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1
EXPERIMENT B4: CHEMICAL EQUILIBRIUM
Learning Outcomes
Upon completion of this lab, the student will be able to:
1) Analyze the absorbance spectrum of a sample.
2) Calculate the equilibrium constant for a chemical reaction using data
obtained by spectrophotometric methods.
Introduction
Electromagnetic Spectrum
A wave is often defined as a “vibrating disturbance by which energy is transmitted”.
An electromagnetic wave is a type of wave that has associated with it an electrical
field and a magnetic field that are perpendicular to one another. Light that can be
seen by the naked eye, also known as visible light, is an example of an
electromagnetic radiation. Waves such as radio waves, microwaves, or x-rays are
also examples of electromagnetic radiation.
Mathematically, waves such as electromagnetic waves are known as propagating
waves, and can be represented by a repeating or periodic function uch as sine wave.
There are three characteristic properties associated with these kinds of waves:
1. Wavelength (λ)- the distance between identical points on successive waves
2. Frequency (ν)- the number of waves that pass through a particular point in a
second
3. Amplitude- the height of the peak or trough of a wave.
What makes one electromagnetic wave different from another wave is the
wavelength and frequency associated with it. These two are inversely related to
each according to the formula:
c = νλ, where c is the speed of light = 3.00 × 108 m/s
The electromagnetic spectrum (Figure 1) is an arrangement of the different kinds of
waves in the order of increasing wavelengths (or decreasing frequencies).
2
Wavelength (nm)
10-2
Gamma
ray
1020
100
102
X-ray
U
V
1018
1016
104
106
Infrare
d
1014
1012
400 nm
108
Microwave
1010
1012
Radio waves
6
1010 Frequency
108
10
(s-1)
700 nm
FIGURE 1
As mentioned above, electromagnetic radiation at certain wavelengths, is visible to
the human eye, ranging from red light with longer wavelengths (~ 700 nm) to violet
light with shorter wavelengths (~400 nm).
A solution containing a substance that absorbs light in the visible region of the
electromagnetic spectrum will appear colored to the eye. The color that is observed
depends on the wavelength of the radiation that substance absorbs. For instance, if
you look at a solution of vitamin B2 (also known as riboflavin) under a white light, it
appears yellow in color. A solution of vitamin B2 absorbs the maximum light at a
wavelength of 450 nm. From Figure 1, light with a wavelength of 450 nm
corresponds to violet-blue light. The molecules of riboflavin therefore are absorbing
the violet-blue parts of the visible light, and all the rest of the visible light will not be
absorbed but instead transmitted through the solution. The riboflavin is essentially
removing the blue-violet light from the white light and as a result the color you
observe for riboflavin is a mixture of the rest of the “un-absorbed” colors. In general
the color of a solution that can be observed by the human eye is the “complement” of
the color of the light it absorbs. The following “color-wheel” is a representation of
complementary colors (Figure 2).
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Violet
400-420 nm
Red
630-720 nm
Deep blue
420-450 nm
Orange
580-630 nm
Light blue
450-490 nm
Yellow
545-580 nm
Green
490-530 nm
Yellow-green
530-545 nm
FIGURE 2
In the case of riboflavin since the solution absorbed light with a wavelength of 450
nm corresponding to blue light, it should appear to be yellow to yellow-green, which
are the complementary colors. And indeed, a solution of riboflavin does appear to be
yellow in color.
Spectrophotometry
A spectrophotometer is an instrument used to measure the amount of light that a
sample absorbs. This method is known as spectrophotometry. The instrument
operates by passing a beam of light through a sample and measuring the intensity of
the transmitted light reaching a detector. The most basic arrangement of a
spectrophotometer is shown in Figure 3.
Source of
light
Sample
Light
detector
FIGURE 3
However, as discussed before different samples absorb light of different
wavelengths. The amount of light absorbed by the sample will depend on the
wavelength of the light. In order to select light of a particular wavelength to shine on
the sample, the light must pass through a monochromator, which is essentially a
filter that allows a selected wavelength of light to pass through the sample.
