Answer:
See answer below
Explanation:
To do this, you need to write down the chemical reaction giving place here.
As this is to explain the thermodynamics of the borax-borate reaction, the general reaction is as follow:
Na₂B₄O₅(OH)₄.8H₂O(s) <---------> 2Na⁺(aq) + B₄O₅(OH)₄²⁻(aq) + 8H₂O(l)
Where:
Na₂B₄O₅(OH)₄.8H₂O(s) = Borax
B₄O₅(OH)₄²⁻(aq) = Borate ion
Now, in order to calculate the concentration of borate, this compound undergoes a titration with HCl. The reaction that takes place here is:
B₄O₅(OH)₄²⁻(aq) + 2HCl + 3H₂O <---------> 4H₃BO₃(aq) + 2Cl⁻(aq)
According to this reaction, it takes 2 moles of HCl to completely react with the borate ion, therefore, the expression to calculate the concentration will be:
2 nHCl = nB₄O₅(OH)₄²⁻
2M₁V₁ = M₂V₂
Replacing the data of concentration and volume of both compounds we have:
2 * 0.1006 * 23.33 = 10M₂
M₂ = 2 * 0.1006 * 23.33 / 10
M₂ = 0.4693 M
This is the concentration of the borate. Now, to calculate the Ksp we need to write the equilibrium reaction taking place with the borax:
Na₂B₄O₅(OH)₄.8H₂O(s) <---------> 2Na⁺(aq) + B₄O₅(OH)₄²⁻(aq) + 8H₂O(l)
Ksp = [B₄O₅(OH)₄²⁻] [Na⁺]²
As we already have the concentration of borax, we can also know the concentration of sodium. If we call concentration as "s" (Stands for solubility), and rewrite the expression of Ksp:
Ksp = s * (2s)²
Finally, replacing the value of the concentration we have:
Ksp = (0.4693) (2*0.4693)²
Ksp = 0.4693 * 0.881
Ksp = 0.4134
Hope this helps
