# The Naked Scientists Forum

### Author Topic: How many water molecules are in a cup of water??  (Read 47276 times)

#### Simulated

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##### How many water molecules are in a cup of water??
« on: 17/01/2008 00:07:34 »
Gotta be huge don't it?

#### another_someone

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##### How many water molecules are in a cup of water??
« Reply #1 on: 17/01/2008 00:46:20 »
Water has a molecular weight of 18 (with some approximation), which gives it a molar weight of 18 (i.e. that 18 grams of water contains approximately 6.022 x 1023 molecules).

The density of water is 1 gram per cc, so 1 mole of water takes 18cc of volume.

1 cup is approximately 250ml (i.e. 250cc) - so 1 cup will contain approximately 13.89 moles of water, which will contain approximately 8.36 x 1024 molecules of water.

#### Simulated

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##### How many water molecules are in a cup of water??
« Reply #2 on: 17/01/2008 01:17:16 »
Thanks George. See I woudln't have got that at all. We skipped over Molar stuff. THanks again

#### Karen W.

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##### How many water molecules are in a cup of water??
« Reply #3 on: 17/01/2008 10:18:06 »
George, What unit of measure equals a mole??? I have never heard that before???

#### another_someone

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##### How many water molecules are in a cup of water??
« Reply #4 on: 17/01/2008 11:18:38 »
A mole is the molecular weight measured in grams.

Hence my comment that water has a molecular weight of approximately 18, and so 1 mole of water is 18 grams.

Oxygen (common diatomic oxygen molecules) has a molecular weight of around 32, so for oxygen 1 mole is 32 grams.

So you can see, since the weight of 1 mole is proportional to the molecular weight of what you are measuring, one mole of any substance (whatever it may be) must contain the same number of molecules.  The number of molecules in a mole is a number known as Avogadro's number, and is approximately 6.022 x 1023.

#### lightarrow

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##### How many water molecules are in a cup of water??
« Reply #5 on: 17/01/2008 14:04:19 »
Gotta be huge don't it?

More water molecules in a cup of water than cups of water in all the oceans...

(Estimated mass of water in all the oceans ~ 1.35*1021 kg, according wikipedia: http://en.wikipedia.org/wiki/Earth
--> water mass of the oceans/water mass in a cup = 1.35*1021 kg/0.25 kg = 5.4*1021 cups of water in all the oceans, against 8.36*1024 water molecules in a cup of water, see George's computation).
« Last Edit: 17/01/2008 14:24:27 by lightarrow »

#### lyner

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##### How many water molecules are in a cup of water??
« Reply #6 on: 17/01/2008 19:20:38 »
George, What unit of measure equals a mole??? I have never heard that before???
The mole was a brilliant concept / invention.
It works because, in a chemical reaction, the atoms of each element all have the same mass.  Their masses are integral numbers of proton (or neutron) mass.
Now a single atom of Oxygen has the mass of 16 atoms of Hydrogen.
When combined with two Hydrogen atoms, the Water molecule ( H2O will have a mass of 16+1+1 = 18.
That's obvious but you can't deal with individual molecules.  But, if you take 16grams of Oxygen and 2grams of Hydrogen, they will react to produce exactly 18grams of water with nothing left over. This is if you take the reaction to completion.
It's like taking boxes of leggo components and ending up with another box full of completed models, with no bits left over.
This allows you to make pure substances by reacting known amounts of the component atoms, working in grams. Chemical factories deal in massive tanks of ingredients and use 'whole tanks' in their processes.

The mole idea also allows you to work out what a substance consists of by weighing the amounts of some known substances which react with the unknown one - as long as you take the process to completion. One example of when  you can tell if the reaction has been taken to completion is when you neutralise a base with an acid.
They were starting to use these ideas  at the time of Humphrey Davey and Lavoisier! Brilliant, don't you think?

There is a teensy problem because not all atoms of all elements are identical in mass; different isotopes may occur with one neutron more or less than others (chemically the same but different atomic masses); naturally occurring Chlorine is a mixture of isotopes and its average atomic mass is 35.5. To deal with this you work with this average 'molar' mass and you get good answers.

I've always said that Chemists need to get things in proportion!
« Last Edit: 17/01/2008 19:22:25 by sophiecentaur »

#### Simulated

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##### How many water molecules are in a cup of water??
« Reply #7 on: 17/01/2008 21:19:32 »
I heard that Lightarrow. Thanks.

What's the molar mass of carbon? It was just on our exam today and we didn't go over it at all and I was like wow. And I just guessed 1 since carbon is one AMU

#### Karen W.

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##### How many water molecules are in a cup of water??
« Reply #8 on: 17/01/2008 22:04:32 »
Water has a molecular weight of 18 (with some approximation), which gives it a molar weight of 18 (i.e. that 18 grams of water contains approximately 6.022 x 1023 molecules).

The density of water is 1 gram per cc, so 1 mole of water takes 18cc of volume.

1 cup is approximately 250ml (i.e. 250cc) - so 1 cup will contain approximately 13.89 moles of water, which will contain approximately 8.36 x 1024 molecules of water.

