Objective: The determination of the formula of a coordination complex formed between the iron(III) ion and the thiocyanate ion, SCN¯ using Job's method of continuous variations. Once the formula is determined, the equilibrium constant for the formation of the coordination complex will be determined by experimentally measuring the concentration of the colored coordination complex. The concentration of the colored coordination complex will be determined using UV-visible spectroscopy.

Coordination complexes are formed when small molecules or ions, collectively called ligands form covalent bonds to metal cations. Remember that a covalent bond is the sharing of a pair of electrons between two atoms. In a coordination complex, the shared pair of electrons between the ligand and the metal cation comes from a lone pair of electrons contained on the ligand. Unlike ionic bonds that break apart in water to form ions, a covalent bond tends not to come apart in water solution. Coordination complexes may exist as a neutral molecule or a polyatomic ion in water solution.

Depending on the nature of the ligand and metal cation, a variable number of ligands may attach to the metal cation to form what is called a coordination complex. The number of ligands attached to the metal cation is called the coordination number of the metal. Coordination numbers can range from 1 to over 6. Common coordination numbers for many transition metal complexes are 4 or 6. An unknown number, referred to here as "x", of thiocyanate ions, SCN¯, form a coordination complex with the iron(III) ion, Fe³⁺, according to the reversible reaction:

(1)

The coordination complex, Fe(SCN)_x^3–x, will have an overall charge of +3 minus 1 for each thiocyanate ion that is attached to the iron ion. The first part of this experiment is to determine the value of x using Job’s Method of Continuous Variations. Job’s Method of Continuous Variations is based on the concept of limiting reactants.

In Job's Method, a number of solutions containing different amounts of each reactant are prepared. For each solution, the total amount of reactants is constant. For example, consider a reaction in which two reactants, call them A and B, react to form a product C. Job's method involves preparing a series of different solutions such as those shown in table 1:

Notice that for each solution, the total number of moles of reactants contained in the mixture is equal to 5.0 moles. Suppose that the stoichiometry of the reaction is:

2 A + 3 B ¾ ¾ ® C

The maximum number of moles of product C may be calculated by performing a limiting reactant problem with each solution. The results of those calculations are presented in the last column of Table 1. Note that the mixture that produces the maximum amount of product is the mixture where the number of moles of A and B are in their stoichiometric ratio of 2:3.

In today's experiment, you will prepare a number of solutions containing different amounts of solutions of Fe³⁺ and SCN¯ of known concentration. The number of moles of Fe³⁺ and SCN¯ added to make the solution may be calculated from the volume of solution used and the solution's concentration. Let n_SCN and n_Fe be equal to the number of moles of SCN¯ and Fe³⁺ added to make the solution. From the calculated number of moles of Fe³⁺ and SCN¯, the mole fraction of SCN¯ in the mixture can be determined as follows:

(2)

In the mixture that contains stoichiometric amounts of Fe³⁺ and SCN¯, it will be true, according to equation (1), that:

x(n_Fe) = n_SCN (3)

(Be careful not to confuse the coordination number, x, with the mole fraction symbolic notation of chi, c). Dividing both sides of equation (3) by the quantity n_Fe + n_SCN:

(4)

The right-hand side of equation (4) is equal to the mole fraction of SCN, c_SCN. The quantity in the parentheses on the left-hand side of equation (4) is equal to the mole fraction of Fe, c_Fe. Making these replacements in equation (4) one obtains:

xc_Fe=c_SCN (5)

Since the sum of mole fractions in a mixture always add up to one, the mole fraction of Fe is related to the mole fraction of SCN by the following equation:

c_Fe = 1 – c_SCN (6)

Substituting equation (6) into equation (5), the following relationship is obtained:

x(1 – c_SCN) = c_SCN (7)

Solving equation (7) for x:

(8)

Therefore, for the mixture containing a stoichiometric amount of Fe³⁺ and SCN¯, the coordination number, x, may be calculated from the value of the mole fraction of SCN¯ in the mixture.

The iron thiocyanate coordination complex has a red color. Therefore, it absorbs in the visible region of the electromagnetic spectrum. Therefore, the concentration of product can be calculated by measuring the amount of visible light that the product absorbs. Using a Ultraviolet-Visible (UV-Vis) absorption spectrophotometer, the amount of visible light absorbed by a sample can be measured experimentally. The basic setup of a UV-Vis absorption spectrophotometer was shown in Figure 1 in last week's lab handout. The instrument measures the intensity of the light before passing through the sample, called the incident light, I₀, and the intensity of light after passing through the sample, called the transmitted intensity, I_t. If a sample absorbs light of a particular wavelength, the transmitted intensity will be lower than the initial intensity. The spectrophotometer calculates two quantities based on these two intensities. The first is called the percent transmittance, %T, which is defined as follows:

(9)

A sample with 100%T absorbs none of the light of that particular wavelength. A sample with 0%T absorbs all of the light of that particular wavelength. In general, the %T of a sample lies somewhere between 0 and 100%T. The other quantity that a spectrophotometer measures is the absorbance of a sample, A, which is defined as follows:

(10)

The absorbance of a sample increases as more light is absorbed. An absorbance of 0.000 corresponds to no light absorbed by the sample.

