- What is the
**mass action law**? - What is
**activity**and how is it related to concentration? - What is
**ionic strength**, and how is it estimated?

A chemist or engineer not only want to know the reactivity of chemicals, but
also the extend of the reaction. When reactants are put together, how
far will the reaction go? How long will it take to reach an equilibrium
state? In dealing with these concerns, the concept of **equilibrium
constant** is devised. In order to get a good approximation for the
prediction of a system, we use *concentrations* or *activities*
to evaluate the equilibrium constant.

[C]where [A], [B], [C], and [D] are stoichiometric concentrations of A, B, C, and D respectively.^{c}[D]^{d}---------------- =K_{eq [A]a [B]b }

However, dilute solutions and concentrated solutions have slight
differences, and a more precise method of calculating and defining the
equilibrium constant is desirable. For such an approach, the
**reactivities** of A, B, C, and D are used in place of the
**concentrations** in the definition of *K*. The reactivity
of A ({A}) is proportional to [A], and the proportional constant in
most text is a gamma, which is called the **activity coefficient**

{B} = g [B]

{C} = g [C]

etc.

The reactivities based on concentrations given above work well for non-electrolytes (or molecular compounds). In dilute solutions, the activity coefficient is unity.

or

{A} = [A]

In solutions of electrolytes, the interactions of charges require some special consideration.

The dissociation of an electrolyte M_{x}X_{m}
is,

For very concentrated solutions, using concentration based on weight of solvent may offer a better approximation than using concentration based on volume. However, at this level, we are only introducing the concept of ionic strength for the calculation of the activity coefficient.

**
Example 1
**

*Solution*

Using the simple formula for ionic strength *I* given above, we have

= 1.00 (a unitless quantity)

*Further exercise*

What is the ionic strength for a 1.0 molar CaCl_{2} solution?
Ans: 3.

**
Example 2
**

*Solution*

For this solution, the concentrations are:

[La^{3+}] = 2.0 M

[SO_{4}^{2-}] = 3.0 M

[Ca^{2+}] = 1.0 M

[Cl^{-}] = 2.0 M

= 18.0

*Discussion*

Note that the sum is taken over all ions.

**
Example 3
**

*Solution*

Using the limiting Debye-Huckel law,

= -1.172 * 1 * (0.01)

= -0.1172

g = 0.90.

*Discussion*

When the coefficient 0.90, the activity is 90% of the concentration.
The activity coefficient for Ca^{2+} under the same condition is
0.63. The activity is much reduced from the higher charge on the ion.

The introduction of activity is to make the equilibrium constant concept (or laws) to be able to be applied to a wider range. By assuming equilibrium constants and other physical properties unchanged, the activity coefficients at different concentrations are aumatically assumed to change. Thus, we can measure the physical property and estimate the activity coefficients at various concentrations.

For example, by measuring the boiling points and freezing points
of solutions with various concentrations, we can estimate the apparent
*activities* of a solute at these concentrations. Dividing the
activities (such as {A}) by the stoichiometric concentrations
(such as [A]) gives the activity coefficients g,
since