Exp.3 Determination of the Thermodynamic functions for the Borax Solution Theory: The relationship between Gibb s energy (ΔG), Enthalpy (ΔH), Entropy (ΔS) and the equilibrium constant (K) for a chemical reaction at a specific temperature (T), is shown in equation (1) below. The Gas Constant, R, is equal to 8.314 J/mol K. ΔG = R T ln K = ΔH TΔS... (1) ΔG (Std. Gibb s Energy Change), ΔH o (Std. Enthalpy Change) and ΔS o (Std. Entropy Change), ΔH o is a measure of the degree of change in the intermolecular forces and the bond energy for the molecules involved (Exothermic and Endothermic reactions). ΔS is a measure of the change in randomness in the system. ΔG o is negative for any reaction for which ΔH o is negative and ΔS o is positive, therefore conclude that any reaction for which ΔG o is negative should be favorable, or spontaneous. ΔG o < 0 Conversely, ΔG o is positive for any reaction for which ΔH o is positive and ΔS o is negative. Any reaction for which ΔG o is positive is therefore unfavorable. ΔG o > 0 11
A process at constant temperature and pressure will be spontaneous in the direction in which Gibbs energy decreases ( ΔG ). When equation (1) is rearranged to eliminate ΔG. log K = ΔH / 2.303RT + ΔS / 2.303R...(2) The solubility of a salt is dependent on the temperature of the solution. When equilibrium is established in a saturated solution at a specific temperature, the rate of formation of ions in solution is equal to the rate of deposition of solid. The equilibrium constant for the dissolution of a solid in a solvent is called the "solubility product constant" (Ksp). It is equal to the product of the concentration of ions in solution. Since the concentration of ions can change with temperature, Ksp is temperature dependent. Sodium tetraborate decahydrate ("borax") dissociates in water to form sodium and borate ions and water molecules: Na 2 B 4 O 7.10 H 2 O(s) 2Na + (aq) + B 4 O 5 (OH) 4 2- (aq) + 8H 2 O(l)...(3) And the solubility product (equilibrium) constant, Ksp, is: Ksp = [Na + ] 2 [B 4 O 5 (OH) 2-4 ]...(4) Note that two sodium ions are produced for each borate ion (B 4 O 5 (OH) 2-4 ) in the reaction. [Na + ] = 2 [B 4 O 5 (OH) 2-4 ]...(5) The equilibrium constant can now be expressed in terms of borate ion concentration alone by substituting the equality from (5) into equation (4), 12
and can be calculated when the borate ion concentration at equilibrium is determined. Ksp = 4 [B 4 O 5 (OH) 2-4 ] 3...(6) The borate ion is a base, its concentration can be determined by a simple acid-base titration. The endpoint is signaled by the color change of bromocresol green or Methyl orange indicator. 2- B 4 O 5 (OH) 4 + 2H + + 3H 2 O 4B(OH) 3...(7) Also If the Equilibrium Constant (Ksp) determined by two different temperatures, T 1 and T 2, apply van't Hoff's formulation for the determine the ΔH for this reaction : ln (Ksp 2 / Ksp 1 ) = - (ΔH / R) x (1/T 2-1/T 1 )...(8) Chemicals and tools: 1. Hydrochloric acid (HCl). 2. Distill water. 3. Sodium tetraborate decahydrate "borax" Na 2 B 4 O 7.10 H 2 O 4. Bromocresol green or Methyl orange indicator. 5. Conical flask. 6. Water bath. 7. Burette. 8. Pipette. 9. Thermometer. 13
10. Stirrer. 11. Volumetric flask. Procedure: 1- Prepare 0.5 N in volume 250 ml from HCl solutions in Volumetric flask and add.to burette. 2- In a 250 ml beaker, dissolve 25g of borax in 50mL of DI water. Heat with stirring to 60 C. 3- If all solid dissolves, add a tittle more borax to the solution until a tiny amount of excess solid is present and the solution is COMPLETELY SATURATED. 4- Transfer 10 ml of borax solution to conical flask be very careful not to transfer any of the solid borax from the beaker to the conical flask and record the exact temperature of the solution. 5- Add 2-3 d of bromocresol green indicator to the conical flask. 6- Add the standard HCl from burette till the end point. 7- Repeat the steps above cooling the solution to 50 and 40 C o. 14
Calculations: Titration Final burette reading Initial burette reading Volume of acid used Temperature 40C o 50C o 60C o 1- Calculate [B 4 O 5 (OH) 4 2- ] unknown at different temperatures. N 1 * V 1 HCl = N 2 * V 2 [B 4 O 5 (OH) 4 2- ] 2- Calculate the Ksp at different temperatures. 3- Draw the equation to calculate ΔH : log ksp = ΔH / 2.303RT + constant Temp(K) 1/T(K -1 ) [B 4 O 5 (OH) 4 2- ] Log ΔH o ΔG o ΔS o Ksp Kj mol -1 KJ mol 1- J mol -1 k -1 Log Ksp Slope = ΔH /2.303R Intercept ΔS / 2.303R 1/T If the System Exothermic (Spontaneous Reactions) 15