When analyzing a sample for the first time, it is unlikely that one will know the
wavelength at which the sample absorbs maximum light. Therefore the complete
absorbance spectrum of the sample must first be determined. The absorbance
spectrum shows how the absorbance of light depends upon the wavelength of the
light. The spectrum is a plot of absorbance (y-axis) versus wavelength (x-axis). The
4
wavelength at which the absorbance is the highest is often denoted as λmax. The λmax
is characteristic of each compound and provides information on the electronic
structure of the analyte.
The absorbance of a particular solution depends on another important parameter:
the amount of the analyte present in the solution.
Beer’s law states that the absorbance is directly proportional to the number of
molecules per unit volume of light-absorbing compound through which the light
passes. The mathematical form corresponding to Beer’s law is given by:
A = ε×c×l
The variables in the above equation are:
•
•
•
•
A = absorbance of the sample (this is a unit-less quantity)
c = concentration of the analyte (typically in units of Molarity or moles/liter)
ε = molar extinction coefficient (units of Molarity-1cm-1)
l = path length through which light travels
The path length depends on the spectrophotometer and the sample holder or
cuvette being used and is typically 1.00 cm for most instruments. The extinction
coefficient ε that is used in the above equation is a constant for a particular sample
at a particular wavelength. The extinction coefficient for several substances has
been experimentally determined.
Chemical Equilibrium
In this experiment, the analytical method of spectrophotometry described in the
preceding section will be used to examine the chemical equilibrium of a particular
reaction. As should be evident from the earlier discussion, in order to use this
5
analytical method, the chemical substances studied must absorb light in the visible
region of the electromagnetic spectrum.
The reaction that will be studied is between aqueous solutions of the iron(III) ion
(Fe3+) and thiocyanate ion (SCN−). The ionic equation for the reaction and the
expression for the equilibrium constant are given below.
3+
−
Feaq
+ SCN aq
⇔ Fe(SCN) 2+
aq
[Fe(SCN) 2+ ]eq
KC =
[Fe 3+ ]eq [SCN − ]eq
At the wavelength of maximum absorbance, λmax, the molar extinction coefficient, ε,
for the product, Fe(SCN)2+, is 6120 M-1cm-1. Since the initial concentrations of the
€
reactants are known and the product concentration is related to its absorbance, the
method of spectophotometry can be used to determine the equilibrium constant for
this reaction.
Assume that the initial concentration of Fe3+ is A and that of CNS− is B. The following
table describes how the concentrations of all ions at equilibrium can be determined.
Since the ions are all in a 1:1 stoichiometric relationship with each other, the
amount of one of the ions consumed in terms of concentration (-x) will be the
sameamount as the other ion consumed and will result in an equal amount of
product being formed (+x).
Fe3+
+
SCN−
Initial concentrations
A
B
Amount reacted to reach equilibrium
-x
€ -x
Equilibrium concentrations
A-x
KC =
B-x
⇔
Fe(SCN)2+
0
+x
x
x
(A − x)(B − x)
Since “A” and “B” are known quantities, in order to determine the equilibrium
constant KC, it is necessary to determine the change in concentration“x”. Fortuntely,
€
the change in concentration is equal to the equilibrium concentration of the
complex, Fe(SCN)2+.
The equilibrium concentration of the complex, Fe(SCN)2+, can be determined by
measuring its absorbance at λmax and employing Beer’s law:
6
A
ε×l
ε = 6120M −1cm −1
l = 1cm
C=x=
The value of “l” (the path length) is specific to the spectrophotometer. The
spectrophotometers used in this laboratory have a path length of 1.00 cm.
€
7
Experimental Design
0.00200 M aqueous solutions of Fe3+ and SCN− are provided. These solutions are
prepared in 0.50 M HNO3. Different initial concentrations of these two solutions will
be combined to form the Fe(SCN)2+ complex. The absorbance of the equilibrium
mixture will be measured at λmax using a spectrophotometer.
