How can I determine the van't Hoff factor of a substance from its formula?

1 Answer
Ernest Z.
Apr 13, 2016

Here's how you do it.

Explanation:

The van't Hoff factor, i, is the number of particles formed in a solution from one formula unit of solute.

Notice that i is a property of the solute. In an ideal solution, i does not depend on the concentration of the solution.

For a nonelectrolyte

If the solute is a nonelectrolyte (i.e. it does not separate into ions in solution), i=1

For example, sucrose(s) → sucrose (aq).

i=1, because 1 molecule of sucrose forms only one particle in solution.

For a strong electrolyte

If the solute is a strong electrolyte (i.e. it separates into ions in solution), i>1.

Some examples are:

NaCl(s)→Na+(aq)+Cl-(aq);i=2

One formula unit of NaCl will form two particles in solution, an Na+ ion and a Cl- ion.

CaCl2(s)→Ca2+(aq)+2Cl-(aq);i=3

One formula unit of CaCl2 will form three particles in solution, a Ca2+ ion and two Cl- ions.

Here's another example:

Fe2(SO4)3(s)→2Fe3+(aq)+3SO2-4(aq);i=5

For a weak electrolyte

If the solute is a weak electrolyte , it dissociates only to a limited extent.

For example, acetic acid is a weak acid. We often set up an ICE table to calculate the number of particles in a 1 mol/L solution.

mmmmmmHA+H2O⇌H3O++A-
I/mol⋅L-1:ml1mmmmmmml0mmm0
C/mol⋅L-1:m-xmmmmmm+xm+x
E/mol⋅L-1:l1−xmmmmmmxmmmx

At equilibrium, we have 1−xlmol of HA,xlmol of H3O+,andxlmol of A-.

Total moles=(1−x+x+x)lmol=(1+x)lmol, so i=1+x.

Usually, x<0.05, so i<1.05≈1.

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