Laboratory Techniques II, CHY 116
Chemistry Department, University of Southern Maine

A Spectrophotometer
Left: setting % transmittance to zero when the sample compartment is empty and no light reaches the detector.
Right: setting absorbance to zero with a blank in the sample holder.
For a closer view, click either image.

Measuring an Equilibrium Constant I:
Using Color to Analyze an Equilibrium Mixture

Assignment

1. Use the index of your class textbook to learn all you can about
   • the electromagnetic spectrum
   • absorption of light by solutes, and absorption spectra
   • the law of mass action
   • equilibrium constants
   • formation constants (or stability constants) of complex ions
   • ICE tables for equilibrium calculations
2. Review Le Chatelier's principle.
3. Read the background materials below on spectrophotometry, and on the reaction under study in this experiment

Goal

You will use spectrometry to measure the concentration of iron (III) thiocyanate ions, Fe(SCN)²⁺, in various aqueous mixtures of iron (III) nitrate and potassium thiocyanate. You will use the results of these measurements to determine the equilibrium constant for the formation of Fe(SCN)²⁺, described by this equation:

Background

A. Determining Solution Concentrations by Spectrometry

Measuring the concentration of a solute by its absorbance of light is an example of a spectrophotometic or colorimetric method. The amount of light absorbed (called absorbance, A) by solutes depends on three factors:

1. Nature of the solute
   Some solutes, such as sugar, absorb no light, while others, like the pigments in grape juice, absorb light strongly. Solutes that absorb visible light produce colored solutions.
2. Distance light travels through the solute
   Obviously, light travelling one meter through a solution encounters more solute particles than light travelling only a centimeter through the same solution. Grape juice in a slender glass looks lighter in color (absorbs less light) than does grape juice in a glass of larger diameter. The absorbance of a solution is directly proportional to the path length (usually called b), the distance light travels through the solution.
3. Concentration of the solute
   Light traveling through a concentrated solutions encounters more particles of solute than does light traveling the same distance through a dilute solution. Grape juice concentrate is more darkly colored (absorbs more light) than is dilute grape juice. The amount of light absorbed by a solution is often, but not always, directly proportional to the concentration of the absorbing solute. If by experiment, we find that absorbance is proportional to concentration, we say that such solutes obey Beer's law:

This simple law relates absorbance A, the light absorbed on passing through b cm of a solution, to the concentration C of the absorbing solute. The constant of proportionality E is called the molar absorptivity (units: M^{-1 •} cm^-1).

As its name suggests, you can also think of E as the the amount of light absorbed when light passes through 1.00 cm of a 1.00 molar solution of the solute. The molar absorptivity is a characteristic of a particular solute (factor #1 above) at a particular wavelength of light. If a solute absorbs visible light (wavelength 400-700 nm), a large value of E means that that even a dilute solution of the solute exhibits noticeable color. In older chemical literature, E is called the extinction coefficient, and A is called the optical density.

When light of intensity I₀ passes through an absorbing medium, such as a solution containing an absorbing solute, the intensity of the light is reduced to intensity I.

The fraction or ratio I/I₀ is called the transmittance, T, of the solution. Many instruments for measuring absorption (called spectrophotometers) allow determination of this ratio, as well as conversion of this ratio to absorbance A by the relationship A = - log T. Many instruments display both absorbance and transmittance, often as a percentage (T x 100%).

If a solute obeys Beer's law, then a graph of A vs C for a series of solutions is a straight line of slope equal to bE. This graph is called a Beer's-law plot, and it has two functions: a) to determine whether the solute obeys Beer's law, and if so, b) to determine E.

If the data on this plot fit a straight line, then you can determine E from the slope of the fitted line. Once you know E, then you can measure A of solutions for which C is unknown, and calculate their concentrations (C) using Beer's law. In the graph above, made with solute X in a sample holder having a path length of 1.00 cm,

An solution containing an unknown concentration of solute X that gives absorption of 0.500 at 460 nm in a 1.00-cm sample holder thus has a concentration of (solving the equation of the straight line for C)

Beer's law applies to only one absorbing solute in solution. A blank is used to cancel out absorption by any other solutes, so that the measured absorbance is directly proportional to the concentration of the solute of interest. Beer's law usually holds only if the light irradiating the sample is of a single wavelength (monochromatic), and corresponds to an absorbance maximum in the absorption spectrum of the solute.

You will make your absorbance measurements with a Baush and Lomb Spectronic 20 Spectrophotometer. For a brief introduction to this instrument, click HERE.

