van't Hoff factor determination

How to determine the approximate van't Hoff factor

Summary

In the following discussion, the solvent is water. The general principles apply to all solvent, but the details vary.

Some relevant definitions:

Electrolyte: This is a compound which forms hydrated ions in solution. It resultant solution has the property that it conducts electricity to some extent.

Nonelectrolyte: This is a compound which does not form hydrated ions in solution. It resultant solution has the property that it conducts electricity about as poorly as pure water..

Strong electrolyte: This electrolyte completely (>98%) dissociates into the hydrated ions in solution. It resultant solution has the property that it conducts electricity very well.

Weak electrolyte: This electrolyte dissociates into the hydrated ions in solution to only a limited extent. It resultant solution has the property that it conducts electricity poorly, but better than pure water.

What is the van't Hoff factor:^footnote1

The van't Hoff factor, symbol i, expresses how may ions and particles are formed (on an average) in a solution from one formula unit of solute.

Examples:

One formula unit of NaCl will create two particles in solution, a Na⁺ ion and a Cl^- ion.
One formula unit of CaCl₂ will create three particles in solution, a Ca⁺ ion and two Cl^- ions.
One formula unit (molecule) of methanol CH₃OH will create only one particle in solution, since methanol is a non electrolyte and does not dissolve as ions.
One formula unit (molecule) of HF will form one particle in solution, since it is a weak electrolyte (weak acid).^footnote2
One formula unit (molecule) of NH₃ will form one particle in solution, since it is a weak electrolyte (weak base).^footnote2

How to determine the approximate van't Hoff factor:

The first step is to be able to recognize whether one is dealing with an electrolyte or a non electrolyte. It is easier to recognize electrolytes, although the student by this point should be able to recognize the following organic functional groups which are associated with non electrolytes (not a complete list). The dashes, - and >, correspond to covalent bonds to another atom, usually C.

The alcohol group -OH
The carboxylic acid group -COOH
The amine groups: primary amine -NH₂, secondary amine >NH and ternary amine >N-
The ether group -O-

If you are not familiar with these groups, go back to some of the CHEM 1100 handouts.

To recognize electrolytes:

All acids, bases and salts are electrolytes. The definitions of these terms are found in CHEM 1110 handouts. This includes the salts and acids of the polyatomic ions. Thus, you need to know your polyatomic ion list which is in your lab manual or in the CHEM 1110 handouts. You must also know this list in order! Below is the some of the list in the form of the acids. Notice the lines which delineate the 8 acids in the upper right.

HClO	HClO₂	HClO₃	HClO₄
HBrO	HBrO₂	HBrO₃	HBrO₄
HIO	HIO₂	HIO₃	HIO₄
	H₂SO₃	H₂SO₄
	HNO₂	HNO₃

H₃PO₂	H₃PO₃	H₃PO₄
		H₂CO₃

Strong acids: (belong to the class of strong electrolytes)

The strong acids completely break up into hydronium ions and the anions in solution. The following are the strong acids:

The binary acids HCl, HBr and HI (the hydrohalic acids except for HF). Thus, for example, HCl dissolves in water by the reaction:

HCl (g) + H₂O → H₃O⁺ + Cl^-

This gives a van't Hoff factor or 2. (i = 2)

The 8 ternary acids in the upper right side of the table above (to the right and above the blank non-tabled boxes presented) are all strong^footnote3. Thus, for example, HClO4 dissolves in water by the reaction:

HClO₄ + H₂O → H₃O⁺ + ClO₄^-

This gives a van't Hoff factor or 2. (i = 2)

All other acids are weak, including the organic acids which have the functional group -COOH.

Weak Acids: (belong to the class of weak electrolytes)

All weak acids have a van't Hoff factor of approximately 1.

Example: The acid HClO₂ has a van't Hoff factor of 1. This acid is, according to the table above, a weak acid.

Example: The acid HF has a van't Hoff factor of 1. This binary acid is not HCl, HBr or HI and is therefore a weak acid.

