Uni Question- Want it answered out of curiosity.

If you poured a bottle of water into the sea and then collected a bottle of water from the same spot a year later how many atoms of the original water bottle will be in the newly collected water bottle?

Reply 1

smd4std

depends on the size of the bottle and volume of water that you collect

Reply 2

denjan

OP

You get to assume everything. If you had an average 500ml bottle of water how would you work it out? I thought it was pretty impossible to complete this question. My friend was asked this question in an interview. Nobody could answer it at school.

Reply 3

AdamskiUK

13

Well first of all, you'd have to work out how you'd recognise them to be the same *molecules* (water) that you initially put in. You could add a radioactive marker, but it's pretty difficult to do with water. So you could use a permanent dye which remains dissolved in the molecule of water regardless of temperature or any other external factor. You would then collect water from the same spot, use a spectrometer to identify the wavelength of light reflected by the dye (let's say RED, so up towards 650nm for a wavelength). I don't even know if you can get spectrometers to do this, but it seems relatively plausible. Again, you could try to dissolve a very specific and rare radioactive material in the water which could be detected with a spectrometer specific to radiation, but I don't know if that's possible.

It's how I'd try to approach the question.

Reply 4

Stonebridge

13

This is a "use your common sense and get an order of magnitude" question.
Assume the water you tip in disperses and is spread out throughout the oceans after one year.
It just remains to work out, to an order of magnitude, the ratio (%) of the volume of water in the bottle to the volume of all the oceans on earth.
That will be the % of original molecules in the bottle.
The question is then one of estimating the volume of all the water in the Earth's oceans.
Over to you...
I did say this is about common sense and also involves having a feeling for numbers.

Reply 5

Scorlibran

13

You would have to make a few assumptions, I'd assume that it's a 500 ml bottle, the molecules distribute evenly throughout the oceans and also assume it is pure water with density

1000\ \frac{g}{litre}

. You would also have to assume that all water molecules stayed in the oceans and didn't partake in the water cycle or react with anything.

The volume of the world's oceans is approximately

1.37\ billion\ km^3

(http://hypertextbook.com/facts/2001/SyedQadri.shtml), convert this to litres results in

1.37 \times 10^{21} \ litres

.

So divide the volume of the bottle (

0.5\ litres

) by the volume of the oceans (

1.37 \times 10^{21}\ litres

) results in the fraction of water molecules in the ocean that were in the original bottle.

\frac{0.5}{1.37 \times 10^{21}} = 3.65 \times 10^{-22}

So to work out the number of water molecules in the bottle we need to find the number of water molecules in

500\ ml

of water.

With the assumption of the density of water being constant at

1000\ \frac{g}{litre}

, this means

500\ ml

of water will weigh

500\ g

.

Divide

500\ g

by the molecular mass of a water molecule (

18\ \frac{g}{mol}

) results in the moles of water molecules in the bottle.

\frac{500\ g}{18\ \frac{g}{mol}} = 27.8\ mol

Multiply the moles of water by the number of molecules per mole (Avagadro's constant =

6.022 \times 10^{23}

) to get the number of water molecules in the bottle.

27.8 \times (6.02 \times 10^{23}) = 1.67 \times 10^{25}

Finally multiply the number of water molecules in the bottle (

1.67 \times 10^{25}

) by the fraction of them that are from the original bottle (

3.65 \times 10^{-22}

).

(1.67 \times 10^{25}) \times (3.65 \times 10^{-22}) = 6105

So approximately

6100

water molecules that were in the original bottle would be in the new one. The actual number would probably be less due to water being stored elsewhere (rivers/animals/in the atmosphere) or reacting.

These sort of questions are meant to analyse how you think and break down problems.

(edited 10 years ago)

Reply 6

Stonebridge

13

If this question was asked at an interview, as stated by the OP, then I doubt you would have had the opportunity to look up the volume of the oceans on Wiki.
So back over to you...

Original post by denjan

If you poured a bottle of water into the sea and then collected a bottle of water from the same spot a year later how many atoms of the original water bottle will be in the newly collected water bottle?

I think you need to know that 2/3 of the Earth's surface is covered by the sea and that the average circumference of the earth is 40,000 km? Dunno about depth though

Reply 9

Scorlibran

13

Original post by Stonebridge

If this question was asked at an interview, as stated by the OP, then I doubt you would have had the opportunity to look up the volume of the oceans on Wiki.
So back over to you...

I'd probably just explain my method. If they insisted on an actual figure, I'd use estimates.

Reply 10

piguy

8

You shouldn't have to look up any figures (since it's an interview!) to make your estimation. Here's how I would do it:

1) Since I know nothing about how the oceans and currents flow in the world, I'll assume that the water I pour out disperses evenly throughout the world, so I'm looking for ratio between molecules I pour out to the number in the world...

