# GCCCD Determination of An Equilibrium Constant Lab Report

EXPERIMENT: Determination of an Equilibrium ConstantIntroduction:

In this experiment you will determine the equilibrium constant for the formation of the

iron(III) thiocyanate complex ion. This will be accomplished using UV-Vis spectroscopy.

The reaction between the iron(III) cation and the thiocyanate anion forms a complex ion,

however it is uncertain whether the reaction will follow Equation 1 or Equation 2. Part of the

experiment will be to determine which of the following reactions is in fact actually occurring.

[πΉπ(ππΆπ)2+ ]

3+

β

πΉπ(ππ)

+ ππΆπ(ππ)

β πΉπ(ππΆπ)2+

(ππ)

πΎππ = [πΉπ 3+][ππΆπβ]

3+

β

πΉπ(ππ)

+ 2 ππΆπ(ππ)

β πΉπ(ππΆπ)+

2 (ππ)

πΎππ = [πΉπ 3+][ππΆπ2β]2

[πΉπ(ππΆπ)+ ]

(Equation 1)

(Equation 2)

In order to determine the equilibrium constant, you will be mixing known amounts of the

reactants. Once mixed, a UV-Vis spectrometer will be used to determine the equilibrium

concentration of the iron(III) thiocyanide complex. An ICE table will then be used to determine

the equilibrium constant. This will be done two different ways, first using the equilibrium from

equation 1 and second using the equilibrium from equation 2.

When light goes through a liquid sample, some of it is absorbed by the sample. A UV-Vis

spectrometer measures the intensity of the light before and after passing through a sample. The

percent of light that passes through the sample is known as transmittance, while the amount of

intensity that stayed in the sample is known as absorbance.

Initial Light Intensity

π΄ππ πππππππ = π β π β [πΆ]

Final Light Intensity

Beer-Lambert Law

(Equation 3)

How light is absorbed can be described by what is known as Beerβs law (equation 3). The

three important variables that determine how much light will be absorbed as it passes through a

sample are: pathlength, concentration, and the molar absorptivity constant. The pathlength (π)

references the distance the light moved through the sample; most spectrometers use cuvettes of a

standard 1.00 cm path length. The concentration ([πΆ]) is the amount of solute present in the

sample, the solute is generally the substance which is absorbing the light that is passing through

the sample. Finally, the molar absorptivity constant (π) is a measure of how strongly a substance

absorbs light at a given wavelength.

Through the making of standardized solutions where the concentration of the absorbing

substance is known, the molar absorptivity constant can be determined. Once the absorbance of a

number of solutions with a known concentration is measured a graph can be made which

linearizes the Beer-Lambert equation. In the graph the y-axis will be absorbance, and the x-axis

is the concentration of absorbing complex. Below is an example graph, in this graph the slope of

the resulting straight line is equal to π β π where βπβ is the pathlength the light traveled through

and βπβ is the molar absorptivity constant.

Absorbance vs [Fe(SCN)2+]

1.4

y = 4293.9x

RΒ² = 0.9998

1.2

Absorbance

1

0.8

0.6

0.4

0.2

0

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0.00035

[Fe(SCN)2+] (M)

In this experiment the calibration curve is made using an iron(III) nitrate solution that is

in dramatic excess. This is to force the equilibrium to the products until at equilibrium the

amount of thiocyanate is negligible. Which effectively means there is no equilibrium under these

conditions and the reaction goes to completion with thiocyanate as the limiting reactant. Below is

an example of how to calculate the concentrations of the iron(III) thiocyanate complexes using

the two different equilibria.

Example Calculation:

Equation 1 Equilibrium:

First we need to determine the moles of thiocyanate, in the lab we will add different volumes of

4.00 x 10-4 M KSCN and dilute to a total volume of 10.0mL, in this example we will use 1.0 mL.

Second a mole ratio from the balanced equation will be used, and then we must divide by total

volume in L (0.0100L from 10.0 mL) to get molarity.

1.0ππΏ Γ

1πΏ

4.00 π₯ 10β4 ππππ ππΆπ β 1 πππ πΉπ(ππΆπ)2+

Γ

Γ

= 4.0 π₯ 10β7 ππππ πΉπ(ππΆπ)2+

1000 ππΏ

1πΏ

1 πππ ππΆπ β

4.0 π₯ 10β7 ππππ πΉπ(ππΆπ)2+

[πΉπ(ππΆπ)

=

= 4.0 π₯ 10β5 π πΉπ(ππΆπ)2+

0.0100πΏ

Equation 2 Equilibrium:

All of the steps are the same however the mole ratio between thiocyanate and the complex is

different.

