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<pre>You can find the following information at following link in <span class="GramE">case</span><o:p></o:p></pre>
<pre>you lose this e-mail (part of the "Helpful Tidbits" link),<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre><a href="https://www.asc.ohio-state.edu/zellmer.1/chem1250/faq/collig_prop.txt"><b>Colligative Properties</b></a><o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>This message deals with colligative properties. Hopefully, this <span class="GramE">helps</span><o:p></o:p></pre>
<pre>those of you having problems with this and the equations, especially<o:p></o:p></pre>
<pre>the "i" in the equations I used in class. These equations are below:<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>del(Tb) = i*m*<span class="SpellE">Kb</span> del(<span class="SpellE">Tf</span>) = i*m*<span class="SpellE">Kf</span> P = i*M*R*T<o:p></o:p></pre>
<pre> (P = osmotic pressure)<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre> This "i" is:<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre> 1 for a <span class="SpellE">nondissociating</span> or nonionizing substance<o:p></o:p></pre>
<pre> (this is most molecular substances, with the<o:p></o:p></pre>
<pre> exception of acids & bases)<o:p></o:p></pre>
<pre> # ions from the formula for an "ideal" ionic solution<o:p></o:p></pre>
<pre> (this means no interionic association, i.e.<o:p></o:p></pre>
<pre> no "ion-paring")<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>m = stated molality of solute (as in "a 1 m NaCl <span class="SpellE">soln</span>")<o:p></o:p></pre>
<pre>M = stated molarity of solute (as in "a 1 M NaCl <span class="SpellE">soln</span>")<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre> i*m = molality of particles i*M = molarity of particles<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>The older editions of the textbook defined del(Tb) and del(<span class="SpellE">Tf</span>) to <span class="GramE">be</span><o:p></o:p></pre>
<pre>positive numbers, as I have in the equations given above and in the<o:p></o:p></pre>
<pre>notes. The latest edition of the textbook redefines them to <span class="GramE">be</span><o:p></o:p></pre>
<pre>(<span class="SpellE">T_final</span> - <span class="SpellE">T_initial</span>), or more precisely as (<span class="SpellE">T_solution</span> - <span class="SpellE">T_solvent</span>).<o:p></o:p></pre>
<pre>This means the del(<span class="SpellE">Tf</span>) would be a negative number and the <span class="SpellE">eqn</span> <span class="GramE">given</span><o:p></o:p></pre>
<pre>above for del(<span class="SpellE">Tf</span>) would need to be written as<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre> del(<span class="SpellE">Tf</span>) = - i*m*<span class="SpellE">Kf</span><o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre><o:p> </o:p></pre>
<pre>For a <span class="SpellE">NONelectrolyte</span> (<span class="SpellE">nondissociating</span> or nonionizing compound) the<o:p></o:p></pre>
<pre>'ideal' "i" is 1 (dissolves as a single particle). This is true for<o:p></o:p></pre>
<pre>most molecular molecules which dissolve as a single particle and<o:p></o:p></pre>
<pre>don't ionize (there are some that do, particularly acids - see below).<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>For an electrolyte (a compound that dissociates or ionizes and gives<o:p></o:p></pre>
<pre>more than 1 particle in solution) the 'ideal' "i" is given by the <span class="GramE">number</span><o:p></o:p></pre>
<pre>of particles resulting from the formula. For NaCl i=2 since you get<o:p></o:p></pre>
<pre>2 particles per formula unit (Na+ and Cl-). For Na2SO4 i=3 since you<o:p></o:p></pre>
<pre>get 3 particles per formula unit (2 Na+ and 1 SO4<sup>2</sup>-, the SO4<sup>2</sup>- stays<o:p></o:p></pre>
<pre>together as a single particle). These are the "ideal" values for "i".<o:p></o:p></pre>
<pre>When I speak of an "ideal" ionic solution it means to use the "ideal"<o:p></o:p></pre>
<pre>value for "i" (<span class="GramE">i.e.</span> the "i" you get from the formula). An "ideal"<o:p></o:p></pre>
<pre>ionic solution has no ion association (does not form ion pairs).<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>For solutions of electrolytes, usually when we speak of the <span class="SpellE">van't</span> <span class="GramE">Hoff</span><o:p></o:p></pre>
<pre>factor we are referring to an observed or effective "i". For a strong<o:p></o:p></pre>
<pre>electrolyte it completely dissociates or ionizes but the hydrated <span class="GramE">ions</span><o:p></o:p></pre>
<pre>(surrounded by waters) still carry a charge and can interact and <span class="GramE">form</span><o:p></o:p></pre>
<pre>ion pairs (interionic association). These ion "pairs" aren't permanent.<o:p></o:p></pre>
<pre>They come apart and the ions might pair with another ion or not. They're<o:p></o:p></pre>
<pre>continually forming and coming apart but an equilibrium is reached <span class="GramE">in</span><o:p></o:p></pre>
<pre>which the number of ion pairs remains constant. This reduces the actual<o:p></o:p></pre>
<pre>number of independent particles (effective number of particles) in solution<o:p></o:p></pre>
<pre>and this observed "i" is less than the ideal "i" you get from the <span class="GramE">formula</span><o:p></o:p></pre>
<pre>unit and varies with the concentration of the electrolyte, <span class="GramE">approaching</span><o:p></o:p></pre>
