Question

I'm trying to find the amount of ethanol in an unkown solution by titration but I'm having trouble calculating it. Molarity of thiosulfate: 0.0806 M, amount of dichromate used: 15 mL

here is what my lab manual says:

The titration is based on the oxidation of ethanol with an oxidizing agent, such as potassium dichromate. Depending on the solution pH and the amount of potassium dichromate added, ethanol can be oxidized to ethanal (acetaldehyde, CH₃CHO) via reaction 1, or to ethanoic acid (acetic acid, CH₃COOH) via reaction 2:

3C₂H₅OH(aq) + Cr₂O₇^2-(aq) + 8H⁺ ? 3CH₃CHO(aq) + 2Cr³⁺(aq) + 7H₂O (1)

3C₂H₅OH(aq) + 2Cr₂O₇^2- (aq) + 16H⁺ ? 3CH₃COOH(aq) + 4Cr³⁺ (aq) + 11H₂O (2)

In order to ensure all ethanol has completely reacted via reaction 2, a known and excess amount of potassium dichromate (let’s call it potassium dichromate total) is added into a sample solution containing ethanol. The amount of unreacted potassium dichromate is then determined by reacting with potassium iodide solution via reaction 3 to form iodine:

Cr₂O₇^2- (aq) + 14H⁺ + 6I^-(aq) ? 2Cr³⁺ (aq) + 7H₂O(l) + 3I₂ (aq) (3)

From the reaction 3, we know that 1 mole of dichromate ions can produce 3 moles of I₂. Therefore, we just need to determine how much moles of I₂ is produced in reaction 3, then, we can get the moles of unreacted potassium dichromate. Subtracting the moles of unreacted potassium dichromate from the moles of potassium dichromate total gives the moles of potassium dichromate that have reacted with ethanol. Then, from the stoichiometry of reaction 2, one should be able to know how much ethanol is in the test solution.

How to know the moles of I₂ produced in reaction 3? The I₂ is titrated with sodium thiosulfate (Na₂S₂O₃) via the following reaction 4:

I₂(aq) + 2S₂O₃^2-(aq) ? 2I^-(aq) + S₄O₆^2-(aq) (4)

Experimental data: For the standardization of thiosulfate it took 31.7 mL of thiosulfate to reach the end point, for the unknown solution, it took 23.85 mL of thiosulfate to reach the endpoint. How do I use these numbers to find the amount of ethanol in the unknown solution?