How to find ksp from absorbance

Determining the Equilibrium Constant of a Chemical Reaction

Purpose To determine the equilibrium constant, Kc (also called Kf) for the formation of a complex ion by measuring equilibrium concentrations of the reacting species involved. Introduction Many methods may be used to determine the equilibrium constant for a given system. A pH meter may be used to determine the acid dissociation constant, Ka, and it is also possible to determine the solubility product equilibrium constant, Ksp. However in this experiment the equilibrium constant, Kc, for the formation of a complex ion will be determined by measuring the concentrations of reactants in the reaction below. The equilibrium expression is also shown below.

Fe3+(aq) + SCN- (aq) FeSCN2+ (aq) 𝐾𝑐 = [𝐹𝑒𝑆𝐶𝑁2+]

[𝐹𝑒3+][𝑆𝐶𝑁−]

The FeSCN2+ complex ion is a strongly colored species; therefore the reaction can be investigated using spectroscopy. In part A, a calibration curve will be constructed using FeSCN2+ solutions of known concentration. Each standard solution contains a large excess of Fe3+ to ensure all SCN- in solution forms the FeSCN2+ complex. Therefore, the concentration of FeSCN2+ at equilibrium is equal to the initial concentration of SCN-. The calibration curve will be used to determine the equilibrium concentration of FeSCN2+ of each sample (prepared in part B) containing similar concentrations of Fe3+ and SCN- at equilibrium. In part B, mixtures containing similar concentrations of Fe3+ and SCN- will be prepared. Each solution will be allowed to reach equilibrium such that the following mass balance equations (1) and (2) are valid. With these equations and the initial concentration of the two ions the equilibrium concentrations can be determined.

[Fe3+]initial = [Fe3+]eq + [FeSCN2+]eq (1)

[SCN- ] initial = [SCN- ] eq + [FeSCN2+] eq (2)

An alternate and probably more familiar way to determine equilibrium concentrations is the ICE box method. The ICE box method uses the same equations as above but arranges them in a chart like format.

Fe3+(aq) + SCN- (aq) FeSCN2+ (aq)

Initial I

Change 

Equilibrium Eq

The initial concentrations of iron Fe3+ and thiocyanate SCN- ions can be easily determined from the concentration of the stock solutions. The absorbance of the iron thiocyanate ion will be determined by spectroscopy and compared with the calibration curve prepared in part A to determine the equilibrium concentration of the ion. The equilibrium concentrations can be found using the ICE box chart.

Short Review of Beer’s Law & Spectroscopy Beer’s Law is defined below in equation: A = a b c In the equation, A is the measured absorbance of the sample, b is the path length of light through the sample, c is the concentration of the sample, and a is a constant that depends on both wavelength and substance. A linear calibration curve, or Beer’s Law plot, of absorbance (y-axis) versus concentration (x-axis) can be constructed from the absorbance and concentration data of standard solutions. A prepared calibration curve can be used to determine the concentration of an unknown solution from its measured absorbance. Experimental Procedure: General Instructions – Read this BEFORE proceeding to Parts A and B. 1. The SpectroVis Spectrometers and LabQuest units will be used for this experiment. The

spectrometers need to be calibrated using the blank solutions for Part A and Part B respectively. See the procedure below for instructions on calibrating the spectrometer. The wavelength to be monitored for all samples is 460 nm.

2. There are four solutions used in this experiment. Do not take more solution than you need and do

not cross contaminate the solutions.

 Obtain two burets to deliver the 0.004 M Fe3+ and 0.004 M SCN- solutions. The burets must be clean prior to use. Be sure to rinse the buret with a few mL of the solution prior using.

 Use your 10.00 mL pipet for the 0.1 M Fe3+.  Use a graduated cylinder for the 1.0 M HNO3 and DI water. You can use a plastic pipet to

accurately fill the cylinder.

For each solution record the exact volumes you deliver in your data tables (and notebook) with the correct number of significant digits.

