Determination of an Equilibrium Constant Rhonda Shuler-Calvaresi , Sharline Paul, Gilbert Huizar, and Brittany Helaire
Abstract The purpose of this laboratory experiment was to determine the equilibrium constant of a chemical reaction using Fe3+ (aq) and SCN- (aq) (1). The experiment equilibrium constant was derived from the average of the trial results. The average a verage equilibrium constant for [FeNCS2+] was calculated and was determined to be 309.3, while the accepted standard equilibrium constant for [FeNCS2+] Kc =271.49; the error analysis for the experiment was 14%; the standard deviation was 23.08 .
Introduction The experiment was completed to determine the equilibrium constant of a chemical reaction using Fe3+ (aq) and SCN- (aq). This chemical reaction created a state of chemical equilibrium. The equilibrium state can be categorized by stating its equilibrium constant as large, greater than one, or small, less than one , but not negative or zero. A large Kc (equilibrium constant) means that at equilibrium, the concentrations of the products will generally be greater than the concentrations of the reactants, meaning it is products favored. A small Kc means that at equilibrium, the concentrations of the reactants will generally be greater than the concentrations of the products, meaning it is reactants favored. The relevant chemical equation for this lab is: Fe3+(aq) + SCN-(aq) ⇌ FeSCN2+(aq)
(1)
1
Once the equilibrium concentration of FeSCN+2 (aq) was determined, the equilibrium concentrations of the reactants (Fe+3 (aq) and SCN– (aq) can be calculated. The stoichiometry was 1:1:1 (reactant: reactant: product); the moles of each reactant was used up in the reaction equaled to the moles of product formed (equation 1). The initial concentrations of the known reactants were subtracted to find the moles of reactant remaining at equilibrium. When the chemical reaction rea ction reached equilibrium, the concentrations of reactants and products no longer change with time (2). Concentrations were measured, the value of the equilibrium constant was easily calculated. Finally, the concentrations of each sample in the experiment were calculated; so, the equilibrium constant was calculated. Kc = [FeSCN2+]/[Fe3+ ][SCN-]
(2)
To find the value of Kc, it is necessary to determine the concentration of several solutions at equilibrium. In this experiment, FeSCN2+ (aq) was a colored solution so that the concentration was determined by measuring its absorbance using spectrophotometric methods (3). A spectrophotometric method of analysis involves using light waves. This method requires a calibration curve using samples of known concentration. This can be done by spectroscopy. Determining a calibration curve for FeSCN2+ (aq) was accomplished by using a spectrophotometer, Figure 1. This was accomplished by using a spectrophotometer, an instrument used to measure the amount of light that passes through a sample (1). Spectroscopy pertains to the Figure 1 Spectrophotometer 2
scattering of an object's light into colors. Light acts like a wave and has properties. The different wavelengths of light can be seen in the different colors. The entire electromagnetic spectrum as shown in the figure below:
Figure 2 Electromagnetic Spectrum
The visible light region of the spectrum is small compared to the range of wavelengths. The reactants in the solutions absorbed the light waves. The greater the concentrations of these ions, the greater the absorbance of the solution was. There were several factors that affected the absorbance of light: concentration of the solution, thickness of the sample of solution, and the probability of the light absorbance of the solution (4). Once the absorbency of the solutions was determined Beer’s law was applied. Beer's law stated that absorbance of a molecule or solution is: A = a*b*c
(3)
where A was the absorbance, "a" was the absorptivity absorptivity (in units of per molar per cm, M-1 cm-1), "b" was the path length (in units of centimeters, cm), and "c" was the concentration
3
(in units of molar, M). This explained why the absorbance was linearly proportional to the factors that affected it, the thickness, the concentration, and the absorptivity, of a given sample. When the chemical reaction reached chemical equilibrium, the forward and the reverse reactions rates were equal. The concentrations of the entire samples become part constant (3). Beer's law equation stated the absorbance (A), the light absorbed that passed through a sample of the solution had a concentration (c) of the absorbing solute. According to Beer's law, the amount of light that was absorbed by the colored sample [FeNCS2+] in solution for the given wavelength was directly related to the concentration of the sample. The absorbance was first measured for several samples of standard solutions with known concentrations. Using Beer’s Law equation (equation 3), the molar absorptivity constant for FeSCN2+ (aq) was determined by measuring its absorbance at different known concentrations of FeSCN2+ (aq). If absorbance is plotted versus concentration, the slope will give the molar absorptivity constant per Beer's Law. If a solute obeys Beer's law, then the equation (equation 3), when graphed "Absorbance versus Concentration," yielded a straight line. This graph was the calibration curve for the solute. From the calibration curve, the absorbance of the solute with an unknown concentration was determined. With the equilibrium, spectroscopy, and Beer’s law, all these were related to by light absorbency concentration used to find the equilibrium constant of the FeNCS2+ (aq) solution (5).
