It is possible to calculate Henry's Law constants and values from solution thermodynamic data, and this application is explored herein.

Henry's Law Example

Consider the Henry's Law constant for carbon dioxide. The chemical reaction would be:

and we note the following table of thermodynamic valuesⁱ:

Using the definition of the Henry's Law constant pertaining to the equilibrium we have

where we use the conventional [] for concentration (knowing that advanced usages exist). Since we would have

Clearly, the Henry's Law Constant is given by

which at 298^oK is

.

The discerning student will note that the units are slightly goofy here, and that the real equation should be

where the "1"'s are in the proper units defining standard states so that the r.h.s. is properly dimensionless. Assuming that the aqueous concentration standard state is 1 molal, and the gaseous standard state is 1 bar, the resultant equation says that the pressure above a 1 molal solution of carbon dioxide solution would be 27.3 bar. This can't be right, since there is no such thing as aqueous carbon dioxide, which is known to dissociate into bicarbonate and hydrogen ions in water, but the idea is certainly clear.

K_sp Example

We will start with a AgCl since this is the prototypical insoluble salt. The reaction is:

for which we know that . We establish another table of relevant thermodynamic values:

which leads to the equation

from which we obtain

which, at 298^oK is which compares with the text value of 1.8x10^-10.

Another K_sp Example

We treat CaCO₃ another prototypical insoluble salt. The reaction is:

for which we know that . We establish another table of relevant thermodynamic values:

which leads to the equation

from which we obtain

which, at 298^oK is which compares with the text value of 4.9x10^-9.

Yet Another K_sp Example

We treat PbCl₂ another prototypical insoluble salt. The reaction is:

for which we know that . We establish another table of relevant thermodynamic values:

which leads to the equation

from which we obtain

which, at 298^oK is which compares with the text value of 1.7x10^-5.

The Last K_sp Example

We treat BaCl₂ another salt. The reaction is:

for which we know that . We establish another table of relevant thermodynamic values:

which leads to the equation

from which we obtain

which, at 298^oK is which implies that this salt is soluble!