Colligative Properties and "i"

[Zellmer, Robert]

You can find the following information at following link in case

you lose this e-mail (part of the "Helpful Tidbits" link),



Colligative Properties<https://www.asc.ohio-state.edu/zellmer.1/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*m*Kb       del(Tf) = i*m*Kf       P = i*M*R*T

                                               (P = osmotic pressure)



 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.

                no "ion-paring")



m = stated molality of solute (as in "a 1 m NaCl soln")

M = stated molarity of solute (as in "a 1 M NaCl soln")



 i*m = molality of particles   i*M = molarity of particles



The older editions of the textbook defined del(Tb) and del(Tf) to be

positive numbers, as I have in the equations given above and in the

notes.  The latest edition of the textbook redefines them to be

(T_final - T_initial), or more precisely as (T_solution - T_solvent).

This means the del(Tf) would be a negative number and the eqn given

above for del(Tf) would need to be written as



        del(Tf) = - i*m*Kf





For a NONelectrolyte (nondissociating or nonionizing compound) the

'ideal' "i" is 1 (dissolves as a single particle).  This is true for

most molecular molecules 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).



For solutions of electrolytes, usually when we speak of the van't Hoff

factor we are referring to an observed or effective "i".  For a strong

electrolyte it completely dissociates or ionizes but the hydrated ions

(surrounded by waters) still carry a charge and can interact and form

ion pairs (interionic association).  These ion "pairs" aren't permanent.

They come apart and the ions might pair with another ion or not.  They're

continually forming and coming apart but an equilibrium is reached in

which the number of ion pairs remains constant.  This reduces the actual

number of independent particles (effective number of particles) in solution

and this observed "i" 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.

Use the eqns given in class and solve for "i". (Remember my Velcro suit

analogy from lecture on why this observed "i" varies with concentration of

solute).



Example: If 10 NaCl formula units are put in water they dissociate to give

10 Na+ and 10 Cl- ions.  If it behaves ideally (no ion pairs form) there

are 20 particles in soln ("i" = 2).  If it doesn't behave ideally it forms

ion pairs due to interionic attractions.  Let's say 2 Na+***Cl- ion pairs form

(the "***" represent the interionic attractions, they do NOT form an NaCl molecule).

That leaves 8 Na+ and 8 Cl- as free ions.  This gives a total of 18 particles in

soln. (8 Na+ ion, 8 Cl- and 2 Na+***Cl- ion pairs), less then the 20 particles

if no ion-pairs formed ("i" < 2).  Thus, the conc. of independent particles is

lower when ion pairs form.



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 has 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 concentration as mentioned above.



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 (mole fraction of particles)

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.  The mole fraction of particles does approach

i*X as the soln becomes more dilute.  Here is 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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