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<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">We had a lecturers’ meeting on Friday.<span style="mso-spacerun:yes">
</span>I have a little more info about<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">what’s on the final from these last two chapters.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Ch 11:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">I briefly mentioned ionic liquids (Chemistry and Sustainability box in<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Section 11.3).
<span style="mso-spacerun:yes"> </span>We did not cover this in any detail and it’s not on the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">final.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">We did not cover liquid crystals.<span style="mso-spacerun:yes">
</span>They are not on the final.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Ch 12:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Look at what I covered class and my notes.<span style="mso-spacerun:yes">
</span>Also, what I have about<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">solids on Carmen.
<span style="mso-spacerun:yes"> </span>Here’s a little more info.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Know how much of a particle is inside a unit cell depending on where<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">it sits in the unit cell.<span style="mso-spacerun:yes">
</span>In other words, what fraction of a particle is<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">within the unit cell.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Corner<span style="mso-tab-count:2">
</span>1/8 <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Edge<span style="mso-tab-count:2">
</span>1/4<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Face<span style="mso-tab-count:2">
</span>1/2<span style="mso-spacerun:yes"> </span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">totally inside<span class="GramE"><span style="mso-tab-count:1">
</span><span style="mso-spacerun:yes"> </span>1</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Understand the unit cells, primitive cubic (pc, also called simple cubic,<o:p></o:p></span></p>
<p class="MsoNormal"><span class="SpellE"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">sc</span></span><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">), body-centered cubic (bcc), and
face-centered cubic <span class="SpellE">fcc</span>).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Packing efficiency in solids (hcp,
<span class="SpellE">ccp</span>/<span class="SpellE">fcc</span>, bcc, pc).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">For ionic substances understand how to determine the empirical<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">formula from a unit cell.<span style="mso-spacerun:yes">
</span>Based on a description of where the ions<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">are placed in the unit cell or a picture of a unit cell be able to come<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">up with the number of cations and anions in the
<span class="SpellE">u.c.</span> and thus the<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">empirical</span></b><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""> formula.<span style="mso-spacerun:yes">
</span>That’s important and people often mess that<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">up.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">For example, with NaCl we found there are 4 Na+ and 4 Cl- ions<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">w/in the unit cell.<span style="mso-spacerun:yes">
</span>That means the empirical formula is NaCl, <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">as it should be, and there are 4 NaCl formula units per
<span class="SpellE">u.c.</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">NaCl is said to have a face-centered cubic structure, although<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">it doesn’t look like the
<span class="SpellE">fcc</span> structure you see for a single-sized<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">particle (such as
<span class="SpellE">fcc</span> Al, CO2, C60, etc.).<span style="mso-spacerun:yes">
</span>For a single-sized<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">particle a
<span class="SpellE">fcc</span> structure has 4 particles per unit cell but has<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">particles only at each corner and each face.<span style="mso-spacerun:yes">
</span>In NaCl you can<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">picture it as having Cl- ions in a face-centered structure with<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Na+ ions on each edge and 1 Na+ in the center.<span style="mso-spacerun:yes">
</span>You can<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">also look at it with Na+ ions in a face-centered structure with<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Cl- ions on the edges and 1 in the center.<span style="mso-spacerun:yes">
</span>Why is it called<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">face-centered?<span style="mso-spacerun:yes">
</span>If you look at the Cl- <span class="GramE">ions</span> they form a<o:p></o:p></span></p>
<p class="MsoNormal"><span class="SpellE"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">fcc</span></span><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""> structure.<span style="mso-spacerun:yes">
</span>If you look at the Na+ <span class="GramE">ions</span> they form a <span class="SpellE">
fcc</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">structure.<span style="mso-spacerun:yes">
</span>You push the <span class="SpellE">fcc</span> Na+ ions and <span class="SpellE">
fcc</span> Cl- ions halfway<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">into each other and pull the part out where the overlap and<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">you get the NaCl unit cell.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">For
<span class="SpellE">CsCl</span> there’s Cl- ions at the corners with a Cs+ in the center<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">of the cube.<span style="mso-spacerun:yes">
</span>You could also picture it as having Cs+ ions in the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">corners with a Cl- in the center of the cube.<span style="mso-spacerun:yes">
</span>It looks like a<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">body-centered but it technically isn’t.<span style="mso-spacerun:yes">
