The thermodynamics of the solubility of borax Determination of ΔH° and ΔS°

Borax Borax has the formula Na2[B4O5(OH)4].8H2O [B4O5(OH)4]2- is the tetra-borate anion Borax is a weak base and reacts with acid Na2B4O7·10H2O + 2 HCl → 4 H3BO3 + 2 NaCl + 5 H2O H3BO3 is the conjugate acid (Boric acid) which as a pH around 4 or so depending on the molarity It is a good water softener Ca2+ (aq) + Na2B4O7 (aq) → CaB4O7 (s)↓ + 2 Na+ (aq) Mg2+ (aq) + Na2B4O7 (aq) → MgB4O7 (s)↓ + 2 Na+ (aq)

Na2[B4O5(OH)4].8H2O(s) ↔ 2 Na+ (aq) + [B4O5(OH)4]2- (aq) + 8 H2O (l) Purpose To determine the thermodynamic quantities ΔH° and ΔS° ,for the solvation reaction of borax in water Na2[B4O5(OH)4].8H2O(s) ↔ 2 Na+ (aq) + [B4O5(OH)4]2- (aq) + 8 H2O (l) by measuring the solubility product constant, Ksp, over the temperature range 50−15°C The temperature dependence of the equilibrium constant Ksp depends on the enthalpy of solvation ΔH° and the entropy of solvation ΔS°

What is ΔS° ? Imagine the solvation is an elementary step reaction Na2[B4O5(OH)4].8H2O(s) 2 Na+ (aq) + [B4O5(OH)4]2- (aq) + 8 H2O (l)

What is ΔS° ? ΔS° is called the entropy of solvation we can see it is somehow related to the ratio of the collision factors for reaction in the forward and backward direction If A1 > A2 ΔS° > 0 If ΔS° > 0 we say that process is spontaneous, it means that it is more probable for the reactants to come together to react, than for the products to come together and react to make reactants

What is ΔS° ? Consider what happens when the borax solid dissolves in water? When the orange particles dissolve in water two things can happen can hang around near the crystal and potentially re-attach themselves they can move off further away from the crystal It’s like reaching a crossroad where the road is going 4 ways. You randomly choose a road – 3 take you further away and 1 takes you back

What is ΔS° ? Consider you are at a crossroads. To choose which direction to go you choose a number between 1 and 4 at random You are 3 times more likely to leave than return home In the same way when borax dissolves there are more choices which take it into solution than back to solid In this case A1 > A2 ΔS° > 0 Entropy is measuring the number of choices available to the system

Objective: knowing Ksp(T) If we know the quantities ΔH° and ΔS° then we know how the equilibrium constant changes with T Make saturated solutions of borax in water at different temperatures Measure the concentration of the tetraborate x=[B4O5(OH)4]2- in the solution (by titration) Determine Ksp at that temperature T using Ksp = 4x3 (ICE table)

Objective: knowing Ksp(T) Plot the ln(Ksp) vs 1/T (where T is in Kelvin) Should give a straight line graph Where

Part A: Preparing a Saturated Borax Solution 20 g Borax in 80 mL of deionized H2O Stirrer and hotplate thermometer Heat to 52oC-55oC DO NOT LET IT GET ABOVE 55oC Leave it at 52oC-55oC for 30 mins While it is heating use a pipette to measure precisely 5.00 mL of water into each of six small test tubes and mark the levels with a wax pencil Label the test tubes ~ 50°, ~ 45°, ~ 35°, ~ 30°, ~ 20°, and ~15 °C After 30 mins remove the beaker from hot plate As it cools decant 5 mL into test tubes at ~ 50°, ~ 45°, ~ 35°, ~ 30°, ~ 20°, and ~15 °C Record the actual temps to nearest 0.1oC

Part B: Standardized HCl Solution While 2 students are making the saturated solutions and marking test tubes, the other student(s) will make a standardized HCl solution for later titrations In a fume hood, add 8 mL of concentrated HCl an empty Florence flask then add about 400mL of distilled Water This gives a solution of approximately 0.2M HCl. To determine the exact concentration of the HCl in the solution, we will titrate it against a base Na2CO3 whose mass can be accurately measured and whose endpoint is pH=4 Na2CO3(aq) + 2 HCl(aq)  2 NaCl(aq) + H2CO3(aq) Since the endpoint is at pH = 4 we use bromocresol green

Part B: Standardized HCl Solution HCl to Standardize endpoint Erlenmeyer Flask 0.15 g anhydrous Na2CO3 50 mL deionized water 12 drops of bromocresol green indicator

Standardization

Part E: Titrating Borax Samples Re-dissolve the borax in the test tubes you saved from last session Place tubes in here Heat to 55oC When you are ready pour contents into Erlenmeyer Use a plastic pipette and hot water to help dissolve borax Titrate with the HCl from last time … Stirrer and hotplate thermometer

Part E: Titration of Borax HCl to Standardize endpoint Erlenmeyer Flask Contents of the test tube 50 mL deionized water 12 drops of bromocresol green indicator

Calculation of Ksp

Getting ΔH° and ΔS° Plot ln(Ksp) vs 1/T where T is in Kelvin ΔH° = -slope x 8.314 J/mol/K ΔS° = intercept x 8.314 J/mol/K