# Reactivity

## Chemical Reactivity: A Study Guide

Discussion Questions

• 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?

## Chemical Reactivity

Chemical reactivity is the tendency of a substance to undergo chemical changes in a system. The chemical reactivity worksheet offers an excellent database of reactivity for over 4,000 common hazardous chemicals. The database includes information about chemical reactivities towards air, water, etc. However, the reactivity may also mean chemical properties. An internet search using the key word "chemical reactivity" also gives databases for health and safety, which is hyperlinked to many sites.

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.

### What Are Equilibrium Constants?

In an early introduction of the mass action law, and chemical euilibria, the equilibrium constant K, for the reaction

a A + b B --> c C + d D

has been defined as

       [C]c    [D]d
----------------  =  Keq
[A]a    [B]b


where [A], [B], [C], and [D] are stoichiometric concentrations of A, B, C, and D respectively.

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

{A} = g [A]
{B} = g [B]
{C} = g [C]
etc.

The application of science (engineering) often requires some refinement, and the use of activity is an refinement base on the theory of equilibrium.

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

g = 1
or
{A} = [A]

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

### What is Ionic Strength?

Whenever we deal with ionic solucitions, we have to be at least aware of their ionic strength, because we generally believe that the ionic strength affects the activity of ions. For comparing experimental results, we work with solutions that have comparable ionic strength, which is a quantity representing interactions of ions with water molecules and other ions in a solution. This quantity is usually represented by I, and an explicit form will be given after we have defined the system.

The dissociation of an electrolyte MxXm is,

MxXm = x Mm+ + m Xx-

Positive ions Mm+ and negative ions Xx- must be present together in one solution, and there is no way to separate activities of positive and negative ions. Thus, we usually use a mean ionic activity (a,

a = g C (mmxx)-(m+x)

for both positive and negative ions, C being the stoichiometric concentration of the electrolyte. The Debye-Huckel limiting law shows that the activity coefficient is related to the ionic strength, I in the following way:

ln g = - A z+ z- I ½

where A is a constant (= 1.172 at 298 K), z+ z- the valence factor and I is the ionic strength which is define by the equation:

I = ½ S zi2mi

where mi is the concentration of the ith ion concentration. The summation, S, is taken over all the possible ions in the solution.

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

What is the ionic strength for a 1.0 M NaCl solution?

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

I = ½ (1*12 + 1*12)
= 1.00 (a unitless quantity)

FURTHER EXERCISE
What is the ionic strength for a 1.0 molar CaCl2 solution? Ans: 3.

Example 2

What is the ionic strength for a solution whose concentrations are 1.0 M La2(SO4)3 plus 1.0 M CaCl2?

SOLUTION
For this solution, the concentrations are:

[La3+] = 2.0 M
[SO42-] = 3.0 M
[Ca2+] = 1.0 M
[Cl-] = 2.0 M

I = ½ (2*32 + 3*22 + 1*22 + 2*12)
= 18.0

DISCUSSION
Note that the sum is taken over all ions.

Example 3

Estimate the activity coefficient for Na+ in a solution whose ionic strength is 0.01 at 298 K.

SOLUTION
Using the limiting Debye-Huckel law,

ln g = - A z+ z- I ½
= -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 Ca2+ under the same condition is 0.63. The activity is much reduced from the higher charge on the ion.

### Can Activity Coefficient Be Determined by Experiment?

The limiting Debye-Huckel law applies to very dilute solutions with ionic strength less than 0.005. For higher concentrations, extended forms of Debye-Huckel law have to be used, and we will not go into these issues in this short document. The topic is usually discussed in a physical and other chemistry courses such as Geochemistry and Chemical Activity

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

{A} = g [A]

We simply point out this possibility here, and observed activity coefficients ploted versus the ionic strength are usually curves.

## Questions

1. Calculate the ionic strength for an aqueous solution containing 0.010 M MgCl2 and 0.020 M AlCl3.

2. A solution contains only 0.010 M NaCl at 298 K. What is the ionic strength?
3. A solution contains only 0.010 M NaCl at 298 K. Estimate the activity coefficient of Na+ ions?

4. A solution contains only 0.010 M NaCl at 298 K. Estimate the activity of Na+ ions?

5. What is the activity coefficient for a 1.0*10-6 M NaCl solution at 298 K?

## Solutions

1. 0.15

Skill -
Calculate ionic strength of an electrolyte solution.

2. 0.010

Skill -
Calculate ionic strength of an electrolyte solution, and use it to evaluate activity coefficient.

3. 0.89

Skill -
Know and apply the limiting Debye-Huckel law.

4. 0.0089 M

Skill -
The solution appreas to have a concentration of 0.0089, slightly less than the stoichiometric solution of 0.010. Calculate the activity for a solution containing only 0.010 M CaCl2.

5. 1.0

Skill -
For a very dilute solution, g = 1.0, and {Na+} = [Na+].