The absorbance, A, is the quantity that is generally measured in a sample. The absorbance of a solution is directly proportional to the concentration of the absorbing species. The Beer-Lambert law, or more usually called Beer's Law, is a simple equation that gives the relationship between absorbance and concentration:

A = elc (11)

where c is the concentration of absorbing species, l is the length of the sample that the light beam passes through, and e is a proportionality constant called the molar absorptivity or the extinction coefficient of the particular complex. The length of the sample, l, sometimes called the path length, is simply the inner diameter of the container (called a cell) that holds the absorbing sample. In all our applications this semester, the path length of our cells is equal to 1.00 cm. The molar absorptivity is related to how efficient the sample is at absorbing the light. Its value depends on the wavelength of the light and the absorbing species. It is generally determined experimentally by measuring the absorbance of solutions of known concentration of absorbing species and plotting absorbance versus concentration in a plot called a Beer’s Law plot. The data points are then fit to a line and the slope of the line will be equal to the molar absorptivity. The units on molar absorptivity are liters per mole per centimeter (L mol^-1 cm^-1). If you know the molar absorptivity of an absorbing species, the concentration can be experimentally determined by measuring the absorbance of a solution of known concentration.

In today’s experiment, you will first determine the formula of the iron thiocyanate complex (the value of x) by using Job’s method. You will measure the absorbance of 10 solutions, each containing different relative amounts of Fe³⁺ and SCN¯ as given by the compositions of equilibrium mixtures in Table 1. For each solution, you will determine the mole fraction of SCN¯ from the given volumes and concentrations of Fe³⁺ and SCN¯ from Table 4. After measuring the absorbance of these ten solutions, you will plot absorbance (vertical axis) versus mole fraction of SCN¯ (horizontal axis) using a plotting program (either Cricket Graph or Excel). For example, suppose that you obtain a set of data as presented in table 2. You will obtain a plot similar to that shown in Figure 1. Find the mole fraction at which the maximum absorbance occurs by triangulating the plot as shown in Figure 1. The mole fraction of SCN¯ at which the maximum absorbance occurs is the mole fraction in which the number of moles of Fe³⁺ and SCN¯ are in the stoichiometric ratio. Plugging this value of the mole fraction into equation 8 will give the value of x. For example, in Figure 1, the maximum absorbance occurs at a mole fraction equal to 0.8. For this plot, the value of x is equal to:

(12)

Remember that x should be equal to a small whole number, so round off your answer to the nearest whole number.

Once the formula of the complex is known, the next step is to determine the molar absorptivity of the complex. To determine this, you will measure the absorbance of 5 solutions of known concentration of iron thiocyanate complex that have been prepared previously. You will make a Beer’s law plot by plotting absorbance (vertical axis) versus concentration (horizontal axis). Using your computer program to fit the data to a straight line, the slope of this line will be equal to the molar absorptivity of the complex.

Using the calculated molar absorptivity, the equilibrium concentration of iron thiocyanate complex in one of your beakers may be calculated by applying Beer’s Law:

(13)

Once the equilibrium concentration of the iron thiocyanate ion is known, the equilibrium concentrations of Fe³⁺ and SCN¯ can be calculated. First, the initial concentrations of Fe³⁺ and SCN¯ are calculated using the dilution formula:

(14)

(15)

According to the chemical reaction given in equation (1), for every mole per liter of iron thiocyanate produced, one mole per liter of Fe³⁺ and x moles per liter of SCN¯ are removed from the solution. Therefore, the equilibrium concentrations of Fe³⁺ and SCN¯ will be equal to:

(16)

(17)

The formation constant (or equilibrium constant) for the reaction can be calculated once the equilibrium concentrations are known:

(18)

The following items will be available to you in the laboratory:

A supply of small beakers

0.25 M HNO₃ solution

0.20 M Fe(NO₃)₃ solution

0.0030 M KSCN solution

5- 100 mL volumetric flasks containing solutions 1 through 5 used in part 1.

Composition of Solutions Used to Determine Molar Absorptivity

1. Set the wavelength on the Spectronics 20 spectrometer to 447 nm. With the cell holder empty and the top closed, and the spectrometer reading %T, adjust the left-hand knob on the front until the reading is 0.0%.

2. Obtain a cell and rinse it with two washes of 0.25 M HNO₃. Fill the cell about three quarters full with 0.25 M HNO₃ and place inside the spectrometer and close the top. Switch the spectrometer reading to absorbance and adjust the right-hand knob on the front until the reading is 0.000 absorbance units. These actions calibrate the spectrometer for the entire experiment.

3. There will be 5 solutions in 100 mL volumetrics available in lab that contain a specific amount of iron thiocyanate complex. The solutions were prepared using the amounts given in Table 1. Using 5 small beakers, pour out approximately 10 mL of each solution into separate beakers keeping track of which solution is in which beaker.

