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/chem1250/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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