C H E M I S T R Y 1 5 0 Chemistry for Engineers DETERMINATION OF AN EQUILIBRIUM CONSTANT DEPARTMENT OF CHEMISTRY UNIVERSITY OF KANSAS
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 concentration of each species is 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, on the other hand, 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. For example, at equilibrium 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 in water: HF (aq) + H2O (l) H3O + (aq) + F - (aq) The equilibrium is established between the forward and backward reactions and is characterized by the concentrations of the reactants and products at equilibrium, i.e., after they stop changing. Specifically, the equilibrium constant, Kc, is given by the ratio Kc = [H3O + ]eq[f - ]eq/[hf]eq where [H3O + ]eq, [F - ]eq, and [HF]eq are the equilibrium concentrations of the hydronium ion, fluoride ion, and hydrofluoric acid, respectively. 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 appreciably 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. In this spectroscopic investigation, the equilibrium constant will be determined for the formation of Fe(SCN) 2+ from the reaction of Fe 3+ and SCN -. During this experiment, clear, soluble solutions of iron(iii) nitrate, Fe(NO3)3, and potassium thiocyanate, KSCN, will be mixed to form a series of solutions containing different equilibrium concentrations of the red Fe(SCN) 2+ complex. The relevant reactions leading to the formation of Fe(SCN) 2+ are summarized below. 2
Fe(NO3)3 (aq) Fe 3+ (aq) + 3 NO3 - (aq) (1) KSCN (aq) K + (aq) + SCN - (aq) (2) Fe 3+ (aq, clear) + SCN - (aq, clear) Fe(SCN) 2+ (aq, red) (3) Aqueous solutions of Fe(SCN) 2+ will be prepared by adding successive 1 ml aliquots of an acidic 0.100 M Fe(NO3)3 solution to a 50 ml sample of an acidic 1.200 10-4 M KSCN solution. (Note: Both solutions contain 0.5 M HNO3 to maintain a constant ionic strength and acidity.) Adding Fe 3+ to each solution has the effect of increasing the equilibrium concentration of Fe(SCN) 2+. The equilibrium constant (Kc) for Reaction (3) is given by Kc = [Fe(SCN) 2+ ]eq/([fe 3+ ]eq[scn - ]eq) (4) To determine Kc, the three concentrations involved must be determined. For the reactants, Fe 3+ and SCN -, this will be based on the amount of the precursor compounds initially added to solution. For the product, Fe(SCN) 2+, 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) Briefly describe the objectives of this experiment. 2) 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. 3
Procedure Part 1 - Spectroscopic Measurement of an 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. Absorbance measurements at λ = 445 nm will be recorded for each of these solutions. These data will be used in Part 2 to determine the value of the room temperature equilibrium constant (Kc) for the formation of the Fe(SCN) 2+ ion. The procedure outlined below will be repeated three times to determine an average value of Kc. 1. Set up the Ocean Optics spectrophotometer. Remember to calibrate the instrument. 2. Construct a table in your lab notebook similar to the one shown below. Volume of Fe(NO3)3 Added (ml) Absorbance Readings at 445 nm Trial 1 Trial 2 Trial 3 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 3. Transfer 50.0 ml of the acidic 1.200x10-4 M KSCN solution to a clean 250-mL beaker. 4. Transfer ~10 ml of the acidic 0.100 M Fe(NO3)3 solution to a clean 25-mL beaker. 5. Pipet 1 ml of the 0.100 M Fe(NO3)3 solution into the KSCN solution. Stir the solution thoroughly. 6. Use a plastic transfer pipette to transfer enough of the Fe(NO3)3/KSCN solution prepared in Step 5 to a clean cuvette so that the cell is ~ ⅔ to ¾ full. Excess solution left in the transfer pipette should be returned to the parent Fe(NO3)3/KSCN solution. Measure the absorbance at 445 nm. 4
7. 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, and DO NOT rinse the cuvette. 8. Perform at least 9 subsequent 1-mL additions of Fe(NO3)3 to the parent Fe(NO3)3/KSCN solution and record the absorbance for each solution. Do not use distilled water or tap water to rinse your cuvette or plastic transfer pipette until you are completely finished with this trial. You must use the same cuvette and the same transfer pipette for all of your measurements in a given trial. 9. Repeat this procedure twice more so that you have absorbance data for three separate trials. Part 2 - Data Analysis to Obtain an Equilibrium Constant In this part of the experiment, the data obtained in Part 1 will be used to calculate the equilibrium constant (Kc) for the given complexation reaction, Reaction (3). Specifically, the data obtained in each of the three trials in Part 1 will be used to determine a value for Kc. An average value of the equilibrium constant will then be calculated from these three Kc values. Before leaving lab for the day, your TA must be given the equilibrium constants obtained from each of the three runs in Part 1 and your average Kc value. 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 at 445 nm 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. Specifically, the FeSCN 2+ ion absorbs strongly at 445 nm. Thus, under conditions where Beer s law is valid, absorbance readings at this wavelength will be related to the equilibrium concentration of FeSCN 2+ (specifically as A = ab[fe(scn) 2+ ]eq). Rearranging this expression and solving for [Fe(SCN) 2+ ]eq gives [Fe(SCN) 2+ ]eq = A/ab. 5
As discussed in the Introduction, this experiment is concerned with the equilibrium of the complexation reaction: Fe 3+ (aq) + SCN - (aq) Fe(SCN) 2+ (aq) The concentrations of the starting species are important in this reaction. In particular, in Part 1 only Fe 3+ and SCN - are initially in the solution with concentrations [Fe 3+ ]0 and [SCN - ]0. Then, the reactant concentrations at equilibrium in the equilibrium constant expression, Eq. (4), can be expressed as [Fe 3+ ]eq = [Fe 3+ ]0 - [Fe(SCN) 2+ ]eq and [SCN - ]eq = [SCN - ]0 - [Fe(SCN) 2+ ]eq, respectively. Furthermore, 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 (milli-molar) or lower, the amount of these Fe(SCN)2 + or Fe(SCN)3 species will never be more than 0.1% of the FeSCN 2+ concentration. These conditions also ensure that [Fe 3+ ]0 >> [Fe(SCN) 2+ ]eq, which means that [Fe 3+ ]eq = [Fe 3+ ]0 [Fe(SCN) 2+ ]eq [Fe 3+ ]0 and Eq. (4) for the equilibrium constant, Kc, can be simplified to Kc = [Fe(SCN) 2+ ]eq/{[fe 3+ ]0 ([SCN - ]0 - [Fe(SCN) 2+ ]eq)}. (5) Since [Fe 3+ ]0 and [SCN - ]0 are known from the preparation of the solution and [Fe(SCN) 2+ ]eq can be obtained spectroscopically, the equilibrium constant can be determined. A key part of this determination is that, in Part 1 of this experiment [SCN - ]0 was held constant while [Fe 3+ ]0 was increased. As the [Fe 3+ ]0 is increased, more FeSCN 2+ complex will be formed at equilibrium according to Le Chatelier s principle which will be discussed in class. The rate at which [FeSCN 2+ ]eq grows as [Fe 3+ ]0 is increased is related to Kc and that is how you will determine the equilibrium constant. Your TA will work through the precise equations with you for obtaining Kc from your measurements. 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. 6
absorbance Glossary 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 macroscopic variable a quantity that describes the state of a system at a level which does not require the knowledge or recognition of an underlying molecular (microscopic) structure, e.g., pressure, temperature, density, volume 7