CHEMISTRY 135 General Chemistry II Determination of an Equilibrium Constant Show above is a laboratory sample from chemistry, not phlebotomy. [1] Is the bloody-looking product the main component of this solution, or is it just a minor but highly visible component? How would you know? DEPARTMENT OF CHEMISTRY UNIVERSITY OF KANSAS 1
Determination of an Equilibrium Constant Introduction A system is at equilibrium when the macroscopic variables describing it are constant with time. These variables include pressure and temperature. In addition, for a solution that can contain multiple species, the concentrations are also independent of time at equilibrium. While equilibrium indicates an unchanging state, note that this is reflected in the macroscopic variables. At the molecular level there is tremendous movement of molecules, exchange of energy, and interconversion of the various molecular species. However, at equilibrium all of these processes are balanced such that the rate of depletion of a molecular species is balanced by the rate of formation of the same species. The equilibrium between different molecular species is characterized by an equilibrium constant. Consider as an example the ionization of the weak acid HF: HF(aq) + H 2O(l) H 3O + (aq) + F - (aq) The equilibrium is established between the forward and backward reactions and is characterized by the concentrations of the reactants and products of the reactions at equilibrium, i.e., after the concentrations stop changing. Specifically, the equilibrium constant is given by the ratio K c = [H 3O + ][F - ]/[HF] where [HF] is the concentration of the acid. Note that the equilibrium constant is given by the product of the product concentrations (raised to their stoichiometric coefficients) divided by the product of the reactant concentrations (also raised to their stoichiometric coefficients). The solvent, here water, is not included because its concentration, which is present in great excess, does not change due to the reactions. In this experiment the equilibrium constant for a reaction involving the complexation of two species will be measured. To do so, a measurable quantity that is proportional to the concentration of a species must be available. The approach here will be to use spectroscopy, where the absorbance at a particular wavelength is proportional to the concentration of the species which absorbs light at that wavelength. The species involved in this laboratory experiment are Fe(NO 3) 3 and KSCN in aqueous solution (which also contains nitric acid, HNO 3 for reasons not important to the equilibrium). These species are simply the precursors to those involved in the equilibrium. Namely, Fe(NO 3) 3 decomposes as Fe(NO 3) 3 (aq) Fe 3+ (aq) + 3 NO 3 - (aq) providing Fe 3+ in solution. Similarly, KSCN decomposes as KSCN (aq) K + (aq) + SCN - (aq) to provide SCN - (thiocyanate) in solution. These processes themselves involve equilibria, but the equilibrium of interest in this experiment is the resulting one between iron and thiocyanate: Fe 3+ (aq) + SCN - (aq) FeSCN 2+ (aq) for which the equilibrium constant is K c = [FeSCN 2+ ]/([Fe 3+ ][SCN - ]) To determine K c, the three concentrations involved must be determined. For the reactants this will be based on the amount of the precursor compounds added to solution. For the products, spectroscopy will be used. 2
Pre-lab Safety: Goggles must be worn at all times. Most chemicals can be toxic and hazardous if splashed on clothing, exposed skin or in the eyes. At the very least, some of the compounds used in this laboratory can permanently stain your clothes. If chemicals splash on skin or clothes, remove the affected clothing and flush the affected areas thoroughly with cold water. Iron/thiocyanate solutions should be collected in a separate container as waste. Take care to keep the thermometer and Vernier temperature probe from direct contact with the liquid nitrogen and the dry ice. Pre-lab Assignment: Please write out the following in your lab notebook. This assignment must be completed before the beginning of lab. You will not be allowed to start the experiment until this assignment has been completed and accepted by your TA. 1) List all of the chemicals you will use for this week's experiment. For each chemical, list specific safety precaution(s) that must be followed. In order to find specific safety information, please obtain a Materials Safety Data Sheet (MSDS) on the chemical of interest. MSDSs can be found through an internet search (e.g., google) or from the following website: www.hazard.com Read the MSDS and find specific safety concerns for each chemical. 2) In solution, the sugar α-glucose undergoes a process called intramolecular rearrangement to produce β-glucose. The molecular formula for both is C 6H 12O 6 (molecular weight 180.2 g/mol). This equilibrium reaction can be simply written as α-glucose β-glucose In the diagram to the right, 2 molecules of α-glucose and 4 molecules of β-glucose are contained in an aqueous solution. Each glucose molecule is represented by a single a symbol (α or β). The net volume of the solution is 10.0 ml. Assume that the solution is at equilibrium. Write an equilibrium constant expression, and calculate a numerical value for the equilibrium constant. 3) Now, obtain a dark-colored beverage such as Pepsi, Coke, iced tea or juice. Get a clear glass and pour half an inch of liquid into the glass. Hold the glass about one foot above a white sheet of paper in a well-lit room. Look down into the glass. Describe the coloration and whether or not you can see the paper through the glass. Pour another half an inch of soda into the glass, and again make observations. Repeat this process until there is between 2 and 3 inches of liquid in the glass. What trend did you observe as your experiment progressed? Describe the relationship between the amount of light that passes through the solution and the distance through which the light travels. Note: You may find it helpful to bring your Chemistry textbook to lab. 3
