Avogadro's number = 6.0221415 × 10^23

[Cory Duchesne]

I understand how to use this number, to do typical high school chemistry problems, but I never did get an answer on how they settled on such a precise number of atoms in a mole. Can anyone explain it?

[Greg the Genius]

its number of moles in a space, i mean 1 atoms in 1 mole. u no wut i mene lolz

[Cory Duchesne]

its number of moles in a space, i mean 1 atoms in 1 mole.

Why do you think that?

Based on what I've read, Avogadro's number is the number of "entities" (usually, atoms or molecules) in one mole. That's a huge ammount of atoms in 1 mole. Why do you think there is only 1 atom in a mole?

[Greg the Genius]

no i dint say that, atoms in 1 mole. its a gesstimashn newaze. bascily ur tryn 2 mesaur velcity AN dirction, aint gon hapn. wel not yet newazee... ROFL

[brad walker]

Did you look at Wikipedia?

[hsandman]

Cory has found as sock... a genius sock!

[Pincho Paxton]

"Stupid moles with their little twitchy noses, I hate them!!! Bang Bang!".. Blackadder redifined.

Moles 12 units of carbon.. 12 in a dozen.. a dozen redifined.

[Cory Duchesne]

Did you look at Wikipedia?

Wikipedia doesn't really deliver the goods on this one.

For instance, it doesn't make sense that equal volumes of gas have equal numbers of molecules. Some elements are bigger than others. Some molecules are bigger than others. Therefore, it makes no sense to say that two equal volumes contain equal number of entities.

[DHodges]

For instance, it doesn't make sense that equal volumes of gas have equal numbers of molecules. Some elements are bigger than others. Some molecules are bigger than others. Therefore, it makes no sense to say that two equal volumes contain equal number of entities.

If you look at the ideal gas law, you will see that the size of an atom or molecule is assumed to be zero; they are essentially pointlike. The space taken up by the actual molecules (compared to the overall volume of a gas at STP) is very small.

Ignoring volume, does it make sense to you that 12 grams of an element with an atomic weight of twelve would contain about the same number of atoms as 18 grams of an element with an atomic weight of 18?

[Imadrongo]

If university wasn't an evil academic satanic place I would recommend CHEM 101.

[Cory Duchesne]

For instance, it doesn't make sense that equal volumes of gas have equal numbers of molecules. Some elements are bigger than others. Some molecules are bigger than others. Therefore, it makes no sense to say that two equal volumes contain equal number of entities.

If you look at the ideal gas law, you will see that the size of an atom or molecule is assumed to be zero; they are essentially pointlike.

But that doesn't make sense in light of what the scanning tunnel microscope tells us. Does it?

Ignoring volume, does it make sense to you that 12 grams of an element with an atomic weight of twelve would contain about the same number of atoms as 18 grams of an element with an atomic weight of 18?

Not really. It's not clear what the difference is between grams and atomic weight. I suppose it might make sense if the two elements had equal mass, but differed in weight. But the difference between mass and weight is another topic I find vague and difficult.

[cat10542]

mass and weight isn't mixed up here standard atomic weight is the same thing as relative atomic mass (average of all isotopes atomic mass for the specific element in their respective percentages in the local environment of Earth). yes, odd terminology, but what can you do.

If oxygen has an atomic mass of 16 and you have 16g of the substance, then you have a gram of substance per each unit of atomic.

If fluorine has an atomic mass of 19 and you have 19g of the substance, then you have a gram of substance per each unit of atomic mass.

Therefore you would have the same number of molecules in 16g of oxygen as you would in 19g of fluorine because the difference in atomic mass is the same ratio as the difference in mass, or because they contain the same gram to atomic mass ratio.

Because reactions occur between molecules and atoms, it is important to know the ratio between the molecules when you are looking at or making a reaction. But molecules are sooooo small and reactions that humans deal with occur on a more macro scale. Therefore scientists decided to use the ratio of gram per atomic mass unit of a substance which they called one mole. Avogadro's number is the conversion factor between atomic mass units and grams, it's not some magical concept to make people feel better.

Reactions would be much more difficult to work without the concept of moles. It's a very useful conversion factor, and allows you to find limiting reactant, and calculate theoretic yeild, and many other things.

At STP you can experimentally and mathematically prove that one mole (atomic mass # of grams) of gas (no matter what substance) is 22.4L. Since there are the same number of moles in a specific volume, there are therefore the same number of molecules because the ratio of moles to molecules is a constant (avogadro's number).

Maybe you should look more into atomic mass unit. Avogadro's number is merely the conversion factor between atomic mass unit and grams after all. http://en.wikipedia.org/wiki/Atomic_mass_unit

Hope that helps.

PS. you seem to be really interested in Chemistry. Have you taken the course? If not, I recommend it.

[ZenMuadDib]

"Stupid moles with their little twitchy noses, I hate them!!! Bang Bang!".. Blackadder redifined.

Moles 12 units of carbon.. 12 in a dozen.. a dozen redifined.

