Thermodynamics of Borax Dissolution Introduction In this experiment, you will determine the values of H, G and S for the reaction which occurs when borax (sodium tetraborate octahydrate) dissolves in water. Typically, H values are determined directly by measuring temperature changes when the reaction occurred. However, in many cases, this technique is not practicable. For example, the reaction may not go to completion, or it may give off such a small amount of heat that the temperature change is too small to measure. In addition, there is no direct method for measuring S for a reaction. It is therefore useful to be able to determine H, G and S indirectly, by using their relationship to the equilibrium constant of a reaction. The equilibrium constant of any reaction can be related to the free energy change of the reaction: G = RT ln K Eq. 1 The free energy change is also related to the enthalpy and entropy changes during the reaction: G = H T S Eq. 2 Combining these two equations gives the general relationship between K, H, and S : RT ln K = H T S Eq. 3 Dividing both sides by RT gives a particularly useful form of this relationship: ln K = œ ΔH R 1 T + ΔS R Eq. 4 This represents a linear equation of the form y = mx + b. In this case, y = ln K and x = 1/T; a plot of ln K against 1/T will therefore be linear. In addition, the slope of this line (m) will equal ( H /R), and its y-intercept (b) will equal ( S /R). It is therefore possible to determine H and S by simply measuring the equilibrium constant at several different temperatures, graphing ln K against 1/T, and measuring the slope and intercept of the resulting line. We can also use equation 4 to determine H by evaluating K at two temperatures. This leads to : Page1
The Gibb s Free energy change, G o, for the dissolution process can be evaluated at each temperature using the equation: ΔG = RT lnk Eq. 6 Once G O and H O are known, the entropy change, S O, can be evaluated from the Gibb s equation: ΔG = H - T S Eq. 7 The reaction you will study is the dissolution of borax (sodium tetraborate octahydrate) in water. Borax is a naturally occurring compound; it is in fact the most important source of the element boron, and it has been used for many years as a water softening agent. Borax is a rather complicated ionic salt which has the chemical formula Na 2 B 4 O 5 (OH) 4 8 H 2 O. When it dissolves, it dissociates as follows: Na 2 B 4 O 5 (OH) 4 8 H2O (s) 2 Na + (aq) + B 4 O 5 (OH) 4 2 (aq) + 8 H2 O (l) Eq. 8 Notice that the products of this reaction are two sodium ions and one other ion (this ion is called tetraborate ), along with the eight molecules of water. Since water does not appear in equilibrium constant expressions, the K expression for this reaction is: K = [Na + ] 2 [ B 4 O 5 (OH) 4 2 ] Eq. 9 You will measure K by analyzing a saturated solution of borax (i.e. a solution in which Eq. 8 has come to equilibrium) for the tetraborate ion (or just borate ion). Tetraborate is a weak base, so it can be titrated with a strong acid (Eq. 10). It may surprise you that tetraborate can react with only two hydrogen ions -- not four! -- and that in this reaction, the tetraborate ion falls apart, producing four molecules of boric acid: B 4 O 5 (OH) 4 2 (aq) + 2 H3 O + (aq) + H 2 O (l) 4 H 3 BO 3 (aq) Eq. 10 Once you know the number of moles of tetraborate in the solution, you can calculate the number of moles of sodium ion by using the stoichiometry of equation 8. Then, you can calculate the molar concentrations of the two ions and, finally, the value of K. Page2