Procedure Part 1 Spectroscopic Measurement of the Equilibrium Concentration In this part of the experiment, successive portions of 0.100 M Fe(NO3)3 in 0.5 M HNO3 are added to a known volume of 1.200x10-4 M KSCN in 0.5 M HNO3. Both solutions contain 0.5 M HNO3 to maintain a constant ionic strength and acidity. The procedure should be repeated three times to compare results and determine an average value. 1. Set up the Ocean Optics spectrophotometer. Remember to calibrate the instrument. 2. Transfer 50.0 ml of the KSCN solution to a 250-mL beaker. 3. Transfer about 10 ml of the Fe(NO3)3 solution into a clean 25-mL beaker. 4. Pipet successive 1-mL portions of the Fe(NO3)3 solution into the KSCN solution. After each addition, stir the solution thoroughly. Then use a plastic transfer pipette to transfer a portion of the solution to a clean cuvette (cuvettes should be about two-thirds to three-quarters full). Measure the absorbance at 445 nm. After you have measured the absorbance, carefully return the contents of the cuvette to the parent solution. Be careful not to spill any of your solution! 5. Perform at least 10 subsequent 1-mL additions of Fe(NO3)3 and record the absorbance for each. Do not use distilled water or tap water to rinse your cuvette or plastic transfer pipette until you're completely finished with this trial. Why? Do use the same cuvette and the same transfer pipette for all of your measurements. 6. Repeat this procedure for a total of three times. Part 2 Data Analysis to Obtain an Equilibrium Constant In this part of the experiment, the data obtained from the three runs in Part 1 will be used to calculate an average value of the equilibrium constant K c. Your TA will work through the equations you will need to determine K c from the results of the measurements in Part 1. You will need to determine the equilibrium constants obtained from each of the three runs in Part 1. An important piece of the analysis is determining the concentration of FeSCN 2+ from the absorbance measurements in Part 1. Previous experiments performed by you and your group members illustrated that the absorbance measured is directly related to the concentration of the absorbing species. It is also related to the distance the light has to travel through the solution, which is called the pathlength. Specifically the transmittance of light through a solution is an exponential function of the pathlength and the concentration of the absorbing species. Since absorbance is proportional to the logarithm of the transmittance, it depends linearly on the pathlength. In 1852, a scientist named Beer put together these findings into an equation of the form: Absorbance = A = abc This equation is known as Beer's law. Here, a is called the molar absorptivity, b is the pathlength of the cell in which the absorbance is measured, and c is the concentration of the absorbing species. The molar absorptivity, a, is a constant that depends upon the molecular properties of the absorbing species and the wavelength of light. In this equation b, the pathlength, is expressed in centimeters; in many spectrophotometers it is 1 cm; indeed, the pathlength of the Ocean Optics cuvettes is 1.00 cm. 4
In this lab, the absorbance, A, was measured in Part 1; with some guidance from your TA, you will see how this data can be used based on its relationship to the concentration to obtain the equilibrium constant. As discussed in the Introduction section, this experiment is concerned with the equilibrium of the complexation reaction: Fe 3+ (aq) + SCN - (aq) FeSCN 2+ (aq) The concentrations of the starting species are important in this reaction. In particular, the SCN - concentration, [SCN - ] must be kept low enough so that species with one Fe 3+ and multiple SCN - ligands, such as Fe(SCN) 2 + or Fe(SCN) 3 are not present (as is the case for higher SCN - concentrations). When [SCN - ] is held around 1 mm (millimolar), the amount of these Fe(SCN) 2 + or Fe(SCN) 3 species will never be more than 0.1% of the FeSCN 2+ concentration. In Part 1 of this experiment [SCN - ] was held constant while [Fe 3+ ] was increased. As the [Fe 3+ ] is increased, more FeSCN 2+ complex will be formed since so, K c = [FeSCN 2+ ]/([Fe 3+ ][SCN - ]) [FeSCN 2+ ] = K c [Fe 3+ ][SCN - ] and since K c is a constant and [SCN - ] is held constant, as [Fe 3+ ] increases, so does [FeSCN 2+ ]. The rate at which [FeSCN 2+ ] grows as [Fe 3+ ] is increased is related to K c and that is how we can determine the equilibrium constant. Report A brief, individually prepared report approximately 3-4 pages in length is due at the beginning of next week s lab period. It is a full report, consisting of All Sections. You have practiced each section of a lab report already, and quality work is expected. The most important parts of your report will be the Results and Discussion sections. Make sure to include data, example numeric calculations, relevant chemical equations, relevant mathematical equations, and your final result. In your Discussion, be sure to interpret your calculated equilibrium constant. For example, are products or reactants favored? If you wanted to shift the equilibrium, what might you do? For additional guidance with your lab report, see the lab website or consult your TA! Reference(s) [1] http://chemistryexperimentphotogallery.blogspot.com/2010_11_01_archive.html accessed June 30, 2016. 5
Glossary Absorbance the ability, tendency, or capacity of a substance to absorb light of a specified wavelength; absorbance is the negative of the logarithm of the transmittance. Blank a solution containing all of the components of a sample except the analyte Calibration the alignment of measured amounts or increments on a device with standard values for amounts or increments Cuvette a vessel or container that holds a fluid sample in a spectrophotometer or other instrument; cuvettes generally do not absorb any of the wavelengths of light being used for the experiment. Equilibrium a state of equal balance ; in chemistry, the condition of unchanging concentrations due to the equal balance of forward and reverse reaction rates; at equilibrium, forward and reverse reaction rates are equal, while concentrations of reactants and products need not be equal Equilibrium Constant; K the ratio, at equilibrium, of the concentrations of the products of a reaction raised to their stoichiometric coefficients to the concentrations of the reactants raised to their stoichiometric coefficients; a measure of the extent to which a reaction proceeds in the forward direction, i.e., favoring products, based on comparing the equilibrium constant s value to the number 1 (products are favored with K >> 1) Spectrophotometer a device that passes a beam of light of known intensity through a sample and measures the intensity of light that reaches a detector on the other side of the sample; spectrophotometers measure absorbance or transmittance of a sample at one or more wavelengths of light Transmittance the ratio of amount of light energy exiting a sample or leaving a substance to the amount of light energy entering a sample or falling upon a substance. 100% Transmittance means all the light entering a sample passes through it, with the sample absorbing or scattering none of it. 6