4
Procedure Preparation for the Samples for the Calibration Curve The spectrophotometer was turned prior to the preparing of the solutions so that it had time to become warm. A set of standard of solutions was created according to Table 1 below.
Table 1 Preparation of Calibration Curve Samples
Sample
0.2 M Fe(NO3) in M HNO3) (mL)
0.001 M NaSCN ( in 0.1 M HNO3)
0.1 M HNO3 (mL)
Blank
10.0
0
15
1
10.0
1
14
2
10.0
2
13
3
10.0
3
12
4
10.0
4
11
5
10.0
5
10
Six 25 mL volumetric flasks were first rinsed and dried to ensure that there was no residue from previous experiments. The volumetric flasks were then labeled blank and 1-5 so that the order would not be confused. Following Table 1, 0.0001 M Na was added to each volumetric flask. A plastic graduated cylinder was used to measure this solution. It was not cleaned after every used of the same liquid. The solution was poured carefully and slowly 5
into the volumetric flask to ensure that none of it was spilled. Then 10 mL of 0.2 M of Fe(NO3)3 was added to each volumetric flask. Using the same plastic graduated cylinder that was now cleaned and dried, the next solution was added to the volumetric flasks. Careful consideration was taken while pouring the measured solution into the volumetric flask, trying to not spill it. Finally l 0.01 M HNO3 was added to each volumetric flask diluting each one to 25 mL (the fill line of the flasks). Again, the same plastic graduated cylinder was used after it was cleaned and dried for the last solution that was added. Once more, while pouring the solution from the plastic graduated cylinder into the volumetric flask, care was taken to that none of it was spilled. When the volumetric flasks were stirred stirred or flipped over to mix the solution, careful consideration was taken into account because the lids were not totally secured when placed on the volumetric flask. Each solution was stirred to make sure that the equilibrium was established throughout the solution. The solutions needed to be measured by the spectrophotometer. Six cuvets, a special piece of glassware that holds solutions to be measured in a spectrophotometer, were gathered so that some of the solution could be put into each cuvet. After carefully mixing the solution, each solution was poured into a cuvet. Each cuvet was filled about three-fourths of the way so that there would be enough of the solution to measure. Lids were securely placed on top of each cuvet to ensure that they were not spilled. All six of the cuvets were brought to the spectrophotometer so that their absorbance could be measured. The first solution in the cuvet to be tested was the blank solution. A Kimwipe was used to wipe down the sides of the cuvet to remove any liquid or fingerprints. The blank solution used to calibrate the spectrometer, which is termed blanking. The cuvet was handled only on the sides that were grooved since the clear sides were used to test for 6
absorbance. The cuvet was place in the compartment aligning aligning the marks of the cuvet with the compartment. For maximum absorption of the wavelength the spectrophotometer was set at 447 nm. No adjustments were made for the remainder of the experiment. The remainder of the solutions (1-5) was then tested in a similar fashion and their absorbency was recorded. After the data were gathered and record, they were plotted in an absorbance versus concentration line slope equation. A calibration curve was created to determine the accuracy and to determine if part one needed to be repeated. Once the R2 was established to be close to one, then the next part of the experiment could be accomplished. Preparations for the Test Solutions Since the spectrophotometer was previously used, it was still warmed for this section of the experiment. All the volumetric flasks and graduated cylinders cylinders were cleaned and dried so that they could either be reused or put away. The test solutions were prepared according to Table 2 in six clean 10 mL volumetric flasks in the identical fashion as the ones in the previous section of this experiment. These new volumetric flasks were labeled blank and 6-10.
7
for the Test Solutions Table 2 Preparation of Samples for Sample
0.002 M Fe(NO) in 0.1 M HNO3 (mL)
0.002 M NaSCN (in 0.1 M HNO3) (mL)
0.1 M HNO3 (mL)
Blank
5
0
5
1
5
1
4
2
5
2
3
3
5
3
2
4
5
4
1
5
5
5
0
Molar concentrations for this part of the experiment were different from the first part. A new blank solution was created and used to recalibrate the spectrophotometer for this section of the experiment. Determining the absorbance of the test samples, procedures were followed from the previous section. All waste from both sections was disposed of in the properly marked containers, “Waste Salts.” All equipment was cleaned with tap water and returned its proper place. The data gathered from the second part of the experiment was used for the calculations of Kc (1).
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Experimental Data The data collected in this experiment follows:
Table 3 Concentration and Absorbance Data for Standard Samples
Blank
1
2
3
4
5
FeNCS2+ M
0
2.5*10-8
5*10-8
7.5*10-8
1*10-7
1.25*10-7
Absorbance
0
0.076
0.214
0.306
0.422
0.548
The line slope equation gathered from the data from Table 1 was graphed; thus, provided Graph 1 and calculated the line slope equation and R2 value : A=2674.3-.0154 and the R2=.9957.
