third of my recent
chemistry postings I want to consider topic that is related to my aufbau post,</span><br />
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<span style="font-size: large;"><a href="http://ericscerri.blogspot.com/">http://ericscerri.blogspot.com/</a></span></div>
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<span style="font-size: large;">I want to think about the question
of the so-called anomalous configurations that occur is some d and f-block
atoms (shown in yellow in the diagram below). </span><br />
<span style="font-size: large;"><br /></span><br />
<div class="separator" style="clear: both; text-align: center;">
<span style="font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgu0kCEJxlpfHGQVjjMG7Iq2YOp808lDt4YkR65phGrm8gnjpNGdUF03sIZhDw_knN7PB0zeJ0BoCzrRHUihdcQ-Q5y3i5dWplfpp9e_Q07Zdk5E7IrogLq4aSB8IMvIdEZ5zs3Nc8tkGLz/s1600/AAanomolous-jpg.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="491" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgu0kCEJxlpfHGQVjjMG7Iq2YOp808lDt4YkR65phGrm8gnjpNGdUF03sIZhDw_knN7PB0zeJ0BoCzrRHUihdcQ-Q5y3i5dWplfpp9e_Q07Zdk5E7IrogLq4aSB8IMvIdEZ5zs3Nc8tkGLz/s640/AAanomolous-jpg.jpg" width="640" /></a></span></div>
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<ul>
<li><span style="font-size: large;">As with the previous posts
there is a strong connection with chemistry teaching. This
is because students are often taught that the configurations of chromium and
copper, in particular, show anomalies from the way that orbitals are occupied
as we traverse the transition element series. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">Chromium is said to have a
configuration of 3d<sup>5</sup> 4s<sup>1</sup> as opposed to 3d<sup>4</sup> 4s<sup>2</sup>. Copper atoms are said to have a configuration
of 3d<sup>10</sup> 4s<sup>1</sup> as opposed to 3d<sup>9</sup> 4s<sup>2</sup>
as might have been expected from the general trend. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">Now there is good
spectroscopic evidence for these anomalous configurations and this is not
something I am proposing to question at least not in this post.<a href="http://www.blogger.com/blogger.g?blogID=5169820381149897125#_edn1" name="_ednref1" title=""><span class="MsoEndnoteReference"><span class="MsoEndnoteReference"><span style="font-family: Cambria;">[1]</span></span></span></a></span></li>
</ul>
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<ul>
<li><span style="font-size: large;">I want to begin to look
closely at the commonly given textbook explanation for <i>why</i> chromium has the configuration that it has. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">Textbooks almost invariably
claim that the configuration of 3d<sup>5</sup> 4s<sup>1</sup> possesses a
half-filled sub-shell and that this is consequently more stable than the
expected configuration of 3d<sup>4</sup> 4s<sup>2</sup>. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">I think that such
an explanation is not very credible but worse, that it is <i>ad hoc</i> in a rather literal sense of the term. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">Of course it may be true that
the energy of the anomalous configuration is lower than that of the expected
one. After all, why else would the
anomalous one be observed if that were not the case? </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">But is it <i>because</i> of the much-cited half-filled
sub-shell stability? I don’t think so
and if you’ll permit me I will replace that mouthful by the abbreviation hfss
to stand for half-filled sub-shell from now on. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">To see the limitations of
such an explanation we can just look at the atoms in the second transition
series that also have anomalous configurations.
There are in fact six of them, </span></li>
<li><span style="font-size: large;"><b>Nb, Mo, Ru, Rh, Pd, Ag</b></span></li>
</ul>
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<ul>
<li><span style="font-size: large;">I am going to ignore
palladium and silver for the moment since they have filled d-orbitals and so
cannot play any role in arguments considering the role of hfss. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">But of the remaining four
cases, only one of them, molybdenum, has a hfss and not surprisingly perhaps it
lies directly below chromium in the periodic table. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">Clearly then the adoption of
an anomalous cannot be explained in general by appealing to a hfss. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">Here is another way of
thinking of this issue by drawing on an approach that is often used in
philosophy, and which goes by the name of “necessary & sufficient
conditions”. </span></li>
</ul>
</div>
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<ul>
<li><span style="font-size: large;">Let me illustrate this with
an example from chemistry-atomic physics.
As is well known, the identity of an element can be established
unambiguously by from a knowledge of the atomic number of its atoms. Moreover the relationship runs in the
opposite sense too, in that a specification of an atomic number serves to
identify the element in question. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">A philosopher looking at this
situation might say that the possession of a particular value of Z is both
necessary and sufficient for the identification of any element. </span></li>
</ul>
</div>
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<ul>
<li><span style="font-size: large;">Let me unpack this a little
further because such language is not all that familiar in chemistry and
physics. If Z = 79, for example, the
element must be gold. We say that having
an atomic number of 79 is sufficient (is enough) to ensure that the element
must be gold. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">Conversely, if the element is
to count as gold, it is necessary (essential) for it to have an atomic number of 79. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">The relationship runs in both
directions without any exceptions.
