Brainteaser... [resolved] <- that's something you don't see much here :D

[arsmakman]

Hello all,

I have a problem I can't quite figure out.

I have to containers: Container A filled with water and containter B filled with acid.



The two containers are connected with a small pipe filled with water so the height of the liquids remains the same.

Then slowly the water out of container A will be drained so the acid out of container B will start flowing into A (as they are connected by the pipe) increasing the molarity slowly. The contents of container A are stirred constantly, so the acid that enters A will be distributed over the fluid equally and (almost) instantly.

Now, will the last drop of C be 100% acid or 50/50 water/acid?

[NoteMe]

I would have guessed 50/50...but I have no idea...too long since I had questions like this at school....put it up as a equation over time....I can't remember what those equations with f(x)' and f(x) are called in English, but you should be able to solve it this way...

[Xcoder]

100% acid

[arsmakman]

Originally posted by Xcoder
100% acid

Why?

[Cander]

50% Cotton
50% Polyester

Seems like a trick question

[arsmakman]

Originally posted by Cander
50% Cotton
50% Polyester

Seems like a trick question

Yeah, but I actually need this for a report. So I'm probably boned...

[Xcoder]

Originally posted by arsmakman
Why?

I believe that its because of the remaining acid left on the connecting pipe

[alkatran]

A= water concentration
B = acid concentration

A(0) = 1, A(x) = A(x-1)*.99 = .99^x
B(0) = 0, B(x) = B(x-1)*.99 + .01

A converges towards 0
B converges towards 1

Take a guess.

[arsmakman]

Originally posted by alkatran
A= water concentration
B = acid concentration

A(0) = 1, A(x) = A(x-1)*.99 = .99^x
B(0) = 0, B(x) = B(x-1)*.99 + .01

A converges towards 0
B converges towards 1

Take a guess.

Thank you! It's all clear to me now

[dglienna]

If the water and acid mix, then the last drop will be a mixture
if not, then the last drop will be acid.


i think

[alkatran]

Originally posted by arsmakman
Thank you! It's all clear to me now

Actually it isn't.

It won't converge exactly the way I described because you have a limited amount of acid. Let's start with 100 'drops' in each

Water: 100 * .99^100 = 36.6
translates: start with 100 divisions and you end with 36.6 left

200 * .99^200 = 26.7
translates: start with 200 divisions and you end with 26.7 left

500 * .99^500 = 3.2

1000 000 * .99^(100 000) = 3.3*10^(-437) VERY low


So it still converges I guess.

[arsmakman]

Originally posted by dglienna
If the water and acid mix, then the last drop will be a mixture
if not, then the last drop will be acid.


i think

I think I can explain it in a totally different, yet understandable way:

If you'd take both A and B and mix them together instantly there would be 50/50 acid/water.

But that's not what you do, you start by getting rid of plain water, so the total amount of acid will be higher that the total amount of water in A and B. And as the progress continues slowly the extract (C) will contain more and more acid from B.

So, because you started by extracting plain water and the concentration of B slowly increases, in the end the mixture will be just acid. (Although 100% acid will only be neared, never reached)

To put in other words: the percentage of A in C will start at 100 and drop to 0, similairily the percentage of B in C will start at 0 and rise to 100.

[alkatran]

or more simply: .5 * .99 <> .5

0*.99 = 0
1*.99+.01 = 1

All fits

[alkatran]

Consider a 3 part one:

You start with 100% water. You dump to 66% and add 33% acid

Dump 33%, so 66*.66 = 43.56%

Oh wait, that's below 50, and we aren't even done.

[demotivater]

What are you? Some kind of math magician?

[arsmakman]

Originally posted by alkatran
Actually it isn't ... So it still converges I guess.

Indeed. And in reality this works on molecular scale, which means that there are practically indefinite 'drops' and the concentration of water in the end will be practically zero.

Thanks!

[dglienna]

so it *IS* a mixture, just highly concentrated. good guess.

[arsmakman]

Thanks all (especially alkatran), but I'm gonna catch some z's now.

It's a quarter to one here and tomorrow I have a six hours of college starting at 8.30. *groan*

[alkatran]

Originally posted by demotivater
What are you? Some kind of math magician?

Irony, we meet again! (math + magician, aha)

This is pre-cal stuff. If not grade 12 math.