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Unformatted text preview: Experiment 14
Determination of an Equilibrium
Constant in Aqueous Solution Learning Objectives
Understand what is meant by the term
chemical equilibria
Know how to determine an equilibrium
constant Kc of a chemical reaction
Understand the mathematical relationship
between absorbance and concentration using
the BeerLambert Law Many Chemical Reactions are
Reversible…
… meaning that the reaction can proceed
from reactants to products and then back, or
in other words, A+B C and A+B C (more
commonly depicted as A+B C)
A reaction is said to be in equilibrium when
the rate of the reaction in the forward
direction is equal to the rate in the reverse
direction. Chemical Equilibrium
Consider the reaction below
N2O4(g) 2NO2(g)
Kinetically,
Rate of the forward reaction, Ratef = kf[N2O4]
Rate of reverse reaction, Rater = kr[NO2]2
At equilibrium, kf[N2O4] = kr[NO2]2
Rearranging this we get, [NO2]2/[N2O4] = kf/kr = a
constant
This constant that we have solved for is called the
equilibrium constant, Kc Equilibrium Constant
In more complex reactions, exemplified by
aA + bB
cC + dD
The equilibrium constant
Kc = [C]c[D]d/[A]a[B]b
Where all concentrations are equilibrium
concentrations Sample Calculation –
Equilibrium Concentration
Consider the reaction,
Fe3+(aq) + SCN(aq) FeNCS2+(aq) If the equilibrium concentration of Fe3+(aq) is
1.00x104M, in a solution that was initially
2.06x103M Fe3+(aq), and 3.00x103 M SCN(aq), determine the equilibrium
concentrations for SCN(aq) and
FeNCS2+(aq). Sample Calculation –
Equilibrium Concentration
Fe3+(aq)
Initial Concentration
(M) 2.06x103M + SCN(aq)
3.00x103 M FeNCS2+(aq)
0 Concentration
(M)
Equilibrium Concentration
(M) 1.00x104M First calculate the Concentration for Fe3+(aq).
2.06x103M  1.00x104M = 1.96x103M
Since this reaction is 1:1, we also know that Concentration for
SCN (aq) and FeNCS2+(aq) is 1.96x103M Sample Calculation –
Equilibrium Concentration
Fe3+(aq)
Initial Concentration
(M)
Concentration
(M)
Equilibrium Concentration
(M) + SCN(aq) FeNCS2+(aq) 2.06x103M 3.00x103 M 0 1.96x103M 1.96x103M +1.96x103M 1.00x104M Now, since we know how much the concentration of FeNCS2+(aq) increased we
simply add Concentration to the initial concentration. Likewise we can subtract
the Concentration from the initial concentration of SCN.
Equilibrium Concentration SCN = 3.00x103 M  1.96x103M = 1.04x103M
Equilibrium Concentration FeNCS2+ = 0.00M + 1.96x103M = 1.96x103M Sample Calculation –
Equilibrium Constant
Fe3+(aq)
Initial Concentration
(M)
Concentration
(M)
Equilibrium Concentration
(M) + SCN(aq) FeNCS2+(aq) 2.06x103M 3.00x103 M 0 1.96x103M 1.96x103M +1.96x103M 1.00x104M 1.04x103M 1.96x103M Now, since we know the equilibrium concentrations we can use them to determine
the equilbrium constant. K eq [FeNCS2+ ]
[1.96x10 3M]
=
=
= 18800
3+
4
3
[Fe ][SCN ] [1.00x10 M][1.04x10 M] NOTE: These are just sample concentrations, the equilibrium constant for this reaction is not 18800. Determining Equilibrium Concentrations
Indirectly Using Colorimetry
While not applicable to all reactions, some reactions can be
monitored by colorimetry
Colorimetry measures the amount of light at a given wavelength
that is transmitted through a solution
In solution some light is absorbed by solute molecules, while the
rest is transmit. The amount absorbed is usually related to the
amount of solute present in solution. By measuring the amount
transmit, the amount absorbed by the solution is also known.
The amount of absorbed light is then used to determine the
concentration of the solute in the solution.
The mathematical relationship used to determine concentration
in colorimetry is called the BeerLambert Law The BeerLambert Law
A= bc
A= Absorbance = log(I/Io), (no units)
I = light intensity of sample
Io = light intensity for the blank solution = Molar extinction coefficient – how strongly a
solution absorbs at a particular wavelength of light,
(M1cm1)
b = path length of light through the solution
in this case b=1cm c = concentration in molarity (mol/L) Constructing a Standard
Calibration Curve
It is important to construct a
calibration curve in order to
experimentally determine
the value for the molar
extinction coefficient
To do this, the absorbance
of known concentrations of
a sample are analyzed and
plot on a graph
Since A= bc, and A is plot
against C, the slope of the
line is equal to b, the molar
extinction coefficient
multiplied by the path length Using a Standard Calibration
Curve
By using the value for b, as
well as absorbance
determined experimentally
we can determine the
concentration.
What is the concentration of
solution whose absorbance
is 0.62?
We know that b = 5M1
from the calibration curve
and A= 0.62
If we solve for
concentration, we get C=A/
b, or C=0.62/ 5M1= 0.12 Experimental Guidelines
An accurate standard curve is important,
make sure to determine the concentrations of
each of your solutions very carefully
Make sure that the colorimeter is set up
properly otherwise your samples may need to
be analyzed multiple times Summary
You will generate a standard curve for one component of a
reaction that you will be observing.
Using the BeerLambert Law, the absorbance of your solution,
and the standard curve you made, you will be able to determine
the concentration of one component in the reaction solution.
Equilibrium concentrations of the remaining reaction components
can be determined by using the equilibrium concentration
determined using the BeerLambert Law, and the initial
concentrations of the other reaction components.
The equilibrium constant can then be calculating using the
equilibrium concentrations that you determined mathematically ...
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 Spring '07
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