Because of this fact, we can be confident that the use of atomic number
really “nails” the identity of all elements. </span></li>
</ul>
</div>
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<ul>
<li><span style="font-size: large;">Now let’s go back to those
pesky anomalous configurations and the possession or otherwise of ‘hfss’.</span></li>
</ul>
</div>
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<ul>
<li><span style="font-size: large;">It turns out, rather
disappointingly, that the possession of a hfss is neither necessary nor
sufficient for an atom to display an anomalous configuration. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">The reason why it is not
necessary should be clear from the fact that Nb, Ru, Rh all show anomalies but <i>none</i> of them in fact have a hfss. The
reason why it is not sufficient is that there are cases which <i>do have</i> hfss and yet <i>do not</i> show anomalous configurations. This is true of manganese, technetium,
rhenium and bohrium all of which have d<sup>5</sup> configurations.<a href="http://www.blogger.com/blogger.g?blogID=5169820381149897125#_edn2" name="_ednref2" title=""><span class="MsoEndnoteReference"><span class="MsoEndnoteReference"><span style="font-family: Cambria;">[2]</span></span></span></a> </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">So where does this leave the
commonly found explanation for the anomaly in chromium in terms of hfss
stability? Simply put – not in a very
good place. It so happens that chromium
shows both a hfss and an anomalous configuration but this is seldom
generalizable. </span></li>
</ul>
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<ul>
<li><span style="font-size: large;">In other words, the
explanation is ad hoc<a href="http://www.blogger.com/blogger.g?blogID=5169820381149897125#_edn3" name="_ednref3" title=""><span class="MsoEndnoteReference"><span class="MsoEndnoteReference"><span style="font-family: Cambria;">[3]</span></span></span></a> in
the literal sense of having been brought to bear at a particular place (Cr) while
being powerless in more general cases.</span></li>
</ul>
</div>
</div>
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<ul>
<li><span style="font-size: large;"><i>So please stop inflicting it
on unsuspecting young students!</i></span></li>
</ul>
</div>
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<ul>
<li><span style="font-size: large;">Have I labored the point a
little? Well perhaps I have but what I
am trying to do is to ask chemistry instructors to think a little more deeply and
more critically about the contents of chemistry courses and the manner in which
material is presented to students.</span></li>
</ul>
<ul>
<li><span style="font-size: large;">Finally, I have said a good deal about
how not to explain the configuration in chromium or other anomalous
cases but have yet to make any positive suggestions. But that will need
to wait for a future blog. There are in fact several better
approaches. </span></li>
</ul>
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<div style="mso-element: endnote-list;">
<span style="font-size: large;"><br /></span><br />
<hr align="left" size="1" width="33%" />
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<span style="font-size: large;"><b>Notes</b></span></div>
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<span class="MsoEndnoteReference" style="font-size: large;"><span class="MsoEndnoteReference"><span style="font-family: Cambria;">[1]</span></span></span><span style="font-size: large;"> The question of precisely what to regard as the
ground state configuration will be taken up in a future posting.</span></div>
</div>
<div id="edn2">
<div class="MsoEndnoteText">
<br />
<span style="font-size: large;"><a href="http://www.blogger.com/blogger.g?blogID=5169820381149897125#_ednref2" name="_edn2" title=""><span class="MsoEndnoteReference"><span class="MsoEndnoteReference"><span style="font-family: Cambria;">[2]</span></span></span></a></span><span style="font-size: large;"> In the f-block Eu and Am have hfss configurations of
f<sup>7</sup> but don’t show anomalous configurations.</span></div>
</div>
<div id="edn3" style="mso-element: endnote;">
<div class="MsoEndnoteText">
<br />
<span style="font-size: large;"><a href="http://www.blogger.com/blogger.g?blogID=5169820381149897125#_ednref3" name="_edn3" title=""><span class="MsoEndnoteReference"><span class="MsoEndnoteReference"><span style="font-family: Cambria;">[3]</span></span></span></a></span><span style="font-size: large;"> Ad hoc is Latin for “to here” in the sense of an
explanation imported into a particular place with little concern for whether it
applies in other places or situations.
Such an explanation is of course considered to be a ‘bad thing’. </span></div>
<div class="MsoEndnoteText">
<br />
<span style="font-size: large;"><b>General References</b></span></div>
<div class="MsoEndnoteText">
<span style="font-size: large;">Eric Scerri, <i>A Very Short Introduction to the Periodic
Table</i>, Oxford University Press, Oxford, 2011.</span></div>
<div class="MsoEndnoteText">
<span style="font-size: large;"><a href="http://www.amazon.com/Periodic-Table-Short-Introduction-Introductions/dp/0199582491/ref=sr_1_3?s=books&ie=UTF8&qid=1308095562&sr=1-3">http://www.amazon.com/Periodic-Table-Short-Introduction-Introductions/dp/0199582491/ref=sr_1_3?s=books&ie=UTF8&qid=1308095562&sr=1-3</a></span></div>
<div class="MsoEndnoteText">
<span style="font-size: large;">For other books please
see,</span></div>
<div class="MsoEndnoteText">
<span style="font-size: large;"><a href="http://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3Dstripbooks&field-keywords=eric+scerri">http://www.amazon.com/s/ref=nb_sb_noss_1?url=search-alias%3Dstripbooks&field-keywords=eric+scerri</a></span></div>
<div class="MsoEndnoteText">
</div>
<div class="MsoEndnoteText">
</div>
</div>
</div>Eric Scerrihttp://www.blogger.com/profile/11518257339531938496noreply@blogger.com42tag:blogger.com,1999:blog-2095584050909565360.post-59218870738117105762012-07-11T10:34:00.002-07:002012-07-11T11:56:41.096-07:00A blog, or more like a rant, against the use of Le Châtelier’s Principle in learning and teaching chemistry<br />
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<br />
<div style="text-align: center;">
Eric Scerri</div>
<div style="text-align: center;">
UCLA</div>
<div style="text-align: center;">
Department of Chemistry & Biochemistry</div>
<div style="text-align: center;">
Los Angeles, CA</div>
<div style="text-align: center;">
website: ericscerri.com/</div>
<br />
<br /></div>
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<span style="font-size: 18pt;">Following
my recent post on the sloppy use of the aufbau principle, </span></div>
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<a href="http://ericscerri.blogspot.com/2012/06/trouble-with-using-aufbau-to-find.html"><span style="font-size: 18pt;">http://ericscerri.blogspot.com/2012/06/trouble-with-using-aufbau-to-find.html</span></a><span style="font-size: 18pt;"> </span></div>
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</div>
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<br />
<span style="font-size: 18pt;">I
have been encouraged to try my hand at another blog on a topic in chemical
education, namely the Le Ch</span><span style="font-size: 18pt;">â</span><span style="font-size: 18pt;">telier Principle.</span></div>
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</div>
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<span style="font-size: 18pt;">Here
is a typical version of the principle that you might find in a chemistry
textbook,</span></div>
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</div>
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<br />
<i><span style="font-size: 18pt;">If a dynamic equilibrium is
disturbed by changing the conditions, the position of equilibrium moves to
counteract the change.</span></i></div>
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</div>
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<br />
<span style="font-size: 18pt;">I
want you to notice the use of the word “counteract” which is frequently also
rendered as “oppose”, because I am going to argue that this is the root of all
the problems associated with the use of this principle. The principle is supposed to aid the student
or even the expert in predicting the effect brought about by a change in
conditions such as changing the total pressure on a system, or the
concentration of one or more reactants or products or the temperature. </span></div>
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</div>
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<br />
<br />
<span style="font-size: 18pt;">In
fact this is going to be more of a rant than a blog because I believe that this
principle is more of a hindrance than a help.
