GCCCD Determination of An Equilibrium Constant Lab Report

EXPERIMENT: Determination of an Equilibrium ConstantIntroduction:
In this experiment you will determine the equilibrium constant for the formation of the
iron(III) thiocyanate complex ion. This will be accomplished using UV-Vis spectroscopy.
The reaction between the iron(III) cation and the thiocyanate anion forms a complex ion,
however it is uncertain whether the reaction will follow Equation 1 or Equation 2. Part of the
experiment will be to determine which of the following reactions is in fact actually occurring.
[𝐹𝑒(𝑆𝐶𝑁)2+ ]
3+
−
𝐹𝑒(𝑎𝑞)
+ 𝑆𝐶𝑁(𝑎𝑞)
⇌ 𝐹𝑒(𝑆𝐶𝑁)2+
(𝑎𝑞)
𝐾𝑒𝑞 = [𝐹𝑒 3+][𝑆𝐶𝑁−]
3+
−
𝐹𝑒(𝑎𝑞)
+ 2 𝑆𝐶𝑁(𝑎𝑞)
⇌ 𝐹𝑒(𝑆𝐶𝑁)+
2 (𝑎𝑞)
𝐾𝑒𝑞 = [𝐹𝑒 3+][𝑆𝐶𝑁2−]2
[𝐹𝑒(𝑆𝐶𝑁)+ ]
(Equation 1)
(Equation 2)
In order to determine the equilibrium constant, you will be mixing known amounts of the
reactants. Once mixed, a UV-Vis spectrometer will be used to determine the equilibrium
concentration of the iron(III) thiocyanide complex. An ICE table will then be used to determine
the equilibrium constant. This will be done two different ways, first using the equilibrium from
equation 1 and second using the equilibrium from equation 2.
When light goes through a liquid sample, some of it is absorbed by the sample. A UV-Vis
spectrometer measures the intensity of the light before and after passing through a sample. The
percent of light that passes through the sample is known as transmittance, while the amount of
intensity that stayed in the sample is known as absorbance.
Initial Light Intensity
𝐴𝑏𝑠𝑜𝑟𝑏𝑎𝑛𝑐𝑒 = 𝜀 ∙ 𝑙 ∙ [𝐶]
Final Light Intensity
Beer-Lambert Law
(Equation 3)
How light is absorbed can be described by what is known as Beer’s law (equation 3). The
three important variables that determine how much light will be absorbed as it passes through a
sample are: pathlength, concentration, and the molar absorptivity constant. The pathlength (𝑙)
references the distance the light moved through the sample; most spectrometers use cuvettes of a
standard 1.00 cm path length. The concentration ([𝐶]) is the amount of solute present in the
sample, the solute is generally the substance which is absorbing the light that is passing through
the sample. Finally, the molar absorptivity constant (𝜀) is a measure of how strongly a substance
absorbs light at a given wavelength.
Through the making of standardized solutions where the concentration of the absorbing
substance is known, the molar absorptivity constant can be determined. Once the absorbance of a
number of solutions with a known concentration is measured a graph can be made which
linearizes the Beer-Lambert equation. In the graph the y-axis will be absorbance, and the x-axis
is the concentration of absorbing complex. Below is an example graph, in this graph the slope of
the resulting straight line is equal to 𝜀 ∙ 𝑙 where “𝑙’ is the pathlength the light traveled through
and “𝜀” is the molar absorptivity constant.
Absorbance vs [Fe(SCN)2+]
1.4
y = 4293.9x
R² = 0.9998
1.2
Absorbance
1
0.8
0.6
0.4
0.2
0
0
0.00005
0.0001
0.00015
0.0002
0.00025
0.0003
0.00035
[Fe(SCN)2+] (M)
In this experiment the calibration curve is made using an iron(III) nitrate solution that is
in dramatic excess. This is to force the equilibrium to the products until at equilibrium the
amount of thiocyanate is negligible. Which effectively means there is no equilibrium under these
conditions and the reaction goes to completion with thiocyanate as the limiting reactant. Below is
an example of how to calculate the concentrations of the iron(III) thiocyanate complexes using
the two different equilibria.
