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 acidNa2B4O7·10H2O + 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 softenerCa2+ (aq) + Na2B4O7 (aq) → CaB4O7 (s)↓ + 2 Na+ (aq)

Mg2+ (aq) + Na2B4O7 (aq) → MgB4O7 (s)↓ + 2 Na+ (aq)

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° ? • 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 now 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

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

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 to about 400mL of distilled Water in a 500mL Erlenmeyer Flask. Stir well. 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

Standardized HCl Solution

HCl to Standardize

Erlenmeyer Flask

0.15 g anhydrous Na2CO3

50 mL deionized water12 drops of bromocresol green indicator

endpoint

Standardization

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