The λmax for the complex, Fe(SCN)2+, must first be determined. In order to do this,
the complete absorbance spectrum of the complex (from 370 nm to 700 nm) must
be obtained.
Reagents and Supplies
0.00200 M Fe3+, 0.00200 M SCN−, 0.50 M HNO3
Spectrophotometer, cuvettes
(See posted Material Safety Data Sheets)
8
Procedure
PART 1: DETERMINATION OF λMAX FOR Fe(SCN)2+
1. Obtain two cuvettes and a spectrophotometer. Power up the spectrophotometer
and allow the instrument to warm up for 10 minutes. The instructor will
demonstrate the proper use of the spectrophotometer.
2. In a large test tube combine 4.00 ml of Fe3+ and 3.00 ml of SCN−. Thoroughly mix
the contents and allow the mixture to equilibrate (~ 5 minutes).
3. Fill one cuvette with 0.50 M HNO3 (this will be the “blank”) and the second
cuvette with the Fe(SCN)2+ complex prepared in step 2 (this will be the
“sample”).
4. Wipe the sides of the cuvettes with kimwipes and make sure there are no
smudges or fingerprints.
5. Set the wavelength of the spectrophotometer to 370 nm.
6. Ensure that there is no sample in the sample compartment and that the lid to the
compartment is closed. Set the spectrophotometer to transmittance mode. Using
the appropriate controls, adjust the transmittance to zero.
7. Place the cuvette containing the “blank” inside the sample compartment, align
the guide mark on the cuvette with the guide mark at the front of the sample
compartment, and close the lid. Set the spectrophotometer to absorbance mode.
Using the appropriate controls adjust the absorbance reading to zero.
8. Now place the cuvette containing the “sample” inside the sample compartment,
align the guide mark on the cuvette with the guide mark at the front of the
sample compartment, close the lid and record the absorbance.
9. Change the wavelength to 380 nm and then repeat Steps 6 through 8. Continue
this process in 10 nm increments of the wavelength, until absorbance values
have been recorded at 700 nm.
10. Empty the contents of the cuvettes into a large beaker labeled as “Waste”. Rinse
and clean the cuvettes. Dispose all the reagents in an appropriate labeled waste
container provided by the instructor
11. Plot a graph of absorbance (y-axis) vs. wavelength (x-axis). From the plot
determine the wavelength at which the absorbance maximum is found. This
wavelength will be used for all subsequent measurements.
9
PART 2: DETERMINATION OF KC FOR THE REACTION BETWEEN Fe3+ AND SCN−
1. Obtain a spectrophotometer and turn the power on and allow the instrument to
warm up for at least 10 minutes.
2. Obtain nine large test tubes and number them from 1 to 9.
3. Combine Fe3+ and SCN− in each of the test tubes according to the following table.
These will be the “sample” test tubes. Thoroughly mix the contents after
combining the two solutions and allow the resulting mixture to equilibrate for at
least five minutes.
Solution Number Fe3+ (mL), Solution A SCN− (mL), Solution B
1
0.50
3.00
2
1.00
2.50
3
1.25
2.25
4
1.50
2.00
5
1.75
1.75
6
2.00
1.50
7
2.25
1.25
8
2.50
1.00
9
3.00
0.50
4. Measure the temperature of the equilibrium mixture. The temperature is not
used in any of the calculations. But equilibrium constant values are always
reported at a particular temperature as the value changes with temperature.
5. In another cuvette obtain about 3.50 mL of nitric acid. This will serve as the
“blank”.
6. Set the wavelength of the spectrophotometer to the value determined from Part
1 of the experiment. Calibrate the spectrophotometer using the method
described in Part 1: Steps 6 & 7.
7. Record the absorbance values of each of the nine samples (use the method
described in Part 1 (Step 8).
8. Dispose all the reagents in an appropriate labeled waste container provided by
the instructor.