The first time I ever taught a chemistry class was in a high school in
London when I was standing in for another teacher and had to teach equilibrium
theory and the use of the Le Ch</span><span style="font-size: 18pt;"> </span><span style="font-size: 18pt;">telier Principle. I made such a mess of the class and tied myself
up in so many knots that I swore I would quit teaching immediately. That is until I began to think more carefully
about this issue and started to realize that the problem lay more with the
wording in the principle rather than just with me. </span></div>
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</div>
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<br />
<br />
<b><span style="font-size: 18pt;">So what’s the problem?</span></b></div>
<div class="MsoNormal">
<span style="font-size: 18pt;">Pretend
for a moment that you are a novice student coming to this topic for the first
time. You are presented with the
principle as a means of predicting the outcome of making one of three possible
changes as mentioned above. Of course you
are happy to be given this guide and begin applying it to changes in pressure
for example. Let us assume we are
discussing the case of the Haber reaction in which three moles of hydrogen
react with one mole of nitrogen to yield two moles of ammonia. You might visualize this mixture as being
placed in a large balloon for example.
Now let’s apply the principle. If
the total pressure is increased you might be tempted to predict that the system
or balloon will expand to a larger volume in order to “counteract” or “oppose”
the increased pressure that is being applied in squeezing the balloon. </span></div>
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</div>
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<br />
<br />
<b style="color: red;"><span style="font-size: 18pt;">But that’s wrong says the
instructor</span></b><span style="font-size: 18pt;"></span></div>
<div class="MsoNormal">
<span style="font-size: 18pt;">Unfortunately
if you follow the letter of the principle in this way the instructor will soon
tell you that you have made a wrong prediction.
Experiments show that on increasing the total pressure the equilibrium
position shifts in such a way as to produce more ammonia, that is to say the
equilibrium moves in the direction of a volume decrease rather than an
increase. </span></div>
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</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br />
<span style="font-size: 18pt;">3 H<sub>2</sub> <sub>(g)</sub>
+ N<sub>2</sub>
<sub>(g)</sub> </span><span style="font-family: Symbol; font-size: 18pt;"><</span><span style="font-family: Symbol; font-size: 18pt;">----</span><span style="font-family: Symbol; font-size: 18pt;">></span><span style="font-size: 18pt;">
</span><span style="font-size: 18pt;">2 NH<sub>3
(g)</sub></span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">So
what went wrong? Well you were supposed
to assume that the volume remains constant for one thing so the analogy with
squashing the balloon was invalid. But
nobody tells that to the poor student.
The change that does actually occur is more a case of ‘accommodating’
the change rather than opposing it, something which leads many textbooks<a href="http://www.blogger.com/blogger.g?blogID=4745866948787875491#_edn1" name="_ednref1" style="mso-endnote-id: edn1;" title=""><span class="MsoEndnoteReference"><span class="MsoEndnoteReference"><span style="font-family: Cambria; font-size: 18pt;">[i]</span></span></span></a>
to alter the wording of the principle to something like the following version,</span></div>
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</div>
<div class="MsoNormal" style="margin-left: .5in;">
<br />
<i><span style="font-size: 18pt;">If a chemical system at equilibrium experiences a
change… then the equilibrium shifts to accommodate the imposed change and a new
equilibrium is established</span></i><span style="font-size: 18pt;">.</span></div>
<div class="MsoNormal" style="margin-left: .5in;">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">But
just a moment! This means making a 180<sup>0</sup>
change to the original statement.
Accommodating is surely the opposite of counteracting? If I try to push you away and you oppose my
push you push me back. If on the other
hand I try to push you away and you accommodate this change you might yield to
my push and fall down to the floor. It
seems rather odd that the principle needs to be rescued by substituting a word
for “oppose” which in facts means the very opposite of oppose. </span></div>
<div class="MsoNormal" style="color: red;">
</div>
<div class="MsoNormal" style="color: red;">
<br />
<br />
<b><span style="font-size: 18pt;">So how can it be done
properly?</span></b></div>
<div class="MsoNormal">
<span style="font-size: 18pt;">As
anyone who teaches high school or college chemistry is aware there is a amore
categorical way to predict the outcome of raising or lowering the total
pressure on a mixture of gases in equilibrium.
