(Updated 091119)
1
Determining An Equilibrium Constant
Using Spectrophotometry and Beer’s Law
Objectives:
1.) To determine the equilibrium constant for the reaction of iron (III) and thiocyanate to
form the thiocyanatoiron(III) complex ion using spectrophotometric data.
2.) To determine the concentration of an unknown by evaluating the relationship
between color intensity and concentration.
Background Information:
One of the fundamental problems in chemistry is how to determine the extent of a
reaction. While not every chemical reaction goes to completion, they usually approach an
equilibrium state. When the system reaches equilibrium, the concentrations of the reactants and
products no longer change over time. This does not mean that the reaction has ceased. In fact,
the reaction continues to progress forward, as well as backward. It is said to be in a dynamic
state of equilibrium where the rate of the products being formed from the reactants is exactly the
same as the rate of the products being decomposed to form the reactants.
For the general equilibrium reaction
aA + bB < = > cC + dD (Eqn. 1)
When studying the equilibrium of chemical systems, one of the most important quantities
to determine is the equilibrium constant, Keq. At equilibrium at a given temperature, the mass
action expression is a constant, known as the equilibrium constant, Keq. The equilibrium
expression for the reaction in Equation 1 is given as:
Keq = [C]c [D]d (Eqn. 2)
[A]a [B]b
The value of the equilibrium constant may be determined from experimental data if the
concentrations of both the reactants and the products are known. Additionally, all equilibrium
concentrations can be calculated if a single equilibrium concentration is known along with all
other “initial” concentrations.
It may be recalled that in spectrophotometric studies, the Beer-Lambert law, or Beer’s
Law, can be used to determine the concentration of highly colored species. Mathematically,
Beer’s Law can be stated as:
A = abc (Eqn. 3)
where “a” is the molar absorptivity, “b” is the pathlength, “c” is the concentration, and “A” is
absorbance. Molar absorptivity, a, is a proportionality constant that has a specific value for
each absorbing species at a given wavelength. The pathlength, b, is the distance across the
solution in centimeters and is dependent upon the size of the cuvette. In this case, the pathlength
will be kept constant at 1.00 cm. The concentration, c, of the absorbing species is in moles of
solute per liter of solution.
Absorbance is mathematically defined as:
A = log (Io / I) (Eqn. 4)
where Io is the initial intensity of the beam prior to going through the solution and I is the
intensity of the beam after it has been transmitted through the solution.