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Absorbance vs. Concentration 0.6
0.5 ) U A ( e n c a b r o s b A
y = 2764.3x - 0.0154 R2 = 0.9957
0.4
0.3
0.2
0.1
0 0
0.00005
0.0001
0.00015
0.0002
Concentration (M)
Graph 1 Absorbance vs. Concentration Graph
Table 4 Concentration and Absorbance Data for Test Samples
FeNCS2+ M Absorbance
Blank
6
7
8
9
10
0
4.110*10-7
9.1*10-7
1.3*10-6
1.7*10-6
2.0*10-6
0.098
.0236
0.347
0.451
0.535
0
10
Calculations The following calculations were made for the test solutions #6 solution.
A. Standard Solutions Solutions to Establish Calibration Calibration Curve [Fe(NO3)3] . 02 [NaSCN] . 001 Vol. NaSCN Mol. SCN-
1 . 001
∗ .001 =
−6
1 ∗ 10
−6 [SCN-] (25.0 mL) . 025 ∗ 1 ∗ 10 [FeSCN2+] 2.5 ∗ 10−8 ∗ 1 = 2.5 ∗ 10−8 Absorbance 0.076
= 2.5 ∗
10−8
B. Absorbance for Test Solutions [Fe(NO3)3] . 002 [NaSCN] . 002
Vol. Fe(NO3)3 5 Mol Fe3+, initial 1 ∗ 10−5 Vol. NaSCN 1 Mol SCN-, initial 2 ∗ 10−6 Absorbance 0.098
C. Calculation of K c [FeSCN2+]eq 4.10 ∗ 10−7 Mol. FeSCN2+eq 4.1 ∗ 10−5 Mol. Fe3+, reacted (mol)
+
= =
2764.3
=
4.102 ∗ 10−710−5
−7 Mol. eq (mol) 4.102 ∗ 10 ∗ .01 = 4.102 ∗ 10 [Fe3+]eq (10 mL) 4.102 ∗ 10−7 = 4.102 ∗ 10−7 1: 1
Fe3+
−5
.098+.0154
SCN-, reacted 1 ∗ 10−5 4.120 ∗ 10−7 = 9.5898 ∗ 10−6 SCN-eq 2 ∗ 10−4 4.102 ∗ 10−7 = 1.5 ∗ 10 −
11
[SCN-]eq
Kc
=
1.589∗106 .01
[FeSCN [Fe
3
+
=
2+
][SCN
1.58 ∗ 10−4
] −
]
Average Kc 309.3 Std. Dev. Kc 23.8
Then these calculations were repeated for the test samples #7-10.
Results and Discussion One set of solutions with known molar concentrations of FeNCS2+ was prepared and tested to create the calibration curve, a plot graph of absorbance versus concentrations. This created a line graph of the slope intercept, y = mx + b
(4)
The second set of FeNCS2+ (aq) solutions was prepared and mixed so that their molar concentration could be determined. From this graph, the mass action expression of equilibrium can be calculated. The data that was gathered was then placed in an Excel spreadsheet so that absorbency versus concentration could be plotted. This graph produced the equation 4. The new line slope equation that was formed formed from this data was A=2764.3c-0.154
(5)
This equation (equation 5) was used to calculate [FeNCS2+], thus finding the Kc value and the Kc average. The R2 = .9957; this number needed to be as close to the value of one (1) as possible. First step was to calculate the absorbance of the standard solutions for the test
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solution samples six through ten. With new absorbance values that could be substituted into the equation 5 (Table 5 is for test sample #6), new calculations were made for the Kc.