Example Calculation:
Equation 1 Equilibrium:
First we need to determine the moles of thiocyanate, in the lab we will add different volumes of
4.00 x 10-4 M KSCN and dilute to a total volume of 10.0mL, in this example we will use 1.0 mL.
Second a mole ratio from the balanced equation will be used, and then we must divide by total
volume in L (0.0100L from 10.0 mL) to get molarity.
1.0𝑚𝐿 ×
1𝐿
4.00 𝑥 10−4 𝑚𝑜𝑙𝑠 𝑆𝐶𝑁 − 1 𝑚𝑜𝑙 𝐹𝑒(𝑆𝐶𝑁)2+
×
×
= 4.0 𝑥 10−7 𝑚𝑜𝑙𝑠 𝐹𝑒(𝑆𝐶𝑁)2+
1000 𝑚𝐿
1𝐿
1 𝑚𝑜𝑙 𝑆𝐶𝑁 −
4.0 𝑥 10−7 𝑚𝑜𝑙𝑠 𝐹𝑒(𝑆𝐶𝑁)2+
[𝐹𝑒(𝑆𝐶𝑁)
=
= 4.0 𝑥 10−5 𝑀 𝐹𝑒(𝑆𝐶𝑁)2+
0.0100𝐿
Equation 2 Equilibrium:
All of the steps are the same however the mole ratio between thiocyanate and the complex is
different.
2+ ]
After the calibration curve has been made, the molar absorptivity constant can be
determined, it is important that you make a calibration curve for each version of the equilibrium
and determine a different molar absorptivity constant for each iron(III) thiocyanate complex
(Equation 1 and Equation 2). Once the constants have been determined, they can be used to
determine the concentration of the iron(III) thiocyanate complex in an unknown solution by
using the Beer-Lambert law and the absorbance of that solution.
g
On the second day of the lab, you will make solutions using different concentrations of
iron(III) nitrate and potassium thiocyanate, in this case the concentrations of the stock solutions
are equal. This means the reaction will reach equilibrium with more significant amounts of
reactants present than on the first day. The goal of the second day will be to determine the
equilibrium constant for the equilibrium. Below is an example of the calculation using equation 1
as the equilibrium.
Example Calculation:
A student mixed 5.0 mL of 2.00 x 10-3 M iron(III) nitrate, with 1.0 mL of 2.00 x 10-3 M KSCN
and 4.0 mL of DI water, measured absorbance and determined it was 0.532. The day before they
found that the molar absorptivity constant for Fe(SCN)2+ was 4294 M-1cm-1.
In order to determine the Keq for this equilibrium the student needs to determine three values
from their data: the initial concentration of Fe3+ in the mixture, the initial concentration of SCNin the mixture, and the equilibrium concentration of Fe(SCN)2+ in the mixture.
