Use of Spectroscopy to Determine an Equilibrium Constant
Ziyue Zhu
2015/2/15
 Introduction:
The objective of this lab was to determine the equilibrium constant of the ferric
thiocyanate by using spectroscopy.
The formation of the ferric thiocyanate complex is:
Fe3+(aq) + SCN-(aq) → Fe(NCS)2+(aq)
(1)
Chemical equilibrium means that the reaction end until the amount of products
formed and the amount of reactants remaining do not change any more. When the
concentrations of reactants and products stop changing, the system has now reached a
state called chemical equilibrium.
The equation expression for this reaction is:
K= [Fe(NCS)2+] / [Fe3+][SCN-]
(2)
Absorbance is directly related to the concentration of the absorbing molecules in
solution. The relationship (Beer’s Law) between absorbance and concentration of the
absorbing species is:
A= ɛ b c
(3)
The ideal relationship between concentration of Fe(NCS)2+ and absorbance is:
Absorbance = (m)(concentration) + b
(4)
The first step of this lab was to prepare stock solution which could be used to
determine the maximum. This is referred to as the maximal wavelength. According to
the given table, prepared four standard solution by adding KSCN solution first. Then
added the Fe(NO3)3 and finally, the HNO3 was added into the solution. This was
because the HNO3 solution was only used for make each of the four solution was
25ml in volume. The reaction (1) occurred after the solution was mixed. Using the
most concentrated solution to get the maximal wavelength and the absorbance at that
wavelength for the other three trials. The four absorbance data was used to find out
the relationship between the absorbance and the concentration of Fe(NCS)2+ . Which
would be equation (4). The value of ɛ could also be calculated by using equation (3).
After that, measured absorbance of the five solutions which were prepared with a
given table at the maximal wavelength. Using the calculated equation which was in
the form of equation (4) to got the equilibrium concentration of each solution. The
value of equilibrium constant K was calculated by using equation (2).
 Data
Table 1: The proportion of four standard solutions
[KSCN]
KSCN ml
Fe(NO)3 ml
HNO3 ml
3x10-4M
6x10-4M
9x10-4M
1.2x10-3M
2.5
5
7.5
10
12.5
12.5
12.5
12.5
10
7.5
5
2.5
Total Volume
ml
25
25
25
25
Table 2: The proportion of five solutions to measure the equilibrium constant K.
Beaker #
1
2
3
4
5
2.0x10-3M Fe(NO3)3
10ml
10ml
10ml
10ml
10ml
3.0x10-3M KSCN
2ml
4ml
6ml
8ml
10ml
0.5M HNO3
8ml
6ml
4ml
2ml
0ml
Table 3: The data of absorbance in different wavelength of No.4 standard solutions.
410n
m
0.539
420n
m
0.546
430n
m
0.542
440n
m
0.586
450n
m
0.593
460n
m
0.584
470n
m
0.559
480n
m
0.517
Figure 1: The relationship between absorbance and the wavelength.
490n
m
0.464
500n
m
0.407
Table 4: Concentration of Fe(NCS)2+ in the four standard solutions
Solution 1
3x10-4M
Solution 2
6x10-4M
Solution 3
9x10-4M
Solution 4
1.2x10-3M
Figure 2: The relationship between the absorbance and concentration of Fe(NCS)2+
Table 5: The equilibrium concentration of five solutions:
Solution 1
Solution 2
Solution 3
Solution 4
-4
-4
-4
1.941x10 M
1.814x10 M
3.23x10 M
3.61x10-4M
Table 6: The K values of five trials
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Average
2274.3
529.38
826.87
673.36
717.51
1004.28
Solution 5
4.335x10-4M
 Results and disscussion
In the first part of the experiment, the proportion of the four standard solutions was
indicated on Table 1. The most concentrated solution was chose to test the maximal
wavelength because the more concentrated the solution was, the more accurate the
maximal wavelength was. According to Table 3 and Figure 1, the maximal
wavelength was determined to be 450nm. After that, the relationship between the
absorbance and concentration of Fe(NCS)2+ was indicated on the Table 3 and figure 2.
The expression of the relationship was y = 551.33x - 0.069 and the R2 value was
0.9849 which meant that the data were quite fit with the equation. Using the equation
(3), the value of ɛ can be calculated as 551.33 while the expected value was 3550. In
that case, the error percentage was 84.47%. The equilibrium concentration was
calculated by the equation posted on Figure 2 and could be found on Table 5. Using
this equilibrium concentration and the rule of ICE, the equilibrium value K was
calculated by using equation (2). The average K value was 1004.28. However, the
expected K value was 280 so that the error percentage was 258.67%. Besides, average
K value of trail 2 to trail 4 was 686.78 which was far closer to the expected value than
the average value that included trail 1. This meant that the trail one had obvious
experimental mistakes.
The most possible reason of the error was the preparing of the solutions was not
accurate. When adding KSCN, the burettes were leakly and the dropper was untight
so that the volume of KSCN was not accurate. What is more, the K value was very
sensitive to the proportion of the solutions. In that case, the K value and ɛ value was
far from the widely accepted expected value. Another possible reason was that when
operated the spectroscopy instrument, the cube container was used. However, it was
not cleaned up with distill water before adding the solutions and blanks. Besides, the
outside part of the cube container was not fully cleaned especially for the solution 1 in
the five measurement solutions. In that case, the absorbance at 450nm was unusual
compared to the other trials.
 Post-Lab Question:
1. [Fe(NO3）3]I = 5x10-4M
2. K = 639.1
[KSCN]I = 1.25x10-3M
[Fe(SCN)2+]I = 0M