Example: The acid CH₃COOH has a van't Hoff factor of 1. This acid is not a mineral acid, but rather an organic acid. All organic acids, if they dissolve, are weak acids in water solutions.

Strong Soluble Bases:

The strong soluble bases are the hydroxide compounds of group I metals and group II metals from Ca down on the periodic chart. All other metal hydroxides are insoluble bases and only a very small amount will dissolve in water. (Notice that OH^- was on your polyatomic ion list!)

Examples:

LiOH has a van't Hoff factor of two. LiOH is a strong soluble base (group 1 metal hydroxide) and dissolves in water according to:

LiOH (s) → Li⁺ + OH^-

Thus, each formula unit yields two ions total.

Ca(OH)₂ has a van't Hoff factor of three. Ca(OH)₂ is a strong soluble base (group 1 metal hydroxide) and dissolves in water according to:

Ca(OH)₂ (s) → Ca²⁺ + 2OH^-

Thus, each formula unit yields three ions total.

Insoluble Bases:

These are irrelevant since they are insoluble in water. Examples include: Mg(OH)₂, Fe(OH)₃,
Zn(OH)₂, etc.

Weak Soluble Bases:

Most weak soluble bases may be recognized by being nitrogen compounds. These are either amines (see above) or are nitrogen compounds with nitrogen covalently bonded to hydrogen.

Examples:

    ammonia NH₃
    methyl amine CH₃NH₂
    hydrazine H₂NNH₂

Salts are Strong Electrolytes:^footnote4

Salt break up into their ions. For binary salts break into the individual metal ions (cations) and nonmetal ions (anions)
Some typical examples of binary salts:
NaCl(s) → Na⁺ + Cl^- i = 2

Li₂S(s) → 2Li⁺ + S^2- i = 3

CaBr₂(s) → Ca²⁺ + 2Br^- i = 3

FeCl₃(s) → Fe³⁺ + 3Cl^- i = 4

Some typical examples of binary salts:
NaCl(s) → Na⁺ + Cl^-	i = 2
Li₂S(s) → 2Li⁺ + S^2-	i = 3
CaBr₂(s) → Ca²⁺ + 2Br^-	i = 3
FeCl₃(s) → Fe³⁺ + 3Cl^-	i = 4

For salts with polyatomic ions (here's where you need to know your polyatomic ions - learn them if you haven't by now) break up into metal ion (cation) and the polyatomic ion as a unit.
Some typical examples that have polyatomic ions
Na₂SO₄^2- (s) → 2Na⁺ + SO₄^2- i = 3

Fe₃(PO₄)₂ (s) → 3Fe²⁺ + 2 PO₄^3- i = 5

Some typical examples that have polyatomic ions
Na₂SO₄^2- (s) → 2Na⁺ + SO₄^2-	i = 3
Fe₃(PO₄)₂ (s) → 3Fe²⁺ + 2 PO₄^3-	i = 5

Salts of weak bases. (Recall that the weak soluble bases are the nitrogen compounds other than HNO₃ and HNO₃.)

Some typical examples of salts formed from weak bases:
NH₄Cl (s) → NH₄⁺ + Cl^-	i = 2
CH₃NH₂NO₃ (s) → CH₃NH₃⁺ + NO₃^-	i = 2
(NH₄)₂SO₄ (s) → 2NH₄⁺ + SO₄^2-	i = 3
(NH₄)₃PO₄ (s) → 3NH₄⁺ + PO₄^3-	i = 4

Summary:

All water soluble compounds have a van't Hoff factor of approximately 1 except:

    Compounds which begin with metal ions. These include salts and strong bases.
    Soluble salts of weak bases (originating from nitrogen compounds - review section on recognizing weak bases.)
    Strong acids - so you need to be able to recognize a strong acid.
    Strong soluble bases (redundant) - so you need to be able to recognize a strong soluble base.     Back to top

Some more subtle caveats

Actual measurements of the van’t Hoff factors often yield values slightly different from that obtain by the calculations so far described. These difference could be due to several factors, but some of these include:

Some momentary association for the anions and cations in solutions. This phenomenon is dependent upon concentration. For example, for HCl the van’t Hoff factor for a 0.001 M solution is 1.98, and for a 0.20 M solution is 1.90. Thus, for these solutions, the van’t Hoff factor is slightly lower than the expected 2.