In order to determine the initial concentrations of the reactants the dilution equation can be used:
2.00 𝑥 10−3 𝑀 𝐹𝑒(𝑁𝑂3 )3 × 5.0 𝑚𝐿 = 𝑀2 × 10.0 𝑚𝐿, M2 = 1.0 x 10-3 M Fe(NO3)3
2.00 𝑥 10−3 𝑀 𝐾𝑆𝐶𝑁 × 1.0 𝑚𝐿 = 𝑀2 × 10.0 𝑚𝐿, M2 = 2.0 x 10-4 M KSCN
Next the concentration of Fe(SCN)2+ is determined using the Beer-Lambert law, the molar
absorptivity constant, and the absorbance of the mixture:
0.532 = 4924 𝑀−1 𝑐𝑚−1 × 1.00 𝑐𝑚 × [𝐹𝑒(𝑆𝐶𝑁)2+ ], [Fe(SCN)2+] = 1.08 x 10-4 M
Finally an ICE table can be used to determine the equilibrium concentrations and the equilibrium
constant for the reaction:
Fe3+(aq)
Solution #5
+ SCN-(aq) ⇌ Fe(SCN)2+(aq)
1.0 x 10-3
2.0 x 10-4
0.0
C -1.08 x 10-4
-1.08 x10-4
1.08 x 10-4
8.9 x 10-4
9.2 x 10-5
1.08 x 10-4
I
E
Now that the concentrations at equilibrium are known they can be plugged into the equilibrium
constant expression from equation 1, and the constant can be determined:
[𝐹𝑒(𝑆𝐶𝑁)2+ ]
1.08 𝑥 10−4
𝐾𝑒𝑞 = [𝐹𝑒 3+][𝑆𝐶𝑁−] = (8.9 𝑥 10−4 )×(9.2 𝑥 10−5 ) = 1320
(this is hypothetical data, do not expect the equilibrium constant to be near this number)
After doing all of this assuming equation 1 as our equilibrium, we would need to do this again
using equation 2. This is due to our uncertainty as to which equilibrium is actually occurring.
Experimental Procedure:
Experimental Procedure: Calibration Curve
1. Label 5 large test tubes with numbers from 1 to 5.
2. Using solutions of 0.0500 M Fe(NO3)3, 0.000400 M KSCN, and DI water make the
following solutions using a graduated cylinder to measure the volumes. Then pour
each volume in the relevant labeled test tube (solution 1 should be in test tube 1, and
so on). Mix each solution thoroughly using a glass stirring rod.
Test
Tube #
1
2
3
4
5
Volume of
0.0500 M
Fe(NO3)3
5.0 mL
5.0 mL
5.0 mL
5.0 mL
5.0 mL
Volume of
4.00 x 10-4 M
KSCN
1.0 mL
2.0 mL
3.0 mL
4.0 mL
5.0 mL
Volume of DI
Water
Total
Volume
4.0 mL
3.0 mL
2.0 mL
1.0 mL
0.0 mL
10.0 mL
10.0 mL
10.0 mL
10.0 mL
10.0 mL
3. Obtain 6 cuvettes, after each solution is mixed bring them and the cuvettes to the
instrument room.
4. Fill the first cuvette with DI water and zero the spectrometer, then fill another cuvette
with the solution in test tube #5. Select the scan function on the UV-Vis Spectrometer
(your instructor will demonstrate how to use this instrument), scan the sample and
identify the wavelength where the maximum absorbance occurs. Record the
wavelength, and what the absorbance is for solution #5 in the data table.
5. Now that the wavelength is known, select the “Live Display” function on the UV-Vis
spectrometer, set the wavelength to the one you recorded. Then fill the next cuvette
with solution #4 and measure the absorbance. Repeat this for solutions #3, #2, and #1.
6. Using the data recorded and Microsoft excel, create the first calibration curve by
graphing absorbance vs. concentration of the Fe(SCN)2+ complex, in the second
calibration curve graphing absorbance vs concentration of the Fe(SCN)2+ complex.
Record the molar absorptivity constant from each calibration curve in the data table
and turn the graphs in with the lab report.
Experimental Procedure: Determination of Equilibrium Constant
1. This procedure is almost exactly the same as when you were gathering data for the
calibration curve. However, the concentrations of the solutions have changed
dramatically, and there is no need to identify the wavelength of maximum absorbance
as we determined that earlier.
2. Label 5 large test tubes with numbers from 1 to 5.
3. Using solutions of 0.00200 M Fe(NO3)3, 0.00200 M KSCN, and DI water make the
following solutions using a graduated cylinder to measure the volumes. Then pour
each volume in the relevant labeled test tube (solution 1 should be in test tube 1, and
so on). Mix each solution thoroughly using a glass stirring rod.
