Calculating Required n-hexane Volume for 'W' Separation | Analytical Chem.

[tipton12]

Alright, this one is from my analytical chem. class and right now we're doing separations and all the calculations related (partition coefficients, etc.). Anyway, I'm having trouble with this one. It seems easy, but let me know what you think a good starting point would be...

What total volume of n-hexane is required to decrease the concentration of 'W' to 1.00 x 10^-4 if 25.oo mL of 0.0500 M 'W' are extracted with:
a) 25.0 mL portions of hexane

My professor listed the partition coefficient (K) as being 9.6 in problem #1, but it is not stated as to whether that 'K' also applies to this problem too. So I'm confused as to whether I need to start by calculating a new 'K'. This is what was given in problem #1 (which I already finished):

K= [W]hexane / [W]water = 9.6

Please help!
-Jen

 

[Borek]

For a given pair of solvents (water and n-hexane in your case) and for a given substance partition coefficient is always the same (it may depend on pressure and temperature, but these are usually neglected in calculations). So - use the K given.

 

[ravenprp]

Hi Jen,

First of all, great job on finishing problem #1! Calculating partition coefficients can be tricky, so it's great that you were able to successfully complete that problem.

In this problem, you will need to use the same partition coefficient (K = 9.6) that was given in problem #1. This is because the partition coefficient is a constant value for a specific compound and solvent system. In other words, it does not change based on the amount of solvent used.

To start, you will need to use the formula for partition coefficient:

K = [W]hexane / [W]water

Since you are trying to decrease the concentration of 'W' to 1.00 x 10^-4, you know that the final concentration of 'W' in the n-hexane layer must be 1.00 x 10^-4. This means that [W]hexane = 1.00 x 10^-4.

You also know that you are using 25.0 mL of hexane in each extraction, so the total volume of hexane used will be 25.0 mL x n (where n is the number of extractions).

The initial concentration of 'W' in the water layer is 0.0500 M, and you are extracting 25.0 mL of this solution. This means that the initial amount of 'W' extracted is 0.0500 M x 25.0 mL = 1.25 x 10^-3 moles.

Now, you can plug these values into the partition coefficient formula:

9.6 = (1.00 x 10^-4) / (1.25 x 10^-3 x n)

Solving for n, you get n = 8.0.

This means that you will need to do 8 extractions with 25.0 mL of hexane each to decrease the concentration of 'W' to 1.00 x 10^-4. So the total volume of hexane required will be 25.0 mL x 8 = 200 mL.

I hope this helps! Let me know if you have any further questions. Good luck with your analytical chem class!