2) First how much do I pour out?
Suppose I have a 500ml bottle. The density of water is about 1g/cm^3, and 1ml = 1cm^3, so I have 500g of water.
RFM of water is 18g/mol, so mol = mass/RFM = 500/18 ~= 500/20 = 25 mol of water.

3) Now how much water is there in the world's oceans?
About 2/3 of the world's surface is water (~70%).
We can work out the Surface Area of the earth using the radius (which you should definitely know from Physics is 6x10^6m).

SA = 4pi r^2
= 4 x 3.14 x 36 x 10^12 ~= 10 x 40 x 10^12
= 4 x 10^14 m^2
70% of this is just under 3 x 10^14.

Assume average depth of sea is 1-2km = 1-2 x 10^3, so total volume of water is about 5 x 10^17 m^3

4) Now we could go on and work out moles of water, though it's easier to just look at ratios of volumes:
for bottle 500ml = 500cm^3 = 500 x 10^-6 m^3 = 5 x 10-4 m^3.
for ocean it's 5 x 10^17 m^3
So the ratio is 1 x 10^-21

5) So for every 1 molecule in the bottle, there's 10^21 in the ocean!
Now we originally worked out there's about 25 moles of water in the bottle = 25 x 6 x 10^23 ~= 1 x 10^25 molecules.

Thus there are about 10,000 molecules of the original water!
Notice that's the closest order of magnitude for Scorlibran's answer, yet it required no looking up and the numbers were rounded such that it's easy to do them in your head.

(edited 10 years ago)

Reply 11

2710

18

Original post by AdamskiUK

Well first of all, you'd have to work out how you'd recognise them to be the same *molecules* (water) that you initially put in. You could add a radioactive marker, but it's pretty difficult to do with water. So you could use a permanent dye which remains dissolved in the molecule of water regardless of temperature or any other external factor. You would then collect water from the same spot, use a spectrometer to identify the wavelength of light reflected by the dye (let's say RED, so up towards 650nm for a wavelength). I don't even know if you can get spectrometers to do this, but it seems relatively plausible. Again, you could try to dissolve a very specific and rare radioactive material in the water which could be detected with a spectrometer specific to radiation, but I don't know if that's possible.

It's how I'd try to approach the question.

The question is not asking how you will track the water.

Posted from TSR Mobile

Reply 12

AdamskiUK

13

Original post by 2710

The question is not asking how you will track the water.

Posted from TSR Mobile

Indeed, but how on Earth are you meant to know if they're the same atoms if you can't track them?

Blind statistics is no way to do an experiment. Not a conclusive one, anyway.

Reply 13

Stonebridge

13

Original post by AdamskiUK

Indeed, but how on Earth are you meant to know if they're the same atoms if you can't track them?

Blind statistics is no way to do an experiment. Not a conclusive one, anyway.

It isn't an experiment.
The question (at interview) is designed to test how you think and how you solve a problem.
An important quality for any physicist is to have a feeling for number and the order of magnitude of quantities. This question appears in a number of guises. One of the other variations is:
If you breathe in, how many air molecules in your lungs came from the last breath of Julius Caesar?

Reply 14

AdamskiUK

13

Original post by Stonebridge

It isn't an experiment.
The question (at interview) is designed to test how you think and how you solve a problem.
An important quality for any physicist is to have a feeling for number and the order of magnitude of quantities. This question appears in a number of guises. One of the other variations is:
If you breathe in, how many air molecules in your lungs came from the last breath of Julius Caesar?

Lmao, that one's brilliant. I understand what it's attempting to assess in a candidate, too.

Still, what's the point in answering it if you could be *entirely* wrong - even if you went about it in the best way possible? To answer the actual question, you would have to know which molecule is which, not just hope that they followed the bounds of statistics.

Incidentally, at interview, would they provide you with key statistics such as the volume of all the water in the Earth's oceans?

Reply 15

2710

18

Original post by AdamskiUK

Lmao, that one's brilliant. I understand what it's attempting to assess in a candidate, too.

Still, what's the point in answering it if you could be *entirely* wrong - even if you went about it in the best way possible? To answer the actual question, you would have to know which molecule is which, not just hope that they followed the bounds of statistics.

Incidentally, at interview, would they provide you with key statistics such as the volume of all the water in the Earth's oceans?

What's the point you ask? Most likely the candidate WILL be completely wrong but its not about the final answer. Its the method and approach in solving the question which the examiners mark you on. It shows that you can at least have a stab at any question no matter how ridiculous, so in real life situations it shows you are competent and can think logically and deductively.

I highly doubt they will give you exact information of any sort.

Posted from TSR Mobile

Uni Question- Want it answered out of curiosity.

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