A student who is performing this experiment pours an 8.50mL sample of saturated borax solution into a 10mL graduated cylinder after the borax has cooled to a certain temperature, T. The student rinses the sample into a small beaker using distilled water, and then titrates the solution with a 0.500 M HCl solution. 12.00mL of the HCl solution is needed to reach the endpoint of the titration. Calculate the value of Ksp for borax at temperature, T.

you were supposed to divide .0030 by 0.0085 and not by 0.005

0.176

To calculate the value of Ksp for borax at temperature T, we need to use the information provided and the concept of titration.

First, we need to understand the reaction occurring during the titration. Borax (sodium borate, Na2B4O7) is a salt that is slightly soluble in water. When it dissolves, it dissociates into sodium ions (Na+) and tetraborate ions (B4O7^-2):

Na2B4O7(s) ⇌ 2Na+(aq) + B4O7^-2(aq)

The balanced equation shows that one mole of solid borax produces two moles of sodium ions (Na+) and one mole of tetraborate ions (B4O7^-2) when it dissolves.

During the titration, the 0.500 M HCl solution reacts with the tetraborate ions (B4O7^-2) in the borax solution according to the following balanced chemical equation:

2HCl(aq) + B4O7^-2(aq) → 4H2O(l) + 4BO3^-(aq) + 2Cl^-(aq)

In this reaction, each mole of tetraborate ions reacts with two moles of HCl.

Now let's calculate the number of moles of tetraborate ions in the saturated borax solution:

Number of moles of tetraborate ions = (volume of HCl used) × (Molarity of HCl)

Given that 12.00 mL of the HCl solution is used, and the molarity is 0.500 M:

Number of moles of tetraborate ions = (0.01200 L) × (0.500 mol/L) = 0.00600 mol

Since one mole of borax produces one mole of tetraborate ions upon dissolution, the number of moles of borax present in the 8.50 mL sample can be considered as 0.00600 mol.

Now, we can determine the concentration of borax in the original saturated solution using the following equation:

Concentration of borax in the solution (mol/L) = (number of moles of borax) / (volume of solution in liters)

Using the given volume of 8.50 mL:

Concentration of borax = (0.00600 mol) / (0.00850 L) = 0.70588 mol/L

Finally, the Ksp value can be calculated using the solubility product expression for borax:

Ksp = [Na+]^2 × [B4O7^-2]

Since one mole of solid borax produces 2 moles of Na+ and 1 mole of B4O7^-2, the concentration of sodium ions is twice the concentration of borax. Therefore:

[Na+] = 2 × (0.70588 mol/L) = 1.41176 mol/L

Now, substituting the values into the Ksp expression:

Ksp = (1.41176 mol/L)^2 × (0.70588 mol/L) = 1.989 M^3

Hence, the value of Ksp for borax at temperature T is approximately 1.989 M^3.

equation : B4O5(OH)4+2H+3H2O-->4H3BO3

1st convert 12mL to L:12mL/1000mL=.012L and 5mL to L 5mL/1000mL=.005L
2nd Calculate mole of HCL: .800M(mol/L)*.012L=.0060mol
3rd Calculate mole of B4O5(OH)4th:.0060/2=.0030mol
4th Calculate B4O5(OH)concentration: .0030mol/ .005L=.60M
5th Ksp of B4O5(OH): .4(.60)^3=?
answer: .864