</span>It’s <span class="GramE">actually a</span> primitive<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">cubic.<span style="mso-spacerun:yes">
</span>What?<span style="mso-spacerun:yes"> </span>The Cl- ions form a pc structure.<span style="mso-spacerun:yes">
</span>The Cs+ ions<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">form a pc structure.<span style="mso-spacerun:yes">
</span>Then push a corner of the pc Cs+ ions<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">into the center of the pc Cl- ions and you get the
<span class="SpellE">CsCl</span> structure.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">In any case, with Cl- ions in each corner you get 1 Cl- ion in the<o:p></o:p></span></p>
<p class="MsoNormal"><span class="SpellE"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">u.c.</span></span><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""> and with 1 Cs+ in the center
you get 1 Cs+.<span style="mso-spacerun:yes"> </span>That gives an<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">empirical formula of
<span class="SpellE">CsCl</span> with 1 <span class="SpellE">CsCl</span> fu/<span class="SpellE">uc</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">For ZnS, the S^2- ions form a
<span class="SpellE">fcc</span> structure, giving 4 S^2- ions<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">w/in the
<span class="SpellE">u.c.</span> and there are 4 Zn^2+ ions inside the unit cell.<span style="mso-spacerun:yes">
</span>That<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">gives an empirical formula of ZnS, as it should be, and 4 ZnS fu/<span class="SpellE">uc</span>.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">For CaF2, the Ca^2+ ions form a
<span class="SpellE">fcc</span> structure, giving 4 Ca^2+<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">ions w/in the
<span class="SpellE">u.c.</span> and there are 8 F- ions inside the unit cell.<span style="mso-spacerun:yes">
</span>That<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">gives an empirical formula of CaF2, as it should be, and 4 CaF2 fu/<span class="SpellE">uc</span>.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">There are figures for all the above in the lecture notes and the
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">material you’ll find on Carmen for solids (as mentioned in previous<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">e-mails).<span style="mso-spacerun:yes">
</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">There are similar things for alloys in the current textbook.<span style="mso-spacerun:yes">
</span>Look at<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">Figure 12.17 in the current edition.<span style="mso-spacerun:yes">
</span>In the current edition, look at<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">EOCEs 12.29, 12.30, 12.57, 12.58, 12.114 and Exam Prep question<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">12.13 for more practice in determining the empirical formula for<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">a solid composed of different elements.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">The Chem dept has a website about crystal structures,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><a href="http://undergrad-ed.chemistry.ohio-state.edu/xtal/index.html"><b>Visualizing Crystal Structures - OSU Chem Dept</b></a>.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">Click on "Crystal Structures".<span style="mso-spacerun:yes">
</span></span><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">It allows you to look at the unit cells,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">rotate them around, see several unit cells together, etc.<span style="mso-spacerun:yes">
</span>You can<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">also find this link at the "Notes" link on my class webpage.
<span style="mso-spacerun:yes"> </span>Make<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">sure to click on "All Atoms".<span style="mso-spacerun:yes">
</span>Also, it can be helpful to ask for more<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">than 1 unit cell.<span style="mso-spacerun:yes">
</span>Don't ask for more than 8 <span class="SpellE">uc</span> at a time, it gets too<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">"busy".<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman""><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">You should also understand the 4 different types of solids, the<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">attractive forces involved and the general properties of each type of<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">solid (conducting or not, melting points, hardness, brittleness, etc.).
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">I went through this in lecture last Thursday. The following link will<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif;mso-bidi-font-family:"Times New Roman"">bring up the summary table, which is in the lecture notes,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><a href="https://www.asc.ohio-state.edu/zellmer.1/chem1210/notes/Table_13-10_solids_no_lines.pdf"><b>Types of Solids and Their Properties</b></a><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">There aren’t a lot of covalent network solids.<span style="mso-spacerun:yes">
</span>Pretty much memorize<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">the ones listed in the table.<span style="mso-spacerun:yes">
</span>They can be “tricky”.<span style="mso-spacerun:yes"> </span>SiO2 is a metalloid<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">with nonmetal and Si is in the same group as C so you might expect<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">SiO2 to behave like CO2.<span style="mso-spacerun:yes">
</span>CO2 is a molecular solid and you might<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">expect SiO2 to be molecular.<span style="mso-spacerun:yes">
</span>That’s not the case. SiO2 is <span class="GramE">a covalent</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">network solid.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">I showed a density calculation in class.<span style="mso-spacerun:yes">
</span>We decided to not include<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">unit-cell calculations on the final exam (density, edge length, etc.).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">There might be one or two density calculations in the Mastering.<span style="mso-spacerun:yes">
</span><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif">Dr. Zellmer<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
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