This involves setting up an expression for the equilibrium constant for
the reaction and expanding the partial pressure of each gas in terms of
products of mole fractions and total pressures,</span></div>
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</div>
<div class="MsoNormal">
<span style="font-size: 18pt;"> </span><br />
<span style="font-size: 18pt;"> K<sub>p </sub>=
<u>(p NH<sub>3</sub>)<sup>2</sup> </u></span></div>
<div class="MsoNormal">
<span style="font-size: 18pt;">
(p H<sub>2</sub>)<sup>3</sup> (p N<sub>2</sub>)</span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;"> = <u>(M.F. NH<sub>3</sub>)<sup>2</sup>
(P<sub>total</sub>)<sup>2</sup></u></span></div>
<div class="MsoNormal">
<span style="font-size: 18pt;"> (M.F. H<sub>2</sub>)<sup>3 </sup>(P<sub>total</sub>)<sup>3</sup>.
(M.F. N<sub>2</sub>)(P<sub>total</sub>)</span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">where </span><span style="font-family: Symbol; font-size: 18pt;">M.F.</span><span style="font-size: 18pt;"> denotes mole fraction in each case. </span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;"> = <u>(M.F.</u><u> NH<sub>3</sub>)<sup>2</sup> </u></span></div>
<div class="MsoNormal">
<span style="font-size: 18pt;"> (M.F. H<sub>2</sub>)<sup>3</sup>
(M.F. N<sub>2</sub>)(P<sub>total</sub>)<sup>2</sup></span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">We
can now argue that since pressure changes do not alter the value of the
equilibrium constant, raising P<sub>total </sub>results in an increase in the
ratio of ,</span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<span style="font-size: 18pt;"> = <u>(M.F.
NH<sub>3</sub>)<sup>2</sup> </u></span></div>
<div class="MsoNormal">
<span style="font-size: 18pt;"> (M.F. H<sub>2</sub>)<sup>3</sup> (M.F. N<sub>2</sub>)</span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">which
in turn implies an increase in the yield of ammonia at the expense of the mole
fraction of the two reacts of hydrogen and nitrogen. </span></div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">The
bottom line is that <i style="mso-bidi-font-style: normal;">more</i> ammonia is
produced by <i style="mso-bidi-font-style: normal;">raising the total pressure</i>
of the system. </span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<div style="color: red;">
<b><span style="font-size: 18pt;">How about changes in concentration?</span></b></div>
</div>
<div class="MsoNormal">
<span style="font-size: 18pt;">Whereas
we are more or less forced to smuggle words like accommodate or alleviate into
the original wording of the Le Ch</span><span style="font-size: 18pt;">â</span><span style="font-size: 18pt;">telier
Principle in order to make sense of what happens on raising the pressure, when
it comes to changes in concentrations of reactants or products, it appears that
the original word “oppose” does a perfect job in making sense of the
situation. Consider the following case
in which substances A and B react together to form C and D,</span></div>
<div class="MsoNormal">
</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br />
<span style="font-size: 18pt;">A + B </span><span style="font-family: Symbol; font-size: 18pt;"><</span><span style="font-family: Symbol; font-size: 18pt;">----</span><span style="font-family: Symbol; font-size: 18pt;">></span><span style="font-size: 18pt;">
</span><span style="font-size: 18pt;"> C + D</span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">If
I raise the concentration of A or of B or even of both of them, the net outcome
is that the equilibrium position will shift to the right and that larger
concentrations of C and D will be produced.
Here the word “oppose” works fine.
As I increase the concentration of A for example the reaction responds
by using up the additional A and as a result larger concentrations of C and D
are formed. </span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">Of
course this can all be done more rigorously by writing an expression for the
equilibrium constant of the reaction and seeing what happens when one of the
concentrations is increased. It is easy
to predict that the concentrations of C and D will be increased since making
changes in concentrations of any substance has no effect of the equilibrium
constant itself. </span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br />
<span style="font-size: 18pt;">Kc =
<u>[C] [D]</u></span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<span style="font-size: 18pt;"> [A] [B]</span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal" style="color: red;">
<br />
<b><span style="font-size: 18pt;">What about temperature
changes?</span></b></div>
<div class="MsoNormal">
<span style="font-size: 18pt;">In
the case of temperature the problem returns.
