Spectrophotometric Determination of An Equilibrium Constant Lab Report

Introduction:

Colorless substances transmit all of the visible wavelengths of light. Colored substances on the other hand absorb certain wavelengths of light in the visible region and transmit other wavelengths. Complex ions such as thiocyanato iron (III) ion (Fe(SCN)2+) absorb light in the visible range. The complementary color is transmitted at a particular wavelength.

A spectrophotometer is an instrument that measures the amount of light absorbed or transmitted by a solution at a particular wavelength. A spectrophotometer consists of a light source, a wavelength selecting device, a means of passing light through a sample and a detector to measure the transmitted light. Transmittance (T) is the ratio of intensity (I) of light passing through a medium to the intensity of light before encountering the medium (Io).

% T =I/ Io (eqn. 1)

Where %T is the percent transmittance, I is the intensity or amount of light that is transmitted through the sample and Io is the intensity or amount of light transmitted through the blank. The reference blank doesn’t absorb light and has 100% transmittance. The absorbance, A, of an ideal solution is directly proportional to the concentration of absorbing species and is given by

A = – log I/Io = 2.000 – log (%T) (eqn. 2)

Absorbance is directly related to the concentration of a sample and path length through the sample and the relation is given by the Beer’s law.

A = bC (eqn. 3)

Where C is the molar concentration of the sample, b is the path length of light through the sample and is the molar absorptivity of the absorbing species at a particular wavelength. The unit of is L.mol-1.cm-1 and is constant for a particular absorbing species and depends on the solute, solvent and , the wavelength. is a measure of how strongly a chemical species absorbs light at a given wavelength. Absorbance maximum (max) for Fe(SCN)2+ is 447 nm and %T will be measured at this wavelength.

In this experiment, you will study the reaction between aqueous iron (III) nitrate, Fe(NO3)3, and potassium thiocyanate, KSCN. The two chemicals react to produce a blood-red complex Fe(SCN) 2+, the absorbing species. We will be recording the % transmittance of samples as %T scale is linear and hence provides more precise results than the absorbance scale. The %T is measured in the range of ~25-85% transmittance for a series of five different equilibrium solutions and absorbance values calculated. Absorbance of Fe(SCN) 2+ is directly proportional to the concentration of Fe(SCN) 2+ .

In Part 1 of the experiment, you will prepare a Beer’s law plot – a calibration curve based on absorbance values for solutions of known concentrations (standard solutions). Beer’s Law plot is a straight line plot and slope of the straight line gives the molar absorptivity (). Knowing the absorbance of a solution, the calibration curve can be used to determine the unknown concentration of FeSCN2+.

(eqn. 4)

The equilibrium constant for the above reaction is given by

(eqn. 5)

In Part 1, we will add a very high concentration of Fe3+ to a small initial concentration of SCN ([SCN]i). The [Fe3+] in the standard solution is 100 times larger than the [SCN]i in the equilibrium mixtures. According to Le Chatelier’s principle, this high concentration forces the reaction far to the right, using up essentially all of the SCN ions. According to the balanced equation, for every one mole of SCN reacted, one mole of FeSCN2+ is produced. Thus, equilibrium moles [FeSCN2+] eq are assumed to be equal to initial moles [SCN] i.

This is true only for the Beer’s Law standard solutions.

Equilibrium moles Fe(SCN) 2+ = initial moles SCN(eqn. 6)

[Fe(SCN) 2+]* Vtot = [SCN]I * Vi (eqn. 7)

[Fe(SCN) 2+] = [SCN]iVi /Veq (eqn. 7)

In Part 2 of the experiment, varying amounts of KSCN will be combined with a less concentrated Fe(NO3)3 solution to obtain varying amounts of FeSCN2+.

The amount of product formed at equilibrium, [FeSCN2+] eq, will be determined from the calibration graph prepared in Part 1 and absorbance values obtained in Part 2.

Knowing the [Fe(SCN) 2+]eq allows us to determine the concentrations of the other two ions at equilibrium. The equilibrium concentration of [Fe3+] eq is the initial concentration of [Fe3+] i (after dilution) minus the amount of [Fe (SCN) 2+] eq (obtained as indicated above) and given by the following equation.

[Fe3+] eq = [Fe3+] i – [FeSCN2+] eq (eqn. 7)

The [Fe (SCN) 2+] eq is determined by using absorbance and the Beer’s Law calibration curve. [SCN]eq is determined by using the following equation.

[SCN] eq = [SCN] i – [FeSCN2+] eq (eqn. 8)

Knowing the values of [Fe3+] eq, [SCN] eq, and [Fe (SCN) 2+] eq you can calculate the value of Kc, the equilibrium constant by using equation 5. Average value for the equilibrium constant is determined from the five measurements.