10
Data Table
PART 1: DETERMINATION OF λMAX FOR Fe(SCN)2+
Wavelength (nm) Absorbance
370
380
390
400
410
420
430
440
450
460
470
480
490
500
510
520
530
540
550
560
570
580
590
600
610
620
630
640
650
660
670
680
690
700
11
PART 2: DETERMINATION OF KC FOR THE REACTION BETWEEN Fe3+ AND SCN−
Solution
Absorbance
1
2
3
4
5
6
7
8
9
Temperature of the equilibrium mixture =
12
Data Analysis
PART 1: DETERMINATION OF λMAX FOR Fe(SCN)2+
1. Draw a graph of absorbance (y-axis) vs. wavelength (nm).
2. From the plot, identify the wavelength at which the maximum absorbance
occurs. There will be two absorbance maxima in this spectrum. Use the larger of
the two wavelengths for all subsequent measurements.
GRAPH
The λ max for Fe(SCN)2+ was found to be =
13
PART 2: DETERMINATION OF KC FOR THE REACTION BETWEEN Fe3+ AND SCN−
The net ionic equation and the expression for the equilibrium constant for the
reaction between Fe3+ and SCN− is given by:
3+
−
Feaq
+ SCN aq
⇔ Fe(CNS) 2+
aq
[Fe(CNS) 2+ ]eq
KC =
[Fe 3+ ]eq [CNS − ]eq
As mentioned before, if the initial concentration of Fe3+ is A and that of CNS− is B,
€
then the following table describes the equilibrium process.
Fe3+
+
SCN−
Initial concentrations
A
B
Amount reacted to reach equilibrium
-x
€ -x
Equilibrium concentrations
A-x
KC =
⇔
B-x
Fe(SCN)2+
0
+x
x
x
(A − x)(B − x)
The equilibrium concentration of the complex, Fe(SCN)2+, can be determined from
its absorbance at λmax and employing Beer’s law.
€
A
ε×l
ε = 6120M −1cm −1
l = 1cm
C=x=
€
1. First the initial concentrations of Fe3+ and SCN− must be determined for each of
the six reaction conditions.
For instance, in sample 1 (0.50 mL of Fe3+ + 3.00 mL of SCN−):
0.50mL × 0.00200M
= 0.000286M
3.50mL
3.00mL × 0.00200M
= 0.00171M
Concentration of SCN− in the mixture =
3.50mL
Concentration of Fe3+ in the mixture =
€
€
14
Determine the concentrations of Fe3+ and SCN− in all the samples in the same
manner.
Solution Number Fe3+ (mL) [Fe3+], M = A SCN− (mL) [SCN−], M = B
1
0.50
0.000286
3.00
0.00171
2
1.00
2.50
3
1.25
2.25
4
1.50
2.00
5
1.75
1.75
6
2.00
1.50
7
2.25
1.25
8
2.50
1.00
9
3.00
0.50
2. Determine the concentration of the complex, Fe(SCN)2+, for each of the six
solutions from the absorbance value.
Solution
Absorbance
[Fe(SCN)2+], M =
1
2
3
4
5
6
7
8
9
€
A
=x=
6120
15
3. Calculate the equilibrium constant KC for each reaction using the formula:
KC =
Solution
€
x
(A − x)(B − x)
KC
1
2
3
4
5
6
7
8
9
AVERAGE
STANDARD DEVIATION
NOTE: Equilibrium constant values are temperature dependent. Be sure to measure
the temperature of the solution and report the average value of the equilibrium
constant at the specific temperature at which the experiment was conducted.
16
Result
The equilibrium constant, KC, for the reaction between aqueous solutions of Fe3+ and
SCN−, which resulted in the complex Fe(SCN)2+, was found to be (specify the
temperature):
6/5/18
Prof. Srinivasan
CHEM 1B
Experiment B4: Chemical Equilibrium
Objective: The purpose of this lab is to analyze the absorbance of a particular sample in which
the equilibrium constant will be calculated through the data collected.