B. Equilibrium Formation of Iron (III) Cyanate Ion (FeSCN²⁺)

Iron (III) ions react with thiocyanate ions (SCN-) to form iron (III) thiocyanate, FeSCN²⁺, which is a stable blood-red complex ion:

The equilibrium constant expression for this reaction is

Solutions of iron (III) ions are weakly colored and thiocyanate ion is colorless, so the primary absorber in a mixture of these components is FeSCN²⁺. This ion obeys Beer's law at 460 nm over a fairly wide range of concentrations, allowing measurement of its concentration in equilibrium mixtures. From its measured equilibrium concentration and the intial concentrations of Fe³⁺ and SCN^-, it is possible to determine the concentrations of all three components, and from them, the equilibrium constant for the reaction.

Iron(III) ion introduces a complication because of its reaction with water to form iron hydroxide, which is insoluble in water:

To avoid precipitation of iron (III) hydroxide, you will include excess nitric acid (HNO₃) in all solutions, to shift this equilibrium far to the left. Because neither hydrogen ions nor nitrate ions are components of the iron (III) thiocyanate equilibrium, nitric acid does not affect the equilibrium position of the reaction that produces FeSCN²⁺.

In Part 1 of this experiment, you will prepare a series of calibration solutions having known concentrations of the iron (III) thiocyanate ion. To do so, you will use a small, known amount of thiocyanate, and a large excess of Fe³⁺ to drive the reaction to the right, incorporating all of the thiocyanate into FeSCN²⁺. In each of these solutions, therefore, the equilibrium concentration of FeSCN²⁺ equals the intial concentration of SCN^-. You will determine the absorbance of each solution, prepare a Beer's law plot, and obtain the equation of the line relating A and C.

In Part 2, you will prepare five mixtures with known initial concentrations of iron (III) and thiocyanate ion. You will determine the absorbance of each mixture after it reaches equilibrium, and then use the equation of your Beer's law plot (Part 1) to determine the concentration of FeSCN²⁺ in each equilibrium mixture. Finally, from the measured [FeSCN²⁺], and the known intial [Fe³⁺] and [SCN^-], you will determine the equilibrium constant K_C for this reaction.

In the five different equilibrium solutions, the equilibrium concentrations, and hence the equilibrium positions, are different. But your measured values of the equilibrium constant should be the same, within expected experimental variation.

Preparing for Lab

The following problems require skills and calculations similar to those called for in the report on this experiment. Learn how to work these problems, showing all calculations with units. Similar questions may appear on your prelaboratory quiz. For guidance, look at the Report Form for this experiment. For problems involving calculation, answers are provided.

1. The absorbance of a solution of solute X in a 1.5-cm sample tube is 0.755. Use the Beer's law plot above to determine the concentration of X in this solution. (Answer: 0.132 M)
2. A calibration solution contains 1.50 mL of 0.00200 M NaSCN, 5.00 mL of FeCl₃, and enough 0.1 M HNO₃ to make a total volume of 25 mL. Assuming that [Fe³⁺] is sufficient to drive the reaction to completion, what is the concentration of FeSCN²⁺ in this solution? (Answer: 1.20 x 10^-4 M)
3. A student prepares an equilibrium solution by mixing 5.00 mL 0.002 M Fe³⁺, 2.00 mL 0.00200 M SCN^-, and 3.00 mL 0.1 M HNO₃. What are the initial concentrations of Fe³⁺ and SCN- in this solution? (Answers: [Fe³⁺] = 1.00 x 10^-3; [SCN^-] = 4.00 x 10^-4)
4. By measuring the absorbance of the solution in question 3, the student finds that [FeSCN²⁺] = 8.70 x 10^-5. Set up an ICE table, using the information in question 3 and this question. Use the ICE table to calculate the equilibrium concentrations of Fe³⁺ and SCN^- in this solution. (Answers: [Fe³⁺] = 9.13 x 10^-4; [SCN^-] = 3.13 x 10^-4)
5. Use the equilibrium concentrations from question 4 to calculate K_C for the formation of FeSCN²⁺. (Answer: 3.04 x 10²)
6. On the Syllabus page, use the link "Recognizing Chemical Hazards" to find out the hazards associated with substances you use and make in this experiment.

Procedures

Download and print the Procedure for this experiment. Study it carefully after reading this page. In your lab notebook, translate the procedure into step-by-step instructions for your lab work. Leave room for alterations in procedure, and for observations. Also prepare spaces or tables in your lab notebook to receive the data you will collect in lab. Bring the printed procedure and your prepared lab notebook with you to lab. Once per semester, you might earn a free perfect quiz score for bringing a well-prepared notebook.

Report

Download and print the Report Form for this experiment. Bring it with you to lab.

If is it not convenient for you to consult this web page online, you might want to print it out also. Save paper by printing it on the back of the Procedure pages (not the Report Form).