DETERMINATION OF AN EQUILIBRIUM CONSTANT

Transcription

1 C H E M I S T R Y F U N D A M E N T A L S O F C H E M I S T Y I I H O N O R S Spring 2011 DETERMINATION OF AN EQUILIBRIUM CONSTANT DEPARTMENT OF CHEMISTRY UNIVERSITY OF KANSAS 1

2 Determination of an Equilibrium Constant Introduction A system is at equilibrium when the macroscopic variables describing it are constant with time. These variables include the ones discussed in class such as pressure and temperature. In addition, for a solution which 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, interconversion of the various molecular species. However, at equilibrium all of these processes are balanced such that, for example, the rate of depletion of a molecular species is exactly 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: 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 they stop changing. Specifically, the equilibrium constant is given by the ratio K c = [H 3 O + ][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 as 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; this was observed in the Introduction to Spectroscopy laboratory. 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 3 providing Fe 3+ in solution. Similarly, KSCN decomposes as 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: 2

3 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. 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. 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) A statement of the objective of the experiment in your own words. (2) A discussion of the safety concerns for the experiment including a list of chemicals to be used and a discussion of any associated hazards. This information can be obtained from Materials Safety Data Sheets (MSDS) for each chemical. The MSDS information can be obtained from a number of sources including the KU EHS website ( and (3) An outline of the procedure. Write out the experimental procedure in your lab notebook according to the Guidelines for Keeping a Laboratory Notebook handout. In addition to these pre-lab requirements, a short quiz will be given at the beginning of lab based on the material in this lab write-up. Procedure Part 1 - Spectroscopic Measurement of an Equilibrium Concentration In this part of the experiment, successive portions of M Fe(NO 3 ) 3 in 0.5 M HNO 3 are added to a known volume of 1.200x10-4 M KSCN in 0.5 M HNO 3. Both solutions contain 0.5 M HNO 3 to maintain a constant 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(NO 3 ) 3 solution into a clean 25-mL beaker. 3

4 4. Pipet successive 1-mL portions of the Fe(NO 3 ) 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(NO 3 ) 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. 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 and report those to your TA before you leave the lab. An important piece of the analysis is determining the concentration of FeSCN 2+ from the absorbance measurements in Part 1. In the Introduction to Spectroscopy experiment, you determined 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 path-length and the concentration of the absorbing species. Since absorbance is proportional to the logarithm of the transmittance, it depends linearly on the path-length. 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 path-length, is expressed in centimeters; in many spectrophotometers it is 1 cm; indeed, the path-length of the Ocean Optics cuvettes is 1.00 cm. In this lab, the absorbance, A, was measured in Part 1 and, as you will see from the presentation by your TA, this can be used - based on its relationship to the concentration - to obtain the equilibrium constant. As discussed in the Introduction, this experiment is concerned with the equilibrium of the complexation reaction: 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 - 4

5 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 (milli-molar), 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 the total number of moles of SCN - is fixed, 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 Your lab report should be a formal, individual report prepared according to the Guidelines for Laboratory Reports you have been given. In addition to the categories discussed in these guidelines you should provide answers to all the questions posed in this laboratory experiment writeup. 5

6 Glossary absorbance a measure of the amount of electromagnetic radiation absorbed as defined by A=log(1/T) where T is the transmittance defined below concentration a measure of the density of a solute (or component) in a solution; concentration is generally reported as molarity=m=(moles of solute)/(liters of solution) and 1 M= one molar ; the concentration of a species X is denoted as [X] equilibrium the state of a system characterized by unchanging macroscopic variables, e.g., pressure, volume, temperature, concentrations; the equilibrium state of a system is the one which minimizes the Gibb s free energy, G 6