3. Prepare all solutions in test tubes large enough to hold 20 mL (provided). 4. Thoroughly mix all solutions by stoppering the tube and inverting at least five times. If the

solutions are not properly mixed there will be significant error in your results. 5. DO NOT PREPARE solutions for part B until you have completed Part A. Instrument Setup and Calibration 1. In the menu bar select Sensors then choose Data Collection. Select the dropdown arrow next to

the Mode box and choose the Time Based option. Leave other settings as is. Tap OK. 2. In the menu bar select Sensors, then choose Calibrate, and select USB:Spectrometer. A

calibration page should appear. Tap OK. 3. After the warm-up period obtain a cuvette filled with water to calibrate the spectrometer. Tap

the Finish Calibration button. When the unit states calibration complete tap OK. 4. Back on the main screen, tap the panel labeled USB: Abs. Select Change Wavelength from the

menu. 5. For the Selected Wavelength enter 460 nm. Tap OK when done.

Part A: Construction of Beer’s Law Plot

1. Prepare blank A and samples 1A – 4A using the 0.10 M Fe3+ solution according to the volumes listed below. Since the measured volumes may vary slightly from the volumes in the table below, record the exact volume of each reagent used in Table 1 on page 5.

Sample Volume (mL) of

0.10 M Fe3+ Volume (mL) of

0.004 M SCN- Volume (mL) of

1.0 M HNO3 Volume (mL) of Deionized H2O

Blank A 10.00 0.00 5.0 5.0

1A 10.00 0.30 5.0 4.7

2A 10.00 0.60 5.0 4.4

3A 10.00 1.20 5.0 3.8

4A 10.00 2.00 5.0 3.0

2. Calibrate the spectrometer with water. When calibrated obtain an absorbance reading for the

Blank A solution. This will be used to correct for any background absorbance in the samples. 3. Record the absorbance of each sample in Table 2 (in your notebook). 4. Calculate the concentration of [FeSCN2+]eq and place the value in Table 2 (in your notebook). NOTE: a) [FeSCN2+]eq = [SCN- ]initial. This is true only for part A

b) Use the dilution equation (M1V1 = M2V2) to calculate [SCN- ]initial 5. Using Excel (or similar) generate a Beer’s Law plot of absorbance versus [FeSCN2+]eq.

Part B: Determination of the Equilibrium Constant

1. Prepare a blank sample B and samples 1B – 6B using the 0.004 M Fe3+ solution according to the volumes listed below. Since the measured volumes may vary slightly from the volumes in the table below, record the exact volume of each reagent used in Table 3 (in your notebook).

Sample Volume (mL) of

0.004 M Fe3+ Volume (mL) of

0.004 M SCN- Volume (mL) of

1.0 M HNO3 Volume (mL) of Deionized H2O

Blank B 0.00 0.00 0.0 20.0

1B 8.00 2.00 5.0 5.0

2B 6.00 4.00 5.0 5.0

3B 5.00 5.00 5.0 5.0

4B 3.00 7.00 5.0 5.0

5B 3.00 2.00 5.0 10.0

6B 7.50 7.50 5.0 0.0

2. Obtain an absorbance reading for the Blank B solution. This will be used to correct for any

background absorbance in the samples. 3. Record the absorbance of each sample in Table 4 (in your notebook). 4. Calculate the concentration of [Fe3+]initial and [SCN- ]initial and place the values in table 4 (in

notebook).

Data Sheet The following data and data tables should be entered neatly in a table in your notebook prior to lab:

Actual concentration of Fe(NO3)3 stock solution used in Part A (approx. conc. = 0.10 M): Actual concentration of Fe(NO3)3 stock solution used in Part B (approx. conc. = 0.004 M): Actual concentration of KSCN stock solution used in Part A & B (approx. conc. = 0.004 M):

Part A: Construction of Beer’s Law Plot Table 1: Fill in the following table with the actual volumes used in Part A:

Sample

Volume (mL) of 0.10 M Fe3+

Volume (mL) of 0.004 M SCN-

Volume (mL) of 1.0 M HNO3

Volume (mL) of Deionized H2O

Total Volume of Solution (mL)

Blank A

1A

2A

3A

4A

Absorbance of Blank A ___________________ Table 2: Fill in the following table with the absorbance readings of each sample in Part A.