If we try to use the wording that involves “oppose” the constraint we
can easily obtain the completely incorrect answer. And I mean <i style="mso-bidi-font-style: normal;">completely</i> incorrect as in the case of pressure changes, in the
sense of an error of 180<sup>0</sup>. </span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<span style="font-size: 18pt;">Consider
again the Haber reaction from above but now let’s include the sign of the
enthalpy change on going from left to right which is in fact negative to denote
an exothermic reaction. </span></div>
<div class="MsoNormal" style="margin-left: .5in;">
</div>
<div class="MsoNormal">
<br />
<div style="text-align: center;">
<span style="font-size: small;">3 H<sub>2</sub> +
N<sub>2</sub> </span><span style="font-family: Symbol; font-size: small;"><</span><span style="font-family: Symbol; font-size: small;">----</span><span style="font-family: Symbol; font-size: small;">></span><span style="font-size: small;"> 2 NH<sub>3</sub> : </span><span style="font-family: Symbol; font-size: small;">Delta </span><span style="font-size: small;">H = - 92 kJ/mol</span></div>
</div>
<div class="MsoNormal" style="color: red;">
<br />
<br />
<b><span style="font-size: 18pt;">How might a student reason?</span></b></div>
<div class="MsoNormal">
<span style="font-size: 18pt;">Let
us again put ourselves in the shoes of a novice student trying to innocently
use the Le Ch</span><span style="font-size: 18pt;">â</span><span style="font-size: 18pt;">telier Principle in order to
predict the outcome of raising the temperature on this system. The student might reason as follows, </span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">If
the temperature of the system is raised and if the outcome is that the system
attempts to <i style="mso-bidi-font-style: normal;">oppose</i> this change then
the system will proceed in the exothermic direction so as to remove the
increased heat. Alas the instructor will
immediately point out that this is the incorrect prediction. Experimental evidence shows clearly that
raising the temperature on any exothermic reaction has the effect of favoring
the reaction which proceeds in the endothermic rather than the exothermic
direction. </span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">Again,
as in the case of pressure changes, the student feels let down by Le Ch</span><span style="font-size: 18pt;">â</span><span style="font-size: 18pt;">telier. Again
in order to rescue the principle many textbooks will cheerfully alter the
wording of the principle in order to say that the system will <i style="mso-bidi-font-style: normal;">accommodate</i> rather than oppose the
change. If so then they can argue that
the additional heat is accommodated by the system’s moving in an endothermic
direction, since absorbing the extra heat amounts to accommodating or
nullifying the change. So once again it
is not a case of opposing the change but quite the opposite a case of yielding
to the change or of accommodating it.</span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<br />
<b><span style="font-size: 18pt;"><span style="color: red;">Taking stock</span> </span></b></div>
<div class="MsoNormal">
<span style="font-size: 18pt;">If
what I am saying is correct, then in the three classic changes that are typically
considered, namely pressure , concentration and temperature changes, the
original Le Ch</span><span style="font-size: 18pt;">â</span><span style="font-size: 18pt;">telier Principle which
features the word “oppose” only works in one out of three cases. That’s not a very good success rate by any
stretch of the imagination!</span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<div style="color: red;">
<b><span style="font-size: 18pt;">What to do?</span></b></div>
</div>
<div class="MsoNormal">
<span style="font-size: 18pt;">My
recommendation to textbook authors and chemistry instructors is quite
simple. Please ditch the use of Le Ch</span><span style="font-size: 18pt;">â</span><span style="font-size: 18pt;">telier’s Principle as a guide to what happens when
changes are made to chemical systems in equilibrium. Instead do it rigorously from first
principles by setting up expressions for the equilibrium constant and seeing
what happens when changes are made to pressure of concentrations of reactants
and products. </span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<br />
<div style="color: red;">
<b><span style="font-size: 18pt;">Except for temperature changes</span></b></div>
</div>
<div class="MsoNormal">
<span style="font-size: 18pt;">Notice
that I have omitted temperature changes.
This is because the rigorous approach to temperature changes is
different from what it is for pressure or concentration for the simple reason
that equilibrium constants actually vary with temperature. But there are simple thermodynamic expressions
which can be used to predict what happens when the temperature is raised or
lowered in cases of exothermic or endothermic reactions respectively. </span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<span style="font-size: 18pt;">For
example it can be shown that for exothermic reactions the equilibrium constant
K is related to temperature in the following manner,</span></div>
<div align="center" class="MsoNormal" style="text-align: center;">
</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br />
<span style="font-size: 18pt;">ln K is proportional to 1/T</span></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<br />
<span style="font-size: 18pt;">from
which it follows that as temperature increases the natural logarithm of K
decreases and so K itself decreases which implies that the reaction proceeds
from right to left rather than the other way round. Bottom line:
Exothermic reactions are favored by lowering the temperature rather than
by raising it. All this without getting
tied up in knots with words and hand waving in trying to use the awful Le Ch</span><span style="font-size: 18pt;">â</span><span style="font-size: 18pt;">telier Principle.
</span></div>
<br />
<hr align="left" size="1" width="33%" />
<div class="MsoEndnoteText">
<a href="http://www.blogger.com/blogger.g?blogID=4745866948787875491#_ednref1" name="_edn1" style="mso-endnote-id: edn1;" title=""><span class="MsoEndnoteReference"><span class="MsoEndnoteReference"><span style="font-family: Cambria; font-size: 12pt;">[i]</span></span></span></a> I don’t claim to have made a full survey of
textbooks but here is an example of the variety in the wording used by a selection of general
chemistry books,</div>
<div class="MsoEndnoteText">
<br />
•Atkins………………………………..….minimizes</div>
<div class="MsoEndnoteText">
•Chan…………………………………..…relieves</div>
<div class="MsoEndnoteText">
•Petrucci et al……………………..….partially offsets</div>
<div class="MsoEndnoteText">
•Whitten, Davis, Peck…….…….... counteracts</div>
<div class="MsoEndnoteText">
•Moore, Stanitsky, Jurs……………partially counteracts</div>
<div class="MsoEndnoteText">
•Brown, Le May, Bursten……..… counteracts</div>
<div class="MsoEndnoteText">
•Kotz, Trichel……………………..…..reduces or minimizes</div>
<div class="MsoEndnoteText">
•Zumdahl……………………………..…reduces</div>
<div class="MsoEndnoteText">