Test
Tube #
1
2
3
4
5
Volume of
0.00200 M
Fe(NO3)3
5.0 mL
5.0 mL
5.0 mL
5.0 mL
5.0 mL
Volume of
0.00200 M
KSCN
1.0 mL
2.0 mL
3.0 mL
4.0 mL
5.0 mL
Volume of DI
Water
Total
Volume
4.0 mL
3.0 mL
2.0 mL
1.0 mL
0.0 mL
10.0 mL
10.0 mL
10.0 mL
10.0 mL
10.0 mL
4. Obtain 6 cuvettes, after each solution is mixed bring them and the cuvettes to the
instrument room.
5. Fill the first cuvette with DI water and zero the spectrometer, then fill another cuvette
with the solution in test tube #1.
6. Select the “Live Display” function on the UV-Vis spectrometer, set the wavelength to
the one you recorded in the calibration curve procedure. Measure the cuvette with
solution #1 in it and record the absorbance. Then fill the next cuvette with solution #2
and measure the absorbance. Repeat this for solutions #3, #4, and #5.
Name: ______________________________
Date: _____________
Experiment: Determination of an Equilibrium Constant
Data and Calculations:
Calibration Curve Data:
Solution #
[SCN-]
[Fe(SCN)2+]
[Fe(SCN)2+]
Absorbance
0.00 M
0.000 M
0.000 M
0.00
#1
0.10
#2
0.19
#3
0.42
#4
0.52
#5
0.64
461
λmax (wavelength at max absorbance): ________________
Absorptivity Constant ε for [Fe(SCN)2+] (Using Equation 1) from graph: _________________
Absorptivity Constant ε for [Fe(SCN)2+] (Using Equation 2) from graph: _________________
Equilibrium Constant Determination:
Solution #
[Fe(SCN)2+]
[Fe(SCN)2+]
Absorbance
0.000 M
0.000 M
0.00
#1
0.06
#2
0.18
#3
0.30
#4
0.36
#5
0.44
Equilibrium Constant Determination using Equation 1
3+
Fe
(aq)
Solution #1
+ SCN-(aq) ⇌ Fe(SCN)2+(aq)
3+
Fe
I
I
C
C
E
E
3+
Fe
(aq)
Solution #3
+ SCN-(aq) ⇌ Fe(SCN)2+(aq)
3+
Fe
I
I
C
C
E
E
3+
Fe
(aq)
Solution #5
+ SCN-(aq) ⇌ Fe(SCN)2+(aq)
I
C
E
Solution #
1
2
3
4
5
Standard Deviation:
Keq
(aq)
Solution #2
+ SCN-(aq) ⇌ Fe(SCN)2+(aq)
(aq)
Solution #4
+ SCN-(aq) ⇌ Fe(SCN)2+(aq)
Equilibrium Constant Determination using Equation 2
3+
Fe
(aq)
Solution #1
+ 2SCN-(aq) ⇌ Fe(SCN)2+(aq)
3+
Fe
I
I
C
C
E
E
3+
Fe
(aq)
Solution #3
+ 2SCN-(aq) ⇌ Fe(SCN)2+(aq)
3+
Fe
I
I
C
C
E
E
3+
Fe
(aq)
Solution #5
+ 2SCN-(aq) ⇌ Fe(SCN)2+(aq)
I
C
E
Solution #
1
2
3
4
5
Standard Deviation:
Keq
(aq)
Solution #2
+ 2SCN-(aq) ⇌ Fe(SCN)2+(aq)
(aq)
Solution #4
+ 2SCN-(aq) ⇌ Fe(SCN)2+(aq)
Calculations:
Please show all your calculations.
Post-Lab Assignment
1. Which of the two equilibriums discussed in the introduction do you believe was actually
occurring in the experiment?
2. What evidence from the experiment made you believe it was that equilibrium? Explain.