2+ ]

After the calibration curve has been made, the molar absorptivity constant can be

determined, it is important that you make a calibration curve for each version of the equilibrium

and determine a different molar absorptivity constant for each iron(III) thiocyanate complex

(Equation 1 and Equation 2). Once the constants have been determined, they can be used to

determine the concentration of the iron(III) thiocyanate complex in an unknown solution by

using the Beer-Lambert law and the absorbance of that solution.

g

On the second day of the lab, you will make solutions using different concentrations of

iron(III) nitrate and potassium thiocyanate, in this case the concentrations of the stock solutions

are equal. This means the reaction will reach equilibrium with more significant amounts of

reactants present than on the first day. The goal of the second day will be to determine the

equilibrium constant for the equilibrium. Below is an example of the calculation using equation 1

as the equilibrium.

Example Calculation:

A student mixed 5.0 mL of 2.00 x 10-3 M iron(III) nitrate, with 1.0 mL of 2.00 x 10-3 M KSCN

and 4.0 mL of DI water, measured absorbance and determined it was 0.532. The day before they

found that the molar absorptivity constant for Fe(SCN)2+ was 4294 M-1cm-1.

In order to determine the Keq for this equilibrium the student needs to determine three values

from their data: the initial concentration of Fe3+ in the mixture, the initial concentration of SCNin the mixture, and the equilibrium concentration of Fe(SCN)2+ in the mixture.

In order to determine the initial concentrations of the reactants the dilution equation can be used:

2.00 π₯ 10β3 π πΉπ(ππ3 )3 Γ 5.0 ππΏ = π2 Γ 10.0 ππΏ, M2 = 1.0 x 10-3 M Fe(NO3)3

2.00 π₯ 10β3 π πΎππΆπ Γ 1.0 ππΏ = π2 Γ 10.0 ππΏ, M2 = 2.0 x 10-4 M KSCN

Next the concentration of Fe(SCN)2+ is determined using the Beer-Lambert law, the molar

absorptivity constant, and the absorbance of the mixture:

0.532 = 4924 πβ1 ππβ1 Γ 1.00 ππ Γ [πΉπ(ππΆπ)2+ ], [Fe(SCN)2+] = 1.08 x 10-4 M

Finally an ICE table can be used to determine the equilibrium concentrations and the equilibrium

constant for the reaction:

Fe3+(aq)

Solution #5

+ SCN-(aq) β Fe(SCN)2+(aq)

1.0 x 10-3

2.0 x 10-4

0.0

C -1.08 x 10-4

-1.08 x10-4

1.08 x 10-4

8.9 x 10-4

9.2 x 10-5

1.08 x 10-4

I

E

Now that the concentrations at equilibrium are known they can be plugged into the equilibrium

constant expression from equation 1, and the constant can be determined:

[πΉπ(ππΆπ)2+ ]

1.08 π₯ 10β4

πΎππ = [πΉπ 3+][ππΆπβ] = (8.9 π₯ 10β4 )Γ(9.2 π₯ 10β5 ) = 1320

(this is hypothetical data, do not expect the equilibrium constant to be near this number)

After doing all of this assuming equation 1 as our equilibrium, we would need to do this again

using equation 2. This is due to our uncertainty as to which equilibrium is actually occurring.

Experimental Procedure:

Experimental Procedure: Calibration Curve

1. Label 5 large test tubes with numbers from 1 to 5.

2. Using solutions of 0.0500 M Fe(NO3)3, 0.000400 M KSCN, and DI water make the

following solutions using a graduated cylinder to measure the volumes. Then pour

each volume in the relevant labeled test tube (solution 1 should be in test tube 1, and

so on). Mix each solution thoroughly using a glass stirring rod.

Test

Tube #

1

2

3

4

5

Volume of

0.0500 M

Fe(NO3)3

5.0 mL

5.0 mL

5.0 mL

5.0 mL

5.0 mL

Volume of

4.00 x 10-4 M

KSCN

1.0 mL

2.0 mL

3.0 mL

4.0 mL

5.0 mL

Volume of DI

Water

Total

Volume

4.0 mL

3.0 mL

2.0 mL

1.0 mL

0.0 mL

10.0 mL

10.0 mL

10.0 mL

10.0 mL

10.0 mL

3. Obtain 6 cuvettes, after each solution is mixed bring them and the cuvettes to the

instrument room.

4. Fill the first cuvette with DI water and zero the spectrometer, then fill another cuvette

with the solution in test tube #5. Select the scan function on the UV-Vis Spectrometer

(your instructor will demonstrate how to use this instrument), scan the sample and

identify the wavelength where the maximum absorbance occurs. Record the

wavelength, and what the absorbance is for solution #5 in the data table.

5. Now that the wavelength is known, select the βLive Displayβ function on the UV-Vis

spectrometer, set the wavelength to the one you recorded. Then fill the next cuvette

with solution #4 and measure the absorbance. Repeat this for solutions #3, #2, and #1.