•Oxtoby, Gillies, Nachtrieb……….counteracts</div>
<div class="MsoEndnoteText">
<i> </i></div>
<div class="MsoEndnoteText">
<i>Also found, “accommodates” the constraint</i></div>Eric Scerrihttp://www.blogger.com/profile/11518257339531938496noreply@blogger.com2tag:blogger.com,1999:blog-2095584050909565360.post-24015859618998021112012-06-24T07:28:00.000-07:002012-07-01T07:32:09.754-07:00The trouble with using the aufbau to find electronic configurations<style>
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<br />
<div style="color: red;">
Eric Scerri</div>
<div style="color: red;">
Department of Chemistry & Biochemistry</div>
<div style="color: red;">
UCLA</div>
<div style="color: red;">
Los Angeles, CA 90095</div>
<div style="color: red;">
<br /></div>
<div style="color: red;">
website: http://ericscerri.com<br />
<br /></div>
<b>The Periodic Table
and the Aufbau</b> <br />
<div class="MsoNormal">
One of the biggest topics in the teaching and learning of
chemistry is the use of the aufbau principle to predict the electronic
configurations of atoms and to explain the periodic table of the elements. This method has been taught to many
generations of students and is a favorite among instructors and textbooks when
it comes to setting questions. In this
blog I am going to attempt to blow the lid off the aufbau because it is deeply flawed, or at least the sloppy version of the aufbau. The flaw is rather subtle and seems to have
escaped the attention of nearly all chemistry and physics textbooks and the
vast majority of chemistry professors that I have consulted on the subject.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The error comes from what may be an innocent attempt to simplify
matters or maybe just an understandable slip as I will try to explain. Whatever the cause there is no excuse for
perpetuating this educational myth as I will try to explain.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">So what’s the
problem?</b></div>
<div class="MsoNormal">
The aufbau method was originally proposed by the great
Danish physicist Niels Bohr who was the first to bring quantum mechanics to the
study of atomic structure and one of the first to give a fundamental
explanation of the periodic table in terms of arrangements of electrons
(electronic configurations). Bohr
proposed that we can think of the atoms of the periodic table as being
progressively built up starting from the simplest atom of all, that of hydrogen
which contains just one proton and one electron. The other atoms differ from hydrogen by the
addition of one proton and one electron.
Helium has two protons and two electrons, lithium has three of each,
beryllium has four of each, all the way to uranium which at that time, (1913),
was the heaviest known atom, weighing in at 92 protons and 92 electrons. Neutron numbers vary and are quite irrelevant
to this story incidentally.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The next ingredient is a knowledge of the atomic orbitals
into which the electrons are progressively placed in an attempt to reproduce
the natural sequence of electrons in atoms that occur in the real world. Oddly enough these orbitals, at least in
their simplest form, nowadays come from solving the Schrödinger equation for the hydrogen
atom but let’s not get too sidetracked for the moment.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">The orbitals</b></div>
<div class="MsoNormal">
The different atomic orbitals come in various kinds that are
distinguished by labels such as s, p, d and f.
Each shell of electrons can be broken down into various orbitals and as
we move away from the nucleus each shell contains a progressively larger number
of kinds of orbitals. Here is the well-known
scheme,</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
First shell contains 1s
orbital only</div>
<div class="MsoNormal">
Second shell contains 2s
and 2p orbitals</div>
<div class="MsoNormal">
Third shell contains 3s, 3p and 3d orbitals</div>
<div class="MsoNormal">
Fourth shell contains 4s, 4p, 4d and 4f orbitals and so
on.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The next part is that one needs to know how many of these
orbitals occur in each shell. The answer
is provided by the simple formula 2(<span style="font-family: "MT Extra";">l</span>+
1) where <span style="font-family: "MT Extra";">l</span>
takes different values depending on whether we are speaking of s, p, d or f
orbitals.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
For s orbitals <span style="font-family: "MT Extra";">l</span>
= 0, for p orbitals l = 1, for d orbitals l = 2 and so on.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
As a result there are potentially one s orbital, three p
orbitals, five d orbitals, seven f orbitals and so on for each shell.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
So far so good. Now
comes the magic ingredient which claims to predict the order of filling of
these orbitals and here is where the fallacy lurks. Rather than filling the shells around the
nucleus in a simple sequential sequence, where each shell must fill completely
before moving onto the next shell, we are told that the correct procedure is
more complicated. But we are also
reassured that there is a nice simple pattern that governs the order of shell
and consequently of orbitals filling.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
And this is finally the point at which the aufbau diagram,
which I am going to claim lies at the heart of the trouble, is trotted out. </div>
<div class="MsoNormal">
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRpOqLhdG0Xh0MjncvxpXpBHviJ2Gz3aFj0reaooaw8j3c607vJUW0wBKJpvyA_hGAOz4hvfarlNSARxeSSAhg51hw-0MrOeUmVe9XkW_Tf-aBMOFFXpclByxZ-Gv1T0DmCy8-bALdNiI/s1600/aufbau+diagram.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRpOqLhdG0Xh0MjncvxpXpBHviJ2Gz3aFj0reaooaw8j3c607vJUW0wBKJpvyA_hGAOz4hvfarlNSARxeSSAhg51hw-0MrOeUmVe9XkW_Tf-aBMOFFXpclByxZ-Gv1T0DmCy8-bALdNiI/s1600/aufbau+diagram.jpg" /></a></div>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The order of filling is said to be obtained by starting at
the top of the diagram and following the arrows pointing downwards and towards
the left-hand margin of this diagram.
Following this procedure gives us the order of filling of orbitals with
electrons according to this sequence,</div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
1s < 2s < 2p
< 3s < 3p < 4s < 3d < 4p < 5s < 4d …</div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal">
This recipe when combined with a knowledge of how many
electrons can be accommodated in each kind of orbital and the number of such
available orbital in each shell is now supposed to give us a prediction of the
complete electronic configuration of all but about 20 atoms in which further
irregularities occur, such as the cases of chromium and copper. Again I don’t want to get side-tracked and so
will concentrate on one of the far more numerous regular configurations.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;">Some examples</b></div>
<div class="MsoNormal">
To see how this simplified and ultimately flawed method
works let me consider a few examples.