Apparatus Three saturated borax solutions; 0 C, 25 C and 35 C Clean 125 ml beaker Primary standard, Na 2 CO 3 Bromocresol green indicator 50 ml buret 10 ml volumetric pipet HCl solution ~ 0.1 M 50 ml graduated cylinder Chemicals Borax Primary standard, Na 2 CO 3 Part A: Preparation and Standardization of 0.1 M HCl While the borax systems are equilibrating, prepare and standardize the 0.10 M HCl. Clean a 50 ml buret, condition it with ~ 5 ml of ~ 0.10 M HCl solution. Then fill the buret with 0.100 M HCl solution. Weigh ~ 0.15 g of the primary standard Na 2 CO 3 (determine mass to 4 places) into two separate Erlenmeyer flasks. Using a graduated cylinder, add 50 ml of distilled water and stir to dissolve the solid. Add 4 drops of bromocresol green indicator to give an initial blue solution. Titrate this solution with the HCl to a yellow color using a magnetic stirrer. There should be no green tint at the endpoint. Add more of the indicator if the color fades. Do a third titration if the first two do not give reproducible results (at least ± 5%). Calculate the molarity of the HCl solution using the balanced chemical equation below: 2 HCl (aq) + Na 2 CO 3(aq) 2 NaCl (aq) + CO 2(g) + H 2 O (l) Part B: Titration of Equilibrated Borax Solutions; 0 C, 25 C and 35 C Prepare a beaker of warm deionized water (~ 60-70 C) and clean a 125 ml Erlenmeyer flask. Into the flask pipet a 10.00 ml aliquot of one of the saturated borax solutions being very careful not to agitate the undissolved borax solid on the bottom of the beaker. Read and record the exact temperature of the saturated borax solution. Using a graduated cylinder add 20.0 ml of the warm deionized water into the flask and add 4 drops of bromocresol green indicator to give an initial blue color. Titrate with the standardized HCl solution to a yellow endpoint (no green tint). Repeat the above procedure with the two remaining saturated borax solutions. Page3
Preparation of Finished Lab Report - Follow the steps below to prepare your finished lab report. Your report should contain the following sections listed in the exact order as shown below: I) Title (front) page (typed) a) Experiment title b) Your name & name of your lab partner c) Date experiment conducted d) Chemistry 220, Canada College, Fall Session, 2014 II) Standardization of HCl 1. Provide a data table for the standardization of HCl as shown in Appendix I. 2. Show how you calculate HCl molarity in the space below the table. Your calculations should be typed or neatly hand written. III) Titration of Saturated Borax Solutions 1. Provide three separate data tables for the titration of the saturated borax solutions as shown in Appendix II. 2. Show your calculations in the space below the table. Your calculations should be typed or neatly hand written. IV) Prepare a data summary table with 7 columns: T( C), T(K), 1/T(K -1 ), [ B 4 O 5 (OH) 4 2 ], [Na + ], K, and lnk. Complete the table using your experimentally determined values. V) Using Excel, plot ln K vs 1/T(Kelvin). Find the equation for the resulting line (which will give you the slope and y-intercept). Using equation (4) and the plot, determine ΔH o (kj/mol) and ΔS o (J/mol-K). A sample plot is shown in Appendix III. Finally, calculate ΔG o using equation (1). Show your calculations for H o, S o and ΔG o in the space below the Excel plot. VI) Post-lab questions. (1) Does the solubility of borax in water increase or decrease as temperature increases? What experimental evidence supports your answer? (2) Is the dissolution of borax in water an exothermic or endothermic process? What experimental evidence supports your answer? (3) Is the dissolution of borax in water a temperature dependent reaction or is it spontaneous at all temperatures at which water is liquid? Briefly explain. Page4
Appendix I Data Table for Standardization of HCl Trial 1 Trial 2 Mass of Na 2 CO 3 weighed (g) Mols of Na 2 CO 3 Mols HCl used Final volume HCl (ml) Initial volume HCl (ml) ml HCl used in titration Molarity of HCl Calculations: Page5
Appendix II Sample Data Table for Titration of Saturated Borax Solution Actual Temperature of Borate Solution Final volume HCl (ml) Initial volume HCl (ml) ml of HCl used in titration Molarity of HCl (from part A) Mols of HCl used in titration Mols of Borate Volume of Borate used (ml) (Aliquot taken) Molarity of Borate Molarity of Na + Calculated K sp of Borax Trial #1 Trial #2 Calculations: Page6
Appendix III Sample Graph, lnk versus 1/T (K -1 ) 5 data points shown here; your graph will have three data points. Page7