Thanks George! I did not get it the first time round.. thanks for repeating it with the explanation.. I am not sure why I missed it the first time...LOL I read it Honestly I did! I am having some difficulties in the comprehension department! Sorry! Thanks so much..

#### Karen W.

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##### How many water molecules are in a cup of water??
« Reply #9 on: 17/01/2008 22:11:42 »
George, What unit of measure equals a mole??? I have never heard that before???
The mole was a brilliant concept / invention.
It works because, in a chemical reaction, the atoms of each element all have the same mass.  Their masses are integral numbers of proton (or neutron) mass.
Now a single atom of Oxygen has the mass of 16 atoms of Hydrogen.
When combined with two Hydrogen atoms, the Water molecule ( H2O will have a mass of 16+1+1 = 18.
That's obvious but you can't deal with individual molecules.  But, if you take 16grams of Oxygen and 2grams of Hydrogen, they will react to produce exactly 18grams of water with nothing left over. This is if you take the reaction to completion.
It's like taking boxes of leggo components and ending up with another box full of completed models, with no bits left over.
This allows you to make pure substances by reacting known amounts of the component atoms, working in grams. Chemical factories deal in massive tanks of ingredients and use 'whole tanks' in their processes.

The mole idea also allows you to work out what a substance consists of by weighing the amounts of some known substances which react with the unknown one - as long as you take the process to completion. One example of when  you can tell if the reaction has been taken to completion is when you neutralise a base with an acid.
They were starting to use these ideas  at the time of Humphrey Davey and Lavoisier! Brilliant, don't you think?

There is a teensy problem because not all atoms of all elements are identical in mass; different isotopes may occur with one neutron more or less than others (chemically the same but different atomic masses); naturally occurring Chlorine is a mixture of isotopes and its average atomic mass is 35.5. To deal with this you work with this average 'molar' mass and you get good answers.

I've always said that Chemists need to get things in proportion!

Thanks Sophiecentaur.. Let me read this some more.. and digest some of the information again!

#### Simulated

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##### How many water molecules are in a cup of water??
« Reply #10 on: 18/01/2008 12:18:49 »
As Karen has said lots of times.

THanks everybody!

#### Nobody's Confidant

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##### How many water molecules are in a cup of water??
« Reply #11 on: 18/01/2008 16:46:44 »
A lot.

#### lightarrow

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##### How many water molecules are in a cup of water??
« Reply #12 on: 18/01/2008 19:52:26 »
I heard that Lightarrow. Thanks.

What's the molar mass of carbon? It was just on our exam today and we didn't go over it at all and I was like wow. And I just guessed 1 since carbon is one AMU
It's 12 g/mol for 12C by definition.
With good approximation an atom's molar mass is numerically equal to the number of protons and neutrons in the nucleus (mass' number); if you remember this you can't mistake.

#### Simulated

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##### How many water molecules are in a cup of water??
« Reply #13 on: 18/01/2008 21:26:52 »
Darn I missed it then. Lol oh well. Thanks you

#### lyner

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##### How many water molecules are in a cup of water??
« Reply #14 on: 20/01/2008 23:12:12 »
This molar mass thing is typically awkward and Chemists are to blame.
The whole system revolves around  Carbon =12  - (not carbon = 1).
Two reasons spring to mind.
1. Carbon 12  is easy to obtain and you can hold it in your hand - unlike Hydrogen.
2. Chemists do a lot of work with Organic molecules, which always contain Carbon.

When you measure the Atomic mass of any isotope, it is never an exact multiple of any other isotope - due, I think, to the mass defect and nuclear binding energy of each element / isotope.
It's certainly 'near enough for jazz' to use H = 1, as Lightarrow says and it makes life for most of us much easier.

'Carbon = 12 ' is a real nuisance when trying to teach secondary School students - it just adds another layer of complexity to the explanation.

#### Simulated

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##### How many water molecules are in a cup of water??
« Reply #15 on: 21/01/2008 00:13:16 »
Thank you. I"ll remember that

#### Bored chemist

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##### How many water molecules are in a cup of water??
« Reply #16 on: 21/01/2008 20:09:47 »
Last time I checked, the nuclear physicists were to blame for things like mass defect and nuclear binding energy; please don't blame us chemists.
A lot of carbon compounds are volatile so it's easy to get them into a mass spectrometer to measure their mass. If you measure the mass of, for example, methane you get fragments like CH3 and CH2, the difference gives you the mass of  the hydrogen and the mass of the carbon can be used as a calibration. Then you can use things like chloromethane to measure the mass of the 2 isotopes of chlorine, and so on. The reason for doing this is that mass spectrometers can relatively easily measure the masses to a part in a million or better. It's more difficult to do that with classical chemistry.
If I were trying to teach schoolchildren I'd not bother to mention the fact that the standard is carbon until I was sure they had got the hang of using the mass of a hydrogen atom. The idea is the same as counting in dozens - it's just the number of things in a mole is rather more than 12.

#### The Naked Scientists Forum

##### How many water molecules are in a cup of water??
« Reply #16 on: 21/01/2008 20:09:47 »