Colligative Properties and "i"

[robert zellmer]

You can find the following information at following link in case you 
lose this e-mail (part of the "Helpful Tidbits" link), *Colligative 
Properties* 
<http://chemistry.osu.edu/%7Erzellmer/chem1220/faq/collig_prop.txt>

This message deals with colligative properties. Hopefully this helps 
those of you having problems with this and the equations, especially the 
"i" in the equations I used in class. These equations are below: del Tb 
= i*Kb*m del Tf = i*Kf*m P = i*M*R*T This "i" is: 1 for a 
nondissociating or nonionizing substance (this is most molecular 
substances, with the exception of acids & bases) # ions from the formula 
for an "ideal" ionic solution (this means no interionic association, 
i.e. "ion-paring") i*m = molality of particles i*M = Molarity of 
particles For a NONelectrolyte (nondissociating or nonionizing compound) 
the "i" is 1 (dissolves as a single particle). This is true for most 
molecular substances, which dissolve as a single particle and don't 
ionize (there are some that do, particularly acids - see below). For an 
electrolyte (a compound that dissociates or ionizes and gives more than 
1 particle in solution) the 'ideal' "i" is given by the number of 
particles resulting from the formula. For NaCl i=2 since you get 2 
particles per formula unit (Na^+ and Cl^- ). For Na2SO4 i=3 since you 
get 3 particles per formula unit (2 Na^+ and 1 SO42-, the SO42- stays 
together as a single particle). These are the "ideal" values for "i". 
When I speak of an "ideal" ionic solution it means to use the "ideal" 
value for "i" (i.e. the "i" you get from the formula). An "ideal" ionic 
solution has no ion association (does not form ion pairs). Usually when 
we speak of the van't Hoff factor we are referring to an observed or 
effective "i". The actual number of effective particles in solution is 
less than the ideal "i" you get from the formula unit and varies with 
the concentration of the electrolyte, approaching the ideal "i" for 
dilute solutions. You can calculate this observed "i" when given the 
observed colligative property and molality or molarity. This behavior is 
due to interionic attractions between the ions in the solution leading 
to the formation of ion pairs. This reduces the number of independent 
particles. While I've mentioned ionic substances above this also applies 
to molecular substances that ionize in solution. These are mostly acids 
and bases such as HCl, HNO3, NH3 (base), acetic acid, etc. The strong 
acids you learned in chapter 4 (table 4.2) are strong electrolytes and 
come apart in H2O, like ionic substances do. So HCl has an ideal "i" of 
2. Weak acids (and bases) do not completely ionize so only some of them 
come apart. This makes determining an ideal "i" very difficult. An 
example of a weak acid is acetic acid, CH3CO2H. This molecule is a weak 
electrolyte and does not completely ionize. So we can't say with 
certainty what "i" is. The most one can say is it's somewhere between 1 
and 2 (1 if it didn't ionize and 2 if it completely ionized). Thus, for 
the same stated conc. of solute, for acetic acid one can say it has a 
larger effect than something like glucose, C6H12O6, which doesn't ionize 
in H2O (i=1) and a smaller effect than something like HCl or NaCl which 
completely ionize or dissociate (ideal i=2) . Of course an observed "i" 
(van't Hoff factor) can be calculated for acetic acid. This is one of 
the ways we determine how much acetic acid actually ionizes (as we will 
discuss further in chapter 16). Also, remember the van't Hoff factor 
varies with conc. The things I've just said apply to all the colligative 
properties. You may have noticed that you didn't see an "i" in the vapor 
pressure lowering equations. Unlike molarity or molality, X_part is not 
exactly equal to i*X_stated, i.e. a NaCl solution with a mole fraction 
of 0.4 NaCl will not simply be 0.8 mole fraction in particles (2*0.4). 
The actual mole fraction of particles (ions) for this NaCl solution is 
0.57 (not 0.8). However, even though the mole fraction of particles 
can't strictly be determined from multiplying the mole fraction of a 
substance times "i", it can be approximated as such (especially as the 
solution becomes more dilute) and you can still use these principles for 
comparing the vapor pressure lowering of several substances. There is 
actually a formula you can derive (prove this for yourself) that gives 
the mole fraction of ions: i * X_solute X_ions = 
-------------------------- X_solvent + i * X_solute Dr. Zellmer

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