Supplies:

0.0020 M iron (III) nitrate, Fe(NO3)3, solution in 1.0 M HNO3

0.200 M iron (III) nitrate, Fe(NO3)3, solution in 1.0 M HNO3

0.00200 M potassium thiocyanate, KSCN

Spectrophotometer

5.0 mL pipette

3.0 mL pipette

plastic cuvettes

pipet pump or bulb

Burette (2)

Burette clamp

20 × 150 mm test tubes (6)

distilled water

test tube rack

50 mL volumetric flask (5)

Thermometer

Procedure:

Part 1 – Plotting the Beer’s Law plot

Table 1 below provides the volumes of reactants needed to prepare the standard solutions for the calibration curve. Accurately prepare the six solutions according to the volumes listed in the table below. Use a 5.00 pipette to deliver 0.200 M Fe(NO3)3 solution and burettes to deliver KSCN solution and water into a 50 mL volumetric flask. Cap the flasks tightly and mix each solution thoroughly by inverting the flask 10 times.

Table 1: Reagent quantities for calibration curve.

Solution

0.00200 M KSCN

0.200 M Fe(NO3)3

DI water

1

0.0 mL

5.0 mL

Fill to the line

2

1.0 mL

5.0 mL

Fill to the line

3

2.0 mL

5.0 mL

Fill to the line

4

3.0 mL

5.0 mL

Fill to the line

5

4.0 mL

5.0 mL

Fill to the line

6

5.0 mL

5.0 mL

Fill to the line

Measure and record the temperature of one of the above solutions to use as the temperature for the equilibrium constant.

Set the wavelength on the Spectrometer to 447 nm. Use solution 1 as the reference blank and fill an empty cuvette ¾ full of solution 1. Place the blank in the spectrophotometer and follow the instructions for using the spectrophotometer.

Fill a new cuvette, ¾ full with solution 2. Record the % transmittance and discard the solution in the cuvette into the waste beaker.

Recheck the blank solution from step 4 for 100% transmittance.

Next fill the cuvette from step 4 with solution 3 and determine the % transmittance.

Follow the procedure in step 5 & 6 for the remaining three solutions. You may use the same cuvette so long as you measure the transmittances from dilute to concentrated solutions.

Rinse the cuvettes with tap water followed by distilled water 3 times and place in the used clean cuvette bin.

Dispose of your equilibrium solutions into the waste container provided.

Calculate the absorbance values for the five solutions and plot an Excel plot, with absorbance on the y-axis and concentration of [Fe(SCN)2+] on the x-axis. Label the axis appropriately and provide a title for the graph. Concentrations of [Fe(SCN)2+] are calculated based on concentrations of KSCN. Construct a calibration curve for the data collected in Steps 4 through 7. Draw a best-fit line though the data points. Report the equation of the line and the R2 value on the graph.

Staple a printout of the data along with Excel graph to your data sheet. This graph will be used to determine the amount of the complex formed in Part 2 of the experiment.

Part 2: Determination of the equilibrium constant

Clean and dry 6 large test tubes and label them Blank & A-E.

Use a 3.00 mL pipette to deliver 0.0020 M Fe(NO3)3 solution and burettes to deliver the required volumes of KSCN solution and DI water into clean and dry test tubes. Note that this set of combinations uses the more dilute Fe(NO3)3 solution (0.002M). Stir each solution with a glass stir rod to mix the reagents.

Trial

Volume

0.0020 M Fe(NO3)3 (mL)

Volume

0.0020 M KSCN (mL)

DI water (mL)

Table 2: Volumes and concentrations of solutions for determining the equilibrium constant

Trial

Volume

0.0020 M Fe(NO3)3 (mL)

Volume

0.0020 M KSCN (mL)

DI water (mL)

Blank

3.00

0.00

7.00

A

3.00

2.00

5.00

B

3.00

3.00

4.00

C

3.00

4.00

3.00

D

3.00

5.00

2.00

E

3.00

6.00

1.00

Measure the % transmittance of each equilibrium solution following the same steps as in Part I, steps 3 through 7.

NOTE: You are not making a graph this time. Simply record the % transmittance values in your data table for further analysis.

Rinse the cuvettes with tap water followed by distilled water 3 times and place in the used clean cuvette bin.

Dispose of your equilibrium solutions into the waste container provided, clean the test tubes with soap and water, rinse twice with tap water and twice with distilled water. Place clean test tubes in the “used clean test tube bin”

NAME: ____________________________ DATE: ___________

Partner: ___________________________

Data Sheet & Calculations.

Part I:

For this part of the experiment assume [SCN]i = [FeSCN2+]

Table 3:

Trial

% Transmittance

[SCN]i

[Fe(SCN)2+]

Absorbance

2

3

4

5

6

Calculate the [SCN]i and [Fe3+]i accounting for dilution using McVc = MdVd, for each solution in Table 1. Show one sample calculation for absorbance, [SCN] and [FeSCN2+]. Enter all calculated values into Table 3 above.