Sample Sample

Absorbance (from Spectrometer)

Corrected Absorbance (Sample - blank)

*[FeSCN2+]eq (from calculation)

1A

2A

3A

4A

* Remember In part A only: [FeSCN2+]eq = [SCN-]initial . See Part A calculations

Part B: Determination of the Equilibrium Constant Table 3: Fill in the following table with the actual volumes used in Part B:

Sample

Volume (mL) of 0.004 M Fe3+

Volume (mL) of 0.004 M SCN-

Volume (mL) of 1.0 M HNO3

Volume (mL) of Deionized H2O

Total Volume of Solution (mL)

Blank B

1B

2B

3B

4B

5B

6B

Absorbance of Blank B ___________________ Table 4: Fill in the following table with calculated concentrations and absorbance readings for each

sample of Part B:

Sample [Fe3+]initial

(dilution calculation)

[SCN-]initial (dilution

calculation)

Sample Absorbance (Spectrometer)

Corrected Absorbance (Sample - blank)

*[FeSCN2+]eq (from Beer’s Law

plot)

1B

2B

3B

4B

5B

6B

* Remember: In Part B: [FeSCN2+]eq ≠ [SCN-]initial. Use the Beer’s Law plot from Part A and absorbance measured in Part B to determine [FeSCN2+]eq for Part B.

Calculations Part A

1. Calculate the concentration of the dilute thiocyanate solutions ([SCN-]initial) using the concentration of the stock solution and the dilution equation (M1V1 = M2V2).

2. Make a graph of the corrected absorbance (y-axis) vs. *[FeSCN2+]eq (x-axis). This is a Beer’s law

Plot. Add a linear best-fit trend line to the data. Include the equation for the best-fit line and the R2 value.

* Remember In part A: [FeSCN2+]eq = [SCN-]initial

Part B

3. Calculate the concentration of the dilute thiocyanate solutions ([SCN-]initial) using the concentration of the stock solution and the dilution equation (M1V1 = M2V2).

4. Calculate the concentration of the dilute iron solutions ([Fe3+]initial) using the concentration of the stock solution and the dilution equation (M1V1 = M2V2).

(Remember in Part B [Fe3+]=0.004M)

5. Using the corrected absorbance data for the six solutions in Part B and the equation for the linear fit

to the Beer’s Law plot in Part A, determine the concentration of iron thiocyanate complex at equilibrium. ([FeSCN2+]eq) for each solution.

Remember In Part B: [FeSCN2+]eq ≠ [SCN-]initial.

5. Set up an ICE-box table similar to the one shown on the first page of this procedure. Using the initial concentrations of Fe3+ and SCN- and the equilibrium value for the iron complex, determine equilibrium values for Fe3+ and SCN-.

6. Calculate the value of Kc using the equilibrium values determined above. Repeat this for each of the six samples in part B.

7. Calculate an average value and the standard deviation for Kc.

8. Calculate the 95% confidence interval for Kc. Look up the true value in your textbook. (These are referred to as Kf in your text, page A-12, Complex ion Formation constants in Water). Does your calculated value agree with the true value at the 95% confidence interval?

Questions 1. In Part A the initial Fe3+ concentration was made to be very large compared to the initial

thiocyanate concentration. Explain why? 2. In part A a blank solution was made containing Fe3+, nitric acid and water but no thiocyanate.

a) What is a blank solution? Why was it necessary to use a blank in this analysis? b) True or False - Once corrected with the blank solution the straight line on the Beer’s law plot

should pass through the origin. (In other words, zero concentration will give zero absorbance.) Explain your answer.

3. In part B the concentrations of Fe3+ and SCN- for each of the six sample were all very different.

As such should the calculated value of Kc be different as well or should it be the same (within error) for all samples. Explain.

4. The value of Kc from the data table in your textbook is 890. At the 95% confidence interval does

your result agree or disagree with the published value. In other words does the accepted (true) value from your book fall in the range of your calculated value?

5. Your value is likely much lower. This has to something to do with the HNO3 in solution. Use

your knowledge of Le Chatlier’s principle to explain why Kc is lower than the table value.