Data:
Part 1: Determination of λmax for Fe(SCN)2+
Wavelength (nm)
Absorbance
370
.275
380
.227
390
.282
400
.294
410
.301
420
.362
430
.402
440
.476
450
.503
460
.556
470
.542
480
.521
490
.481
500
.469
510
.443
520
.434
530
.390
Nadhavajhala 1
540
.318
550
.253
560
.200
570
.157
580
.127
590
.092
600
.061
610
.041
620
.033
630
.025
640
.019
650
.011
660
.008
670
.007
680
.005
690
.002
700
.001
Part 2: Determination of Kc for the reaction between Fe3+ and SCN-
Solution
Absorbance
1
.188
2
.304
3
.330
4
.344
5
.353
Nadhavajhala 2
6
.344
7
.327
8
.298
9
.187
Temperature of the equilibrium mixture = 25.3 celsius
Data Analysis:
Part 1: Determination of λmax
for Fe(SCN)2+
The λmax for
Fe(SCN)2+ was found to be = 460 nm
Part 2: Determination of Kc for the reaction between Fe3+
and SCN-
Solution 2 Calculation:
Concentration of Fe3+ in the mixture = (1.00 mL * 0.00200 M) / (3.50 mL) = 0.000571
Concentration of SCN- in the mixture = (2.50 mL * 0.00200 M) / (3.50 mL) = 0.00143
Nadhavajhala 3
Solution number
Fe3+ (mL)
[Fe3+], M = A
SCN- (mL)
[SCN-], M = B
1
0.50
0.000286
3.00
0.00171
2
1.00
0.000571
2.50
0.00143
3
1.25
0.000714
2.25
0.00129
4
1.50
0.000857
2.00
0.00114
5
1.75
0.00100
1.75
0.00100
6
2.00
0.00114
1.50
0.000857
7
2.25
0.00129
1.25
0.000714
8
2.50
0.00143
1.00
0.000571
9
3.00
0.00171
0.50
0.000286
Solution 1 Calculation:
A / 6120 = (.188) / 6120 = 0.0000307
Solution
Absorbance
[Fe(SCN)2+], M =
1
.188
.0000307
2
.304
.0000497
3
.330
.0000539
4
.344
.0000562
5
.353
.0000577
6
.344
.0000562
7
.327
.0000534
8
.298
.0000487
9
.187
.0000306
Kc =
A
6120
=x=
x
(A−x)(B−x)
Solution 1 Kc Calculation:
Nadhavajhala 4
Kc =
.0000307
(.000286 − .0000307)(.00171 − .0000307)
= 71.6
Solution
Kc
1
71.6
2
69.1
3
66.1
4
63.5
5
65.0
6
64.8
7
65.4
8
67.5
9
71.3
Average
67.1
Standard Deviation
2.93
Average:
71.6 + 69.1 + 66.1 + 63.5 + 65.0 + 64.8 + 65.4 + 67.5 + 71.3
9
= 67.1
Standard Deviation:
(71.6-67.1)2 + (69.1-67.1)2 + (66.1-67.1)2 + (63.5-67.1)2 + (65.0-67.1)2 + (64.8-67.1)2 +
(65.4-67.1)2 + (67.5-67.1)2 + (71.3-67.1)2 = 68.6
= √(68.6) / (9 − 1)
= √68.6 / 8
= 2.93
Conclusion:
Nadhavajhala 5
The equilibrium constant. Kc, for the reaction between aqueous solutions of Fe3+ and SCN-,
which resulted in the complex Fe(SCN)2+, was found to be 67.1
Discussion:
The Kc values were not as consistent as they should have been. The spread of the data values
ranged from as low as 63.5 to as high as 71.6. The large difference could be attributed to the
Fe(SCN)2+ concentration which was calculated in the prior step. Otherwise, the values found in
part 1 aligned with our expectations of what the data was supposed to be.
Nadhavajhala 6
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