Table 5
2+
ICE Chart for [FeNCS ]
Fe
3+
+
SCN
I
0.02
-
0.001
0
C
-x
-
-x
+x
E
0.02-x
-
0.001-x
x
-4
9.59*10
-
⇌
-4
1.59*10
2+
FeNCS
-5
4.102*10
With the concentrations of each ion, these values can be substituted into the Kc equation (2). The average Kc =309.3. The accepted value is 271. The standard deviation for the results is 23.08. This means that the data plotted will most likely lie in the range of 286.22-332.38. Looking at the Kc values, this statement is true for the values that were calculated in this experiment. The relative standard deviation for this experiment was 7.46%. The relative standard deviation is the percent that each of the Kc values for each test (6-10) will only be 7.46% away from each other. The relative or accepted analysis error is for this experiment was14%; the acceptable error is 5% (1). The significance of knowing an equilibrium constant was to be able to know if the reaction is products favored or reactants favored. From a practical standpoint, producing a given chemical product, it would be essential to know the Kc of a reaction so that the yield 13
of the product could be optimized. If Kc was very large, the concentration of the products was much greater than the concentration of the reactants. The reaction essentially "goes to completion." All or most of the reactants were used up to form the products. If Kc was very small, the concentration of the reactants was much greater than the concentration of the products. The reaction does not occur to any great extent. Most of the reactants remain unchanged and there were few products produced. When Kc was not very large or not very small (close to a value of 1), then approximately equal amounts of reactants and products were present at equilibrium. The significance of the experimental results showed that the Kc was large so that this reaction was products favored (6). The errors that affected the results were due to several items: human factors and equipment or instruments used. There were several different people who measure the liquids. Each one with a different perspective perspective on when volumes have been reached. Each measurement was checked by all, but there was still the chance for errors. The cylinder was to measure the liquids was not washed and dried dried after each use of the same solution. The cylinder was plastic and not glass; plus, it was made of a cloudy and not clear plastic. Also, The experiment called for the use of measuring pipettes, but in this experiment graduated cylinders were used instead. This allowed for some larger errors to happen. The lids in the first section of the experiment had to be held on as the solution was stirred. Some of the solution might have leaked out of the volumetric flasks. Also, the lids had to be washed and dried after each used. The cuvets that were used had to be checked very carefully since quite a few of them were damaged with scratches and others defects. With all of these opportunities for errors, the K c values for the test solutions had a huge probability of being erroneous. The data showed that the test #6 was right close to the accepted value 14
compared to tests #7-10. The accepted Kc value for FeNCS 2+ (aq) was 271.49. Most of the test solutions fell into the range of 310-323. The standard deviation of the experiment was 23.08. This stated that most of the data plotted would be within 23.08 of the average Kc value of 309.3. The error analysis for this experiment was 14%; while the accepted error analysis is 5%. The standard deviation and the error analysis figures helped to reinforce that mistakes were made while conducting con ducting this experiment. One set of solutions with known molar concentrations of FeNCS2+ (aq) was prepared and tested to create the calibration curve, a plot graph of absorbance versus concentrations. This created a line graph of the slope intercept, y = mx + b. The second set of FeNCS2+ (aq) solutions was prepared and mixed so that their molar concentration could be determined. From this graph, the mass action expression of equilibrium can be calculated. If some of the data was removed, then the graph and the data changed. If the test results for sample #1(0.076) was removed from the graphing of the line slope, what would happen to the values of R2 and the line slope equation? The plotted concentration points that remained and were graphed creating points that were closer to the line. The average Kc value decreased to 307.06, but the standard deviation increased to 31.67. The R2 value became .9993 thus moving closer to one.
Conclusion This experiment was to determine the equilibrium constant of a chemical reaction using Fe3+ (aq) and SCN- (aq). The concentration of [FeNCS2+] was taken from several known standard concentrations and then graphed to form a line slope equation to determine the Beer’s law equation and the R2 value to be applied to several unknown 15
concentrations and experimentally calculate the average Kc value which was derived from several test solutions. The results of these measurements determined the equilibrium constant for the formation of [FeNCS2+]. This was accomplished by using a spectrophotometer to measure the light absorbency and the data from this was used to graph a calibration curve to determine the molar absorptivity that was proportional to the thickness of the sample, concentrations of the absorbing solution, and the absorptivity of the samples. From which equilibrium concentrations were calculated with the Beer’s Law. The average equilibrium constant for [FeNCS2+] was calculated and was determined to be 309.3 with the accepted standard Kc=271.49 [FeNCS2+]; the error analysis for the experiment was 14% which could be derived from several factors: human error, using graduated cylinders instead of measuring pipettes, scratched or irregular cuvets.; the standard deviation was 23.08(1).
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Works Cited (1)
Beran, J. (2009). Laboratory manual for principles of general chemistry. (8th ed., pp. 371-382). United States: John Wiley & Sons, Inc.
(2)
Tro, N. (2008). Chemistry a molecular approach. (pp. 616-661). United States: Princeton Hall.
(3)
Miller, K. (2006, December 06). Determination of the equilibrium constant . Retrieved from http://www.jackson.k12.ga.us/teachers/rbryan/AP_Chemistry_Online/LabReport ExampleKeq.pdf
(4)
Kulesa, C. (1997, Febraury 11). What is spectroscopy?. Retrieved from http://loke.as.arizona.edu/~ckulesa/camp/spectroscopy_intro.html
(5)
Lab #11:Determination of the equilibrium constant . (n.d.). Retrieved from
http://www.doctortang.com/AP%20Chemistry%20(Old)/Lab%2011%20Chemical %20Equilibrium%20Constant.pdf
(6)
Determination of an equilibrium constant . (n.d.). Retrieved from
http://mhchem.org/223/pdfLabs223/DetEquilConst.pdf
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