Thermodynamics of the dissolution of borax calculations

HOW CAN ΔHº, ΔGº, AND ΔSº BE DETERMINED FOR A REACTION? INTRODUCTION In the 1960s, there was a TV show, hosted by Ronald Reagan, that was sponsored by “20-Mule Team Borax” (see https://www.youtube.com/watch?v=qC0H6mPyfZA). The product is still being sold (see https://www.20muleteamlaundry.com/). It is added to laundry detergent to increase its ability to clean dirty clothes. The name of the product comes from the fact that one of the largest deposits of borax in the world was discovered in Death Valley in the late 1800s. From 1883 to 1889 there was no way to ship ore from this borax mine to the nearest railway in Mojave, except by mule train across 165 miles of desert. It took 16 days, 18 mules and 2 horses to carry 37.5 tons of ore and water across this desert. The formula for borax is often written as Na2B4O7 • 10H2O, but this is slightly misleading. Two of the water molecules are part of the molecular formula of the B4O5(OH)42- ion that lies at the heart of this compound, and the other eight water molecules are trapped in holes in the crystal. Thus, we might write the formula for borax as Na2B4O5(OH)4 • 8H2O and illustrate the molecular structure of the B4O5(OH)42- ion as follows: THE SOLUBILITY PRODUCT EQUILIBRIUM FOR BORAX IN WATER Borax is sparingly soluble in water, dissolving to form the Na+ and B4O5(OH)42- ions, and releasing the eight hydrated water molecules into the solution. Na2B4O5(OH)4 • 8H2O(s) ⇌ 2Na+(aq) + B4O5(OH)42-(aq) + 8H2O(l) 1 The solubility product equilibrium constant expression for borax would be written as follows: Ksp = [Na+]2[B4O5(OH)42-] We don’t have to measure the concentrations of both the Na+ and B4O5(OH)42- ions at equilibrium to determine the value of Ksp for this compound. We can start with the relationship between the concentrations of these ions at equilibrium: [Na+] = 2 [B4O5(OH)42-] Substituting this equality into the expression that defines Ksp for borax gives the following result: Ksp = (2 [B4O5(OH)42-])2[B4O5(OH)42-] = 4 [B4O5(OH)42-]3 In this experiment, the equilibrium concentration of the B4O5(OH)42- ion in a saturated solution of borax in water will be determined by titrating the solution with a standardized solution of hydrochloric acid. B4O5(OH)42-(aq) + 2HCl(aq) + 3H2O(l) → 4B(OH)3(aq) + 2 Cl-(aq) Note that two moles of HCl are consumed in this reaction for each mole of B4O5(OH)42- formed when borax dissolves in water. THE THERMODYNAMIC RELATIONSHIPS The standard free energy of reaction (ΔGº) for the reaction that occurs when borax dissolves in water is related to the solubility product equilibrium constant (Ksp) for this reaction by the following equation: Eq. 1 The standard enthalpy change (ΔHº) and standard entropy change (ΔSº) are related to the standard free energy of reaction (ΔGº) as follows: Eq. 2 2 Combining these equations and then solving for the natural logarithm of the solubility product constant gives the following equation: But this can be turned into the classic “y = mx + b” form of the equation for a straight line: A plot of “ln Ksp” on the y-axis versus “1/T” on the x-axis should therefore give a straight line with a slope of “-ΔHº/R” and a y-intercept of “ΔSº/R”. SAFETY Wear your SAFETY GOGGLES. If you spill any acid on your skin or clothing, wash it off immediately with copious amounts of running water. PROCEDURE Preparation of Test Tubes Obtain a test tube rack and 10 test tubes. Using a burette, add exactly 5.0 mL of water to each of the 10 test tubes. Mark the level of the water on each test tube with a marker or grease pencil. Label two test tubes as “45 °C”, two as “35 °C”, two as “25 °C”, two as “15 °C”, and two as “5 °C”. Empty the test tubes and allow the water to drain thoroughly. Preparation of the Saturated Borax Solution Warm a mixture of about 30 g of borax and 150 mL of water in a 250-mL beaker to at least 45 °C, but no higher than 50 °C. It is not necessary to record the exact mass of the borax that is added to water. It is, however, important that the borax solution be saturated. Therefore, if all of the solid dissolves, add a little more borax until excess solid is present and the solution is truly saturated. 3 NOTE THAT STIRRING RODS COST LESS THAN A DOLLAR EACH, BUT THERMOMETERS COST $10. The TAs WILL THEREFORE QUESTION THE INTELLIGENCE OF ANYONE SEEN USING A THERMOMETER TO STIR THIS SOLUTION! Sampling the Saturated Borax Solution Note: The main source of error in this experiment is the measurement of the temperature at the moment of sampling.