<pre>the ideal "i" for dilute solutions. You can calculate this observed "<span class="GramE">i</span>"<o:p></o:p></pre>
<pre>when given the observed colligative property and molality or molarity.<o:p></o:p></pre>
<pre>Use the <span class="SpellE">eqns</span> given in class and solve for "i". (Remember my Velcro suit<o:p></o:p></pre>
<pre>analogy from lecture on why this observed "i" varies with concentration of<o:p></o:p></pre>
<pre>solute).<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>Example: If 10 NaCl formula units are put in water they dissociate to give<o:p></o:p></pre>
<pre>10 Na+ and 10 Cl- ions. If it behaves ideally (no ion pairs form) there<o:p></o:p></pre>
<pre>are 20 particles in <span class="SpellE">soln</span> ("i" = 2). If it doesn't behave ideally it forms<o:p></o:p></pre>
<pre>ion pairs due to interionic attractions. Let’s say 2 Na+***Cl- ion pairs <span class="GramE">form</span><o:p></o:p></pre>
<pre>(the "***" represent the interionic attractions, they do NOT form an NaCl molecule).<o:p></o:p></pre>
<pre>That leaves 8 Na+ and 8 Cl- as free ions. This gives a total of 18 particles in<o:p></o:p></pre>
<pre>soln. (8 Na+ ion, 8 Cl- and 2 Na+***Cl- ion pairs), less then the 20 particles<o:p></o:p></pre>
<pre>if no ion-pairs formed ("i" < 2). Thus, the conc. of independent particles <span class="GramE">is</span><o:p></o:p></pre>
<pre>lower when ion pairs form.<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>While I've mentioned ionic substances above, this also applies to <span class="GramE">molecular</span><o:p></o:p></pre>
<pre>substances that ionize in solution. These are mostly acids and bases <span class="GramE">such</span><o:p></o:p></pre>
<pre>as HCl, HNO3, NH3 (base), acetic acid, etc. The strong acids you <span class="GramE">learned</span><o:p></o:p></pre>
<pre>in chapter 4 (table 4.2) are strong electrolytes and come apart in H2O<o:p></o:p></pre>
<pre>like ionic substances do. So HCl has an ideal "i" of 2. Weak acids (and<o:p></o:p></pre>
<pre>bases) do not completely ionize so only some of them come apart. This<o:p></o:p></pre>
<pre>makes determining an ideal "i" very difficult. An example of a weak acid<o:p></o:p></pre>
<pre>is acetic acid, CH3CO2H. This molecule is a weak electrolyte and <span class="GramE">does</span><o:p></o:p></pre>
<pre>not completely ionize. So, we can't say with certainty what "i" is. The<o:p></o:p></pre>
<pre>most one can say is it's somewhere between 1 and 2 (1 if it didn't ionize<o:p></o:p></pre>
<pre>and 2 if it completely ionized). Thus, for the same stated conc. of<o:p></o:p></pre>
<pre>solute, for acetic acid one can say it has a larger effect than <span class="GramE">something</span><o:p></o:p></pre>
<pre>like glucose, C6H12O6, which doesn't ionize in H2O (i=1) and has a smaller<o:p></o:p></pre>
<pre>effect than something like HCl or NaCl which completely ionize or <span class="GramE">dissociate</span><o:p></o:p></pre>
<pre>(ideal i=2) . <span class="GramE">Of course</span> an observed "i" (<span class="SpellE">van't</span> Hoff factor) can be calculated<o:p></o:p></pre>
<pre>for acetic acid. This is one of the ways we determine how much acetic <span class="GramE">acid</span><o:p></o:p></pre>
<pre><span class="GramE">actually ionizes</span> (as we will discuss further in chapter 16). Also, <span class="GramE">remember</span><o:p></o:p></pre>
<pre>the <span class="SpellE">van't</span> Hoff factor varies with concentration as mentioned above.<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>The things I've just said apply to all the colligative properties.<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre>You may have noticed that you didn't see an "i" in the vapor pressure <span class="GramE">lowering</span><o:p></o:p></pre>
<pre>equations. Unlike molarity or molality, <span class="SpellE">X_part</span> (mole fraction of particles)<o:p></o:p></pre>
<pre>is not exactly equal to i*<span class="SpellE">X_stated</span>, <span class="GramE">i.e.</span> a NaCl solution with a mole fraction<o:p></o:p></pre>
<pre>of 0.4 NaCl will not simply be 0.8 mole fraction in particles (2*0.4). The<o:p></o:p></pre>
<pre>actual mole fraction of particles (ions) for this NaCl solution is 0.57 (not 0.8).<o:p></o:p></pre>
<pre>However, even though the mole fraction of particles can't strictly <span class="GramE">be</span><o:p></o:p></pre>
<pre>determined from multiplying the mole fraction of a substance times "i", <span class="GramE">it</span><o:p></o:p></pre>
<pre>can be approximated as such (especially as the solution becomes more dilute)<o:p></o:p></pre>
<pre>and you can still use these principles for comparing the vapor <span class="GramE">pressure</span><o:p></o:p></pre>
<pre>lowering of several substances. The mole fraction of particles does <span class="GramE">approach</span><o:p></o:p></pre>
<pre>i*X as the <span class="SpellE">soln</span> becomes more dilute. Here is a formula you can derive (prove<o:p></o:p></pre>
<pre>this for yourself) that gives the mole fraction of ions:<o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre><o:p> </o:p></pre>
<pre> i * <span class="SpellE">X_solute</span><o:p></o:p></pre>
<pre> <span class="SpellE">X_ions</span> = --------------------------<o:p></o:p></pre>
<pre> <span class="SpellE">X_solvent</span> + i * <span class="SpellE">X_solute</span><o:p></o:p></pre>
<pre><o:p> </o:p></pre>
<pre><o:p> </o:p></pre>
<pre><o:p> </o:p></pre>
<pre> Dr. Zellmer<span style="font-size:11.0pt;font-family:"Arial",sans-serif"><o:p></o:p></span></pre>
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