The atom of magnesium has a total of 12 electrons. Using the method above this means that we
obtain an electronic configuration of,</div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
1s<sup>2</sup>, 2s<sup>2</sup>,
2p<sup>6</sup>, 3s<sup>2</sup></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal">
in beautiful agreement with experiments which can examine
the configuration directly through the spectra of atoms. Let’s look at another example, an atom of calcium
which has 20 electrons. Following the
well-known method gives a configuration of,</div>
<div align="center" class="MsoNormal" style="text-align: center;">
1s<sup>2</sup>, 2s<sup>2</sup>,
2p<sup>6</sup>, 3s<sup>2</sup>, 3p<sup>6</sup>, 4s<sup>2</sup></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal">
and once again there is perfect agreement with experiments
on the spectrum of calcium atoms. </div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
But now let’s see what happens for the very next atom, namely
scandium with its 21 electrons.
According to the time honored aufbau method the configuration should be,</div>
<div class="MsoNormal">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center;">
1s<sup>2</sup>, 2s<sup>2</sup>,
2p<sup>6</sup>, 3s<sup>2</sup>, 3p<sup>6</sup>, 4s<sup>2</sup>, 3d<sup>1</sup></div>
<div align="center" class="MsoNormal" style="text-align: center;">
<br /></div>
<div class="MsoNormal">
and indeed it is. But
many books proceed to spoil the whole thing by claiming, not unreasonably
perhaps, that the final electron to enter the atom of scandium is a 3d electron
when in fact experiments point quite clearly to the fact that the 3d orbital is
filled <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><u>before</u></i></b> the 4s orbital.
The correct version can be found in very few textbooks but seems to have
been unwittingly forgotten or distorted in many cases by generations of
instructors and textbook authors as I mentioned at the outset. How can such an odd situation arise?</div>
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<b style="mso-bidi-font-weight: normal;">Why the mistake
occurs</b></div>
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But how can such an apparently blatant mistake have occurred
and taken such root in chemical education circles? The answer is as interesting as it is
subtle. First of all there is the fact
that the overall configuration is in fact correctly given by following the
sloppy approach. But if one asks
questions about the order of filling the sloppy approach gives the wrong answer
as I have been pointing out. But even
worse, it has led many teachers and textbooks to invent all kinds of contorted
schemes in order to explain why even though the 4s orbital fills preferentially
(as it does in the sloppy version) it is also the 4s electron that is
preferentially ionized to form an ion of Sc<sup>+</sup>. Since these contortions are pure inventions I
will not waste the reader’s time by looking into them. They are quite simply incorrect since as a
matter of fact, the 4s orbital fills last and consequently, as simple logic
dictates, is the first orbital to lose an electron on forming a positive
ion. </div>
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<b style="mso-bidi-font-weight: normal;">What’s the
evidence? </b></div>
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But how can I be so confident in claiming that the vast
majority of chemistry teachers, professors and textbook authors have erred in
presenting the sloppy version. The
answer is that one can just consider the experimental evidence on the ions of
any particular transition metal atom such as scandium, </div>
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<br /></div>
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<span lang="IT">Sc<sup>3+</sup> (tri-positive
ion) </span>1s<sup>2</sup>,
2s<sup>2</sup>, 2p<sup>6</sup>, 3s<sup>2</sup>, 3p<sup>6</sup>, <span lang="IT">3d<sup>0</sup>, 4s<sup>0</sup></span></div>
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<span lang="IT">Sc<sup>2+</sup> (di-positive
ion) </span>1s<sup>2</sup>, 2s<sup>2</sup>, 2p<sup>6</sup>, 3s<sup>2</sup>,
3p<sup>6</sup>, <span lang="IT">3d<sup>1,</sup> 4s<sup>0</sup></span></div>
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<span lang="IT">Sc<sup>1+</sup> </span>(mono-positive ion) 1s<sup>2</sup>, 2s<sup>2</sup>,
2p<sup>6</sup>, 3s<sup>2</sup>, 3p<sup>6</sup>, 3d<sup>1</sup>, 4s<sup>1</sup></div>
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<span lang="IT">Sc<sup> </sup></span> (neutral atom) 1s<sup>2</sup>, 2s<sup>2</sup>, 2p<sup>6</sup>,
3s<sup>2</sup>, 3p<sup>6</sup>, 3d<sup>1</sup>, 4s<sup>2</sup></div>
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On moving from the <span lang="IT">Sc<sup>3+ </sup></span>ion to that of <span lang="IT">Sc<sup>2+ </sup></span>it is plain to see that the additional electron
enters a 3d orbital and not a 4s orbital as the sloppy scheme dictates. Similarly on moving from this ion to the <span lang="IT">Sc<sup>1+ </sup></span>ion the additional
electron enters a 4s orbital as it does in finally arriving at neutral scandium
atom or Sc. Similar patterns and
sequences are observed for the subsequent atoms in the periodic table including
titatium, vanadium, chromium(with further complications), manganese and so on.</div>
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<b style="mso-bidi-font-weight: normal;">Psychological factors</b></div>
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I have been thinking about what psychological factors
contribute to the retention of the sloppy aufbau. As I already mentioned it does give the
correct overall configuration for all but about 20 atoms that show anomalous
configurations, such as chromium, copper, molybdenum and many others.</div>
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Another factor is that it gives chemistry professors the
impression that they really can predict the way in which the atom is built-up
starting from a bare nucleus to which electrons are successively added. Presumably it also gives students the
impression that they can make similar predictions and perhaps convinces them of
the worthiness of the aufbau and scientific knowledge in general. </div>
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The fact remains that it is not possible to predict the
configuration in any of the transition metals, and indeed the lanthanides, or
if it comes down to it even the p-block elements. Let’s go back to scandium. Contrary to the sloppy aufbau that is almost