6. Using the data recorded and Microsoft excel, create the first calibration curve by

graphing absorbance vs. concentration of the Fe(SCN)2+ complex, in the second

calibration curve graphing absorbance vs concentration of the Fe(SCN)2+ complex.

Record the molar absorptivity constant from each calibration curve in the data table

and turn the graphs in with the lab report.

Experimental Procedure: Determination of Equilibrium Constant

1. This procedure is almost exactly the same as when you were gathering data for the

calibration curve. However, the concentrations of the solutions have changed

dramatically, and there is no need to identify the wavelength of maximum absorbance

as we determined that earlier.

2. Label 5 large test tubes with numbers from 1 to 5.

3. Using solutions of 0.00200 M Fe(NO3)3, 0.00200 M KSCN, and DI water make the

following solutions using a graduated cylinder to measure the volumes. Then pour

each volume in the relevant labeled test tube (solution 1 should be in test tube 1, and

so on). Mix each solution thoroughly using a glass stirring rod.

Test

Tube #

1

2

3

4

5

Volume of

0.00200 M

Fe(NO3)3

5.0 mL

5.0 mL

5.0 mL

5.0 mL

5.0 mL

Volume of

0.00200 M

KSCN

1.0 mL

2.0 mL

3.0 mL

4.0 mL

5.0 mL

Volume of DI

Water

Total

Volume

4.0 mL

3.0 mL

2.0 mL

1.0 mL

0.0 mL

10.0 mL

10.0 mL

10.0 mL

10.0 mL

10.0 mL

4. Obtain 6 cuvettes, after each solution is mixed bring them and the cuvettes to the

instrument room.

5. Fill the first cuvette with DI water and zero the spectrometer, then fill another cuvette

with the solution in test tube #1.

6. Select the βLive Displayβ function on the UV-Vis spectrometer, set the wavelength to

the one you recorded in the calibration curve procedure. Measure the cuvette with

solution #1 in it and record the absorbance. Then fill the next cuvette with solution #2

and measure the absorbance. Repeat this for solutions #3, #4, and #5.

Name: ______________________________

Date: _____________

Experiment: Determination of an Equilibrium Constant

Data and Calculations:

Calibration Curve Data:

Solution #

[SCN-]

[Fe(SCN)2+]

[Fe(SCN)2+]

Absorbance

0.00 M

0.000 M

0.000 M

0.00

#1

0.10

#2

0.19

#3

0.42

#4

0.52

#5

0.64

461

Ξ»max (wavelength at max absorbance): ________________

Absorptivity Constant Ξ΅ for [Fe(SCN)2+] (Using Equation 1) from graph: _________________

Absorptivity Constant Ξ΅ for [Fe(SCN)2+] (Using Equation 2) from graph: _________________

Equilibrium Constant Determination:

Solution #

[Fe(SCN)2+]

[Fe(SCN)2+]

Absorbance

0.000 M

0.000 M

0.00

#1

0.06

#2

0.18

#3

0.30

#4

0.36

#5

0.44

Equilibrium Constant Determination using Equation 1

3+

Fe

(aq)

Solution #1

+ SCN-(aq) β Fe(SCN)2+(aq)

3+

Fe

I

I

C

C

E

E

3+

Fe

(aq)

Solution #3

+ SCN-(aq) β Fe(SCN)2+(aq)

3+

Fe

I

I

C

C

E

E

3+

Fe

(aq)

Solution #5

+ SCN-(aq) β Fe(SCN)2+(aq)

I

C

E

Solution #

1

2

3

4

5

Standard Deviation:

Keq

(aq)

Solution #2

+ SCN-(aq) β Fe(SCN)2+(aq)

(aq)

Solution #4

+ SCN-(aq) β Fe(SCN)2+(aq)

Equilibrium Constant Determination using Equation 2

3+

Fe

(aq)

Solution #1

+ 2SCN-(aq) β Fe(SCN)2+(aq)

3+

Fe

I

I

C

C

E

E

3+

Fe

(aq)

Solution #3

+ 2SCN-(aq) β Fe(SCN)2+(aq)

3+

Fe

I

I

C

C

E

E

3+

Fe

(aq)

Solution #5

+ 2SCN-(aq) β Fe(SCN)2+(aq)

I

C

E

Solution #

1

2

3

4

5

Standard Deviation:

Keq

(aq)

Solution #2

+ 2SCN-(aq) β Fe(SCN)2+(aq)

(aq)

Solution #4

+ 2SCN-(aq) β Fe(SCN)2+(aq)

Calculations:

Please show all your calculations.

Post-Lab Assignment

1. Which of the two equilibriums discussed in the introduction do you believe was actually

occurring in the experiment?

2. What evidence from the experiment made you believe it was that equilibrium? Explain.