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<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">I got a question from someone about a MC problem. I've changed it slightly.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">"Why is the ion-solvent attractive force greater for a smaller ion, such as Mg^2+<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">compared to Ca^2+?" Related to this would be "Which is more soluble in H2O,<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">NaCl or Fe2O3"?<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">This has to do with the form of the ion-ion interaction energy and the form of<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">the ion-dipole interaction energy. The equations for the energy due to these<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">interactions are very similar.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">The lattice energy (LE) is the energy required to separate the ions in order<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">for them to dissolve in solution.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">LE (for ionic cmpds) = (Q+)(Q-)/d<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Q is charge on an ion<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">d is the distance between the ions (measured center-to-center)<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">The ion-dipole (ID) energy is the energy released when ions from an ionic<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">solid dissolve and are solvated (surrounded) by the solvent. This is due to<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">the ion-solvent interaction. This term (energy) is negative since it's energy<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">released when attractive forces are formed.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">ID energy (ions in polar solvent) = (Q+)(u)/d^2<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Q is charge on an ion<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">u is dipole moment of the polar molecule<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">d is the distance between the particles (measured center-to-center)<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Look at both equations just in terms of these variables and what they tell us<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">about these energies.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">If the value for Q (the charge on an ion) inc. then both types of energies inc.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">The more polar the solvent (large dipole moment) the greater the ID energy.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">The smaller the ions or molecules the shorter the distance between them. A<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">smaller distance means greater energy for both LE and ID energy.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Thus, as the charge on the ions inc. the greater the LE and ID energy.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">The smaller the ions the greater the LE and ID energy.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">In terms of solubility of an ionic cmpd dissolved in a polar solvent, both terms<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">increase as the charges on the ions inc. and the size of the ions (and solvent<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">molecules) dec. This is the "charge density" in my notes and I spoke about in<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">class (charge per unit volume or charge/distance). So why does the solubility<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">of ionic cmpds decrease as charges inc. and the ions get smaller if both terms<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">inc.? That's due to the form of the two eqns. As the charge density inc. (larger<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">charges and smaller ions) the LE inc. more than does the ID energy. Thus, the<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">delta(H)_soln becomes more positive (more endothermic, i.e. the energy gap<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">between the solute/solvent and solution gets bigger). As this occurs the<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">delta(H)_soln can become so positive that not enough disorder, entropy, can be<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">created during the solution formation to overcome this uphill energy difference.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Think about the energy diagrams I covered in lecture. The first step would be to<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">separate the ions in the ionic solid from each other. The energy required to do<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">this is related to the lattice energy. The third step is due to the formation of<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">attractive forces between the ions and the solvent molecules (lets say H2O) and<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">is the ion-dipole energy. Both of these steps are relatively large. The second<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">step would be the energy req. to separate the H2O molecules, del(H)2 (this is<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">approx. zero, very small compared to the energy of the first and third steps).<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">So lets say we're talking about comparing the solubility of two ionic cmpds in<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">which one of them has larger charges (to keep things simple we'll say the sizes<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">of the different ions remains about the same). As the charges on the ions inc.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">both the LE and ID energies increase for both ionic cmpds. However, the inc.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">in del(H)1 is bigger than the inc. in del(H)3 (for example del(H)1 inc. by a factor<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">of 2 while del(H)3 inc. by a factor of 1.5.). This would mean the del(H)soln for<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">the cmpd with bigger charges is more positive than del(H)soln for the cmpd with<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">smaller charges. This will tend to make the one with larger charges less soluble.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">In summary, for ionic cmpds the bigger the charges on the ions and the smaller<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">the ions (the greater the LE) the higher the melting pt. and the less soluble the<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">ionic cmpd. NaCl is very soluble in water while Fe2O3 is insoluble.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">In a similar vein, I discussed a diamond dissolving in a liquid. Diamonds<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">are a covalent-network solid (i.e. a crystal of carbon atoms held together with<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">covalent bonds). The first step would be separating the C atoms from each other<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">(breaking a huge number of covalent bonds). A tremendous amount of energy<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">is required to do this, even if you don't break every last C-C bond (del(H)1 is huge).<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Again, the energy req. to separate the solvent molecules (such as water, C6H14,<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">etc.) is very small compared to the first step. The third step, the mixing (solvation)<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">step would involve only London Forces between the C atoms/fragments and the<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">solvent molecules. This del(H)3 would be very small compared to del(H)1. Thus,<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">the del(H)soln would be very large (very positive). Even though the del(S)soln<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">would be positive (there's an inc. in disorder, entropy, going from very ordered<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">diamond to C atoms/fragments) not enough entropy can be created to overcome<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">this large positive del(H)soln so that a solution would form spontaneously.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Diamonds are insoluble even at relatively high temps (except in solvents in which<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">they would react with the solvent to form a soluble product, like nitric acid, HNO3).<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">I hope this helps.<o:p></o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif"><o:p> </o:p></span></p>
<p class="MsoPlainText"><span style="font-size:12.0pt;font-family:"Arial",sans-serif">Dr. Zellmer<o:p></o:p></span></p>
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