However other effects might increase this number. For example, for HCl at 1.00 M, the van’t Hoff factor is 2.12, that is higher than expected. The following is a table of van’t Hoff factors reprinted from “Fundamental Principles of Physical Chemistry” by Carl F. Prutton and Samuel H. Maron, (revised, The MaMillan Company, NY 1951)

**van't Hoff factors for some electrolytes**
C_m /M	HCl	HNO₃	NH₄Cl	CuSO₄	H₂SO₄	CoCl₂	K₂SO₄	K₃Fe(CN)₆
0.0005								3.92
0.001	1.98						2.84	3.82
0.002	1.97					2.88		3.70
0.0025				1.61	2.72		2.83
0.005	1.95	1.97	1.95	1.54	2.59	2.80	2.77	3.51
0.01	1.94	1.96	1.92	1.45	2.46	2.75	2.70	3.31
0.05	1.90	1.91	1.88	1.22	2.21	2.64	2.45	3.01
0.10	1.89	1.89	1.85	1.12	2.12	2.62	2.32	2.85
0.20	1.90	1.87	1.82	1.03	2.04	2.66	2.17	2.69
0.40		1.86			1.98	2.78	2.04
1.00	2.12	1.92	1.79	0.93	2.17	3.40
2.00	2.38	2.04	1.80		2.73	4.58
4.00	3.40	2.24	1.80		3.79

You should notice that some of the numbers are higher and some are lower than the numbers predicted from the simple treatment above. The ones that are above, for example, H₂SO₄ may be involved in other equilibria such as:

H₂SO₄ + H₂O → HSO₄^- + H₃O⁺ since the first protonic hydrogen is strong and
HSO₄^- + H₂O ⇌ SO₄^2- + H₃O⁺ since HSO₄^- is a weak acid to the extent of approximately 1%.

These facts largely account for the factor that is greater than the strong acid value of 2.

On the other hand, most salts have a van't Hoff factor smaller than expected, and gets smaller as the concentration goes up. It is thought that this is due to the strong tendency for the cations (+) and anions (-) to stay in close proximity and behave as if they were chemically bound.

Solutions, however, can be quite complex, expecially as the concentrations of the salts approach saturation. For example, the case for CoCl₂ which approaches the expected 3 as the concentration goes down, but also goes up at the higher concentrations. (...and a minimum at about 0.1 M.) General rules under these conditions are not readily available and each case must be considered individually.

footnote 1: This discussion is for the determination of the van't Hoff factor in very dilute solutions. The effect of the associated ionic species will be ignored in this discussion. The student should be cautioned that in concentrated solutions the van't Hoff factor will be somewhat less than that figured by this discussion. This is due to some association of the ions with each other in solutions to form dimer (two particle) and large species. Such corrections to the van't Hoff factor may be typically be found in handbooks. At 0.01 M or less this association effect is a very small correction. BACK

footnote 2: Both weak acids and weak bases dissociate to a small extent, but not enough to change the conclusion about the approximate van't Hoff factor. This dissociation will become a topic of considerable study in the next few sections of CHEM 1110 BACK

footnote 3: H₂SO₄ is a strong acid for only the removal of the first proton. HSO₄^- is a weak acid. This complication will be avoided for the present, but will be revisited with the lead acid battery. BACK

footnote 4: Ok, Ok! I know there are some very rare exceptions, after all I've worked with water glass. We will avoid the exceptions. If the student runs into some in the future, let the amazement flow. BACK