4. Measure and record the absorbance of each solution by rinsing the cell twice with small portions of each solution and then filling the cell about three-quarters full of the solution and placing in the spectrometer and reading off the absorbance. All rinse solutions containing Fe³⁺ and SCN¯ are to be discarded into a waste container. Therefore, pour all your waste solution into a large beaker and pour the waste into the waste container after you are done with the experiment.

5. Clean and dry the small beakers and use them in the next part of the experiment.

1. Clean and number eleven small beakers 1 through 10. Be sure the beakers are dry.

2. Clean and label 3 small 10-mL graduated pipets as SCN¯, Fe³⁺, and HNO₃.

3. Rinse each pipet with a small portion of its labeled solution and use each to prepare the following solutions in the numbered beakers as shown in Table 4.

4. Rinse the cell with deionized water. Shake the tube as dry as possible. Wipe the outside of the tube with a kimwipe to remove any fingerprints from the side. After wiping, handle only the upper portions of the cell to avoid putting any fingerprints where light passes through.

5. Rinse the cell twice with deionized water. Shake dry, and rinse two or three times with small portions of the solution in beaker 1. After rinsing your cell two or three times, fill the cell about three quarters full with solution from beaker 1.

6. Place the cell into the spectrometer and record the absorbance of this solution.

7. Repeat steps 5 and 6 for the remaining solutions in beakers 2 through 10.

Calculations

1. For the solutions in beakers 1 through 10 from part 2, calculate the initial number moles of Fe³⁺ and SCN¯ present from the volumes and the concentrations of the solutions used.

2. Calculate the number of moles of Fe³⁺ and SCN¯ added to each beaker using the following equation:

(19)

(20)

2. Calculate the mole fraction of SCN¯ in beakers 1 through 10 using equation 2.

3. Prepare a graph of absorbance (vertical axis) versus mole fraction of SCN¯ (horizontal axis) using a graphing program. Print out the graph. Determine the mole fraction of SCN¯ at maximum absorbance by triangulating the plot and finding where the maximum occurs. Attach the plot to your data sheet.

4. Determine the coordination number of the complex (the value of x) from the mole fraction of SCN¯ at maximum absorbance.

5. Write the correct formula for the complex including the charge of the complex on your data sheet.

Part IV: Determination of molar absorptivity

1. In solutions 1 through 5 from part 1 of the experiment, there is a large excess of Fe³⁺ ion present. This means that essentially that SCN¯ is the limiting reagent in this reaction. Therefore, the concentration of iron thiocyanate complex present will be equal to the initial concentration of SCN¯ divided by the coordination number x. Calculate the initial concentration of SCN¯ in each solution using the dilution formula:

(21)

2. Calculate the concentration of iron thiocyanate complex in solutions 1 through 5 from part 1 of the experiment.

(22)

3. Plot the absorbance (vertical axis) versus the concentration of iron thiocyanate complex (horizontal axis) using a graphing program. Fit the data points to a straight line and print out the equation of the line. Be sure to include the value of R² in your graph. The slope of this line is equal to the molar absorptivity of the iron thiocyanate complex. Record the molar absorptivity on your data sheet. Attach the graph to your data sheet.

Part V: Calculation of the Equilibrium Constant

For Part V, consider the solution in beaker 5 (from part II) only!!!

1. Calculate the initial concentrations of Fe³⁺ and SCN¯ by using equations 14 and 15.

2. Using Beer’s Law, calculate the equilibrium concentration of iron thiocyanate complex in beaker 5 from its absorbance using equation 13.

3. Calculate the equilibrium concentrations of Fe³⁺ and SCN¯ from the balanced chemical reaction using equations 16 and 17:

4. Using the expression for the equilibrium constant (equation 18), calculate the value of K for this reaction.

 

 

Answer the following problem to the best of your ability showing all work necessary to obtain the answer. The answer should be reported with the correct number of significant figures and with the appropriate units on it.

Warning!! The solution of this preliminary problem requires some computer graphing. DO NOT WAIT UNTIL THE LAST MOMENT TO DO THIS PRELIMINARY PROBLEM!!

The ligand 1,10-phenanthroline (abbreviated as o-phen) forms a coordination complex with Fe²⁺ according to the reaction:

Fe²⁺(aq) + x(o-phen)(aq) ¾ ¾ ® Fe(o-phen)_x²⁺(aq)

A series of solutions were prepared with different relative amounts of Fe²⁺ and o-phen while keeping the total amount of reactants constant. The coordination complex absorbs light at 508 nm. The absorbance of each mixture and the mole fraction of o-phen in each mixture is presented in the table below. From this table, construct a Job's plot of absorbance (vertical axis) versus mole fraction of o-phen. Triangulate the plot and determine the coordination number, x, of this complex from the mole fraction of maximum absorbance. (Attach Job's plot to this handout)