Container with a 2 part mixture.

[Averagesupernova]

My dad and I were having a discussion about filling a container with a 2 part mixture (50/50), draining off X amount of it and then refilling it with only 1 part of the mixture. For example:
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Suppose we have a container that holds 10 gallons. We fill it with 5 gallons of water and 5 gallons of ethyline-glycol anti-freeze. (Yes, this discussion was born out of a real world scenario.) Now suppose we drain off 2 gallons of this mixture, add 2 gallons of water and allow it to mix completely. Then, we drain off 2 gallons of this mixture and add 2 gallons of the pure anti-freeze. What is the current mixture in the tank? Is it extra water, extra anti-freeze, or back to 50/50? At first I thought it was one way, then a different way, and when I did a little quick math/logic I determined that it was in fact it was neither of those.
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It's not exactly a brain-teaser so I thought it would be appropriate to post it in GD. I'm curious to know how all of you think. So please post what you would intuitively think the end mix would be without throwing math at the problem, and finally post what you find using math or logic. And please post the computed answer with the appropriate text as to not spoil it for others.
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Incidentally, dad and I didn't agree clear up until the end.

Spoiler

The final mix will be extra anti-freeze. The logic being that the first 2 gallons drained will be 50/50. The second 2 gallons drained is is extra-water. We went through a total of 7 gallons of each with the whole experiment and we know that the 4 gallon mixture outside the tank that we drained is extra-water so the mixture inside the tank has to be extra anti-freeze.

 

[lewdtenant]

I guessed wrong, but here's what I discovered.

Spoiler

30 iterations of the procedure are shown below (in volume):

5 5
6 4
4.8 5.2
5.84 4.16
4.672 5.328
5.7376 4.2624
4.59008 5.40992
5.672064 4.327936
4.5376512 5.4623488
5.63012096 4.36987904
4.504096768 5.495903232
5.603277414 4.396722586
4.482621932 5.517378068
5.586097545 4.413902455
4.468878036 5.531121964
5.575102429 4.424897571
4.460081943 5.539918057
5.568065555 4.431934445
4.454452444 5.545547556
5.563561955 4.436438045
4.450849564 5.549150436
5.560679651 4.439320349
4.448543721 5.551456279
5.558834977 4.441165023
4.447067981 5.552932019
5.557654385 4.442345615
4.446123508 5.553876492
5.556898806 4.443101194
4.445519045 5.554480955
5.556415236 4.443584764

After an infinite amount of iterations, the system will oscillate between (5/9 water, 4/9 antifreeze) and (4/9 water, 5/9 antifreeze) with each successive iteration. For all practical purposes it will show this tendency after about 25 iterations.

 

[Architeuthis Dux]

I would approach this scenario by first identifying the components of the mixture and their properties. In this case, we have water and ethylene-glycol anti-freeze. Water is a polar molecule while ethylene-glycol is a nonpolar molecule. This means that they will not mix evenly and will form layers in the container.

When the container is initially filled with a 50/50 mixture of water and ethylene-glycol, the two liquids will form distinct layers due to their different polarities. When we drain off 2 gallons of this mixture and add 2 gallons of water, we are essentially diluting the ethylene-glycol layer. This will result in a higher concentration of water in the mixture, but it will still be separated into distinct layers.

When we drain off 2 gallons of this diluted mixture and add 2 gallons of pure ethylene-glycol, we are essentially adding more of the nonpolar molecule to the mixture. This will result in a higher concentration of ethylene-glycol in the mixture, but it will still be separated into distinct layers.

Therefore, the current mixture in the tank will not be back to 50/50, but it will also not be extra water or extra ethylene-glycol. It will be a slightly more diluted version of the initial 50/50 mixture, with a higher concentration of water and a lower concentration of ethylene-glycol. The exact proportions of the mixture can be calculated using math or logic, but it will still result in distinct layers due to the polarity of the components.

In conclusion, as a scientist, I would say that the end mixture in the tank will be a diluted version of the initial 50/50 mixture, with a higher concentration of water and a lower concentration of ethylene-glycol, still separated into distinct layers.