invariably taught, the 3d orbitals have a lower energy than 4s starting with
this element. If we were to try to
predict the way that the electrons fill in scandium we might suppose that the
final three electrons after the core argon configuration of</div>
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1s<sup>2</sup>, 2s<sup>2</sup>,
2p<sup>6</sup>, 3s<sup>2</sup>, 3p<sup>6</sup></div>
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would all enter into some 3d orbitals to give,</div>
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1s<sup>2</sup>, 2s<sup>2</sup>,
2p<sup>6</sup>, 3s<sup>2</sup>, 3p<sup>6</sup>, 3d<sup>3</sup></div>
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<br /></div>
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The observed configuration however is,</div>
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<br /></div>
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1s<sup>2</sup>, 2s<sup>2</sup>,
2p<sup>6</sup>, 3s<sup>2</sup>, 3p<sup>6</sup>, 3d<sup>1</sup>, 4s<sup>2</sup></div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;">What’s really
happening?</b></div>
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This amounts to saying that all three of the final electrons
enter 3d but two of them are repelled into an energetically less favorable
orbital, the 4s, because the overall result is more advantageous for the atom
as a whole. But this is not something
that can be predicted. Why is it 2
electrons, rather than one or even none?
In cases like chromium and copper just one electron is pushed into the
4s orbital. In an analogous case from
the second transition series, the palladium atom, the competition occurs between the 5s and 4d
orbitals. In this case none of the electrons are pushed up into the 5s orbital and the resulting configuration has an outer shell of [Kr]4d<sup>10</sup>. </div>
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None of this can be predicted in simple terms from a rule of
thumb and so it seems almost worth masking this fact by claiming that the
overall configuration can be predicted, at least as far as the cases in which
two electrons are pushed up into the relevant s orbital. To those who like to present a rather
triumphal image of science it is too much to admit that we cannot make these
predictions. The use of the sloppy
aufbau seems to avoid this problem since it gives the correct overall
configuration and hardly anybody smells a rat.</div>
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<br /></div>
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<b style="mso-bidi-font-weight: normal;">But why do electrons
get pushed up into the relevant s orbital?</b></div>
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Finally, it is natural to now ask why it is that one or two
electrons are usually pushed into a higher energy orbital, other than the
answer I already gave which is to say that doing so produces a more stable atom
overall. The answer lies in the fact
that 3d orbitals are more compact than 4s to consider the first transition, and
as a result any electrons entering 3d orbitals will experience greater mutual
repulsion. </div>
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The slightly unsettling feature is that although the
relevant s orbital can relieve such additional electron-electron repulsion
different atoms do not always choose to make full use of this form of
sheltering because the situation is more complicated than the way in which I
have described it. After all there is
the fact that nuclear charge increases as we move through the atoms. At the end of the day there is a complicated
set of interactions between the electrons and the nucleus as well as between
the electrons themselves. This is what
ultimately produces an electronic configuration and contrary to what some
educators would wish for, there is no simple qualitative rule of thumb that can
cope with this complicated situation.
</div>
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<b style="mso-bidi-font-weight: normal;">Bottom line</b></div>
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There is absolutely no reason for chemistry professors and
textbook authors to continue to teach the sloppy version of the aufbau. Not only does it give false predictions
regarding the order of electron filling in atoms but it also causes authors and
instructors to tell further educational lies.
They are forced to invent some elaborate explanations in order to undo
the error in an attempt to explain why 4s is occupied preferentially (which it
is not) but also preferentially ionized which it is.</div>
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The sloppy version also implies that the 4s orbital has a
lower energy than 3d for all atoms which is not the case, or that the 5s
orbital has a lower energy than 4d which is not the case for all atoms and so
on. Similar issues arise in the f-block
elements.</div>
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It is high time that the teaching of aufbau and electronic
configurations were carried out properly in order to reflect the truth of the
matter rather than taking a short-cut and compounding it with a further
imaginary story.</div>
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<b style="mso-bidi-font-weight: normal;">References</b></div>
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The following references are among the few that give the
correct explanation;</div>
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S-G.
Wang, W. H. E. Schwarz, <i style="mso-bidi-font-style: normal;">Angew. Chem. Int.
Ed</i>. 2009, 48, 19, 3404–3415. </div>
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S. Glasstone, <i style="mso-bidi-font-style: normal;">Textbook of Physical Chemistry</i>, D. Van Nostrand, New York, 1946.</div>
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<u><a href="http://www.amazon.com/David-W.-Oxtoby/e/B001ILM8CI/ref=ntt_athr_dp_pel_1"><span style="color: windowtext; text-decoration: none;"></span></a></u>D.W. Oxtoby, H.P. Gillis, A. Campion,<i style="mso-bidi-font-style: normal;"> Principles of Modern Chemistry</i>, Sixth Edition, </div>
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Thomson/Brooks Cole, 2007.</div>
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<b>General Reference on the Periodic Table</b><br />
Eric Scerri, <i>A Very Short Introduction to the Periodic Table</i>, Oxford University Press, 2011 </div>
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<br /></div>Eric Scerrihttp://www.blogger.com/profile/11518257339531938496noreply@blogger.com180