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)-½
= -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.