Absorbance: Use Eqn. # 2 (2.000 – log (%T))

Dilution Formula

[SCN-]i

[FeSCN2+] _______________________________

[Fe3+] >> [SCN]; equilibrium in eqn. 4 is far to the right, using up essentially all of the SCN ions. For every one mole of SCN reacted, one mole of FeSCN2+ is produced. Thus, equilibrium moles and molarity of FeSCN2+eq are assumed to be equal to initial moles SCNi.

Graph:

Plot Absorbance vs. [FeSCN2+] from the data from Table 3 above & fit a trendline.

Print a well-labeled graph with a complete Data Table, showing original data and calculated and graphed values. Report the trendline equation along with the R2 value.

Part II: Data and Calculations

Table 4:

Trial

% Transmittance

Absorbance

A

B

C

D

D

E

Calculate the absorbance and complete Table 4 above.

Calculate the initial concentrations of SCN and Fe3+ in the test tubes A-E (Table 2). Show two sets of calculations and complete Table 5 below.

Table 5. Initial Concentrations of SCN and Fe3+

Test tube #

A

B

C

D

E

[SCN]i
[Fe3+]i

Use the calculated absorbance values from Table 4 in Part II (y values) and the best-fit line equation from Part I to calculate the [FeSCN2+]eq at equilibrium. Show two sets of calculations and complete Table 6 below.

Sample Calculation

with hypothetical values

of Absorbance from Table 4

& fitted eqn. from Table 3

y = mx + b (y is absorbance)

0.0620 = 2000x -0.0250

x = 0.0620 + 0.0250

2000

= 4.35 x 10-5

Use the trendline equation from Table 3 and calculate value of x = using absorbance values from Table 4

Table 6. Equilibrium concentration of [FeSCN2+]eq

Test tube #

A

B

B

C

D

[FeSCN2+]eq

These are ICE Table calculations

Initial [Fe3+]initial [SCN]initial 0.00

Change – [FeSCN2+]eq – [FeSCN2+]eq + [FeSCN2+]eq

Equilibrium [Fe3+]eq [SCN]eq [FeSCN2+]eq

Calculate the equilibrium concentrations for Fe3+ and SCN for the mixtures in test tubes A-E. Use the equations 7 & 8 respectively. Give two examples of your calculations and complete Table 7 below.

Initial 0.00

Change

Final

Table 7. Equilibrium concentrations of SCN and Fe3+

Test tube #

A

B

C

D

E

[SCN]eq

[Fe3+]eq

[FeSCN2+]eq

Calculate the value of Keq (eqn. 8) based on equilibrium concentrations of SCN , Fe3+ and FeSCN2+ solutions. Show two sample calculations and complete Table 8 below.

(Sample Exercise 15.7 from Test Book)

Table 8. Keq

Test tube #

A

B

C

D

E

Average

Keq

Spectrophotometric Determination of an Equilibrium Constant

NAME: ____________________________________ Date: _____________

Post-Laboratory Assignment

A student determined the molar absorptivity () to be 4800 L/mol.cm for the thiocyanatoiron (III) ion. What is the % T for a solution that is 1.2 X 10-4 M in thiocyanatoiron (III) ion? The path length for the light is 1.00 cm?

Assuming that the equilibrium concentration of [FeSCN2+] is 6.08 x 10-5 M in a solution that initially was 1.00 x 10-3 M in Fe3+ and 2.00 x 10-4 M in SCN, calculate the equilibrium concentrations of Fe3+ and SCN and the value of Keq.

Review Sample Exercise 15.8 for solving this problem

Initial 0.00

Change + 6.08 x 10-5

Final 6.08 x 10-5

At a given temperature, the Keq for the systems studied in this experiment is 1.4 x102. Suppose 100.0 mL of 2.00 x10-3 M KSCN was mixed with 100.0 mL of 2.00 x10-3 M Fe(NO3)3 . Calculate the equilibrium molar concentration of thiocyanatoiron (III) ion? Show complete calculations (you may have to solve a quadratic as the assumption that x << initial concentrations of Fe3+ and SCN may not be valid)

Calculate the concentrations by the dilution formula.

Review Sample Exercise 15.11 for solving this problem (K < 103)

Initial

Change -x -x +x

Final x

Spectrophotometric Determination of an Equilibrium Constant

Pre-Laboratory Assignment

NAME: __________________________________ DATE: _____________

Why is the experiment run at a wavelength of 447 nm?

Why is the Fe3+ concentration so much higher than the KSCN in Part 1 of the experiment?

If the percent transmittance of a solution is 82.7 what is the absorbance of that solution?

What is the relationship between concentration and absorbance in Part 1 of the experiment?

If the concentration of the solution in question 3 above is 2.50 x 10-3 M, calculate the value of molar absorptivity of the solution.

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