No, it really depends on the molar mass of the element or compound. You are right in the sense that because carbon's atomic mass is 12.01 amu, or 12.01 g, then there is a mole, 6.022 x 10^23 atoms, if you have 12.01 grams of carbon. Likewise it would take 18.02 grams of water to have a mole of water molecules.

[Cory Duchesne]

mass and weight isn't mixed up here standard atomic weight is the same thing as relative atomic mass (average of all isotopes atomic mass for the specific element in their respective percentages in the local environment of Earth). yes, odd terminology, but what can you do.

My understanding is that Atomic weight is roughly the amount of particles comprising the nucleus (the amount of protons and neutrons). If an element's nucleus is comprised of one neutron and one proton, then is has an AW of approximately 2.

Electrons reportedly hardly make up any weight at all. And I accept that each element has different versions of itself (different isotopes), and that the atomic weight of an element is the result of finding out the average amongst the various isotopes. That's all clear.

If oxygen has an atomic mass of 16 and you have 16g of the substance, then you have a gram of substance per each unit of atomic mass.

According to you, what exactly is a unit of atomic mass? If you're referring to either a single neutron or proton, then what you're saying seems equivalent to saying: one proton weighs one gram. I hope I've misinterpreted. But I see no other way of interpreting what you've said.

If fluorine has an atomic mass of 19 and you have 19g of the substance, then you have a gram of substance per each unit of atomic mass.

Until I know what you mean by a unit of atomic mass, I don't know what you mean.

Therefore you would have the same number of molecules in 16g of oxygen as you would in 19g of fluorine

This conclusion does not at all seem to follow from your premises at all. In fact, I can't make any sense out of the initial premises, therefore everything else you said only compounds the confusion.

the difference in atomic mass is the same ratio as the difference in mass, or because they contain the same gram to atomic mass ratio.

The only thing you seem to be demonstrating above is that 1 gram = 1 proton or neutron. Which seems extremely false. I'm sure you're probably getting at something else, but due to either you're erroneous explanation or due to my intellectual defects, I can't make any sense of what you're trying to say.

-----

[brad walker]

http://en.wikipedia.org/wiki/Mole_(unit)

[Cory Duchesne]

http://en.wikipedia.org/wiki/Mole_(unit)

Wikipedia says:

"The mole [is a] unit that measures an amount of substance."

That's why I ask: What's the point in using a mole when we already have have grams? In other words, grams measures an amount of a substance just fine, so what's the point in introducing a different way of measuring?

This question is especially pertinent when we realize that Avogadro's number is purely hypothetical and isn't the result of any actual measurements.

[Cory Duchesne]

Avogadro's number is the number of molecules in one mole.

Ok, but are we talking molecules or are we talking atoms?

You see, the difference between a gram and a mole, is that the units comprising a gram are clearly defined as either milligrams, nanograms, picograms, etc. A gram is easily converted into different forms of units. A mole seems much less clear.

One mole is used as a basic unit of measurement.

Why not just use grams? What's the point in introducing the mole?

Since different molecules, or elements, have different atomic masses the mass of a mole of molecules depends on the molecule.

Ok, am I correct to say that moles measure mass, while grams measure weight?

Avogadro's number is simply the number that allows simple conversion of a molecules atomic mass to the mass in grams of one mole of the substance.

This doesn't register in my brain as having any meaning. I'm seriously starting to wonder if there is something wrong with me.

In what real life situation would we need to do make this conversion?

Atomic mass is the mass of one element. One proton=1 unit of atomic mass. The atomic mass on the periodic table is the average weight of all naturally occurring isotopes of an element.

That's easy enough to accept on it's own, but I fail to see the value in Avodagro's number

[Ryan Rudolph]

I’m was curious myself as to why this number is important so I did a search, and I found this site, which gives a fairly decent explanation –

http://www.garlikov.com/chemistry/mols.html

[brad walker]

http://en.wikipedia.org/wiki/Mole_(unit)

Wikipedia says:

"The mole [is a] unit that measures an amount of substance."

That's why I ask: What's the point in using a mole when we already have have grams? In other words, grams measures an amount of a substance just fine, so what's the point in introducing a different way of measuring?

http://en.wikipedia.org/wiki/Mole_(unit ... y_of_moles

If you have 8g of hydrogen gas and 16g of oxygen gas, how much water can you produce? Try this problem and you'll see that you need a conversion factor (the mole).

Avogadro's number is the number of molecules in one mole.

Ok, but are we talking molecules or are we talking atoms?

Like you said before, the mole's not tied to molecules or atoms but indivisible entities, as in if they're divided they become something else. Molecules and atoms both share this characteristic, but so do these: http://en.wikipedia.org/wiki/Mole_(unit ... y_entities

[cat10542]

My understanding is that Atomic weight is roughly the amount of particles comprising the nucleus (the amount of protons and neutrons). If an element's nucleus is comprised of one neutron and one proton, then is has an AW of approximately 2.

Electrons reportedly hardly make up any weight at all. And I accept that each element has different versions of itself (different isotopes), and that the atomic weight of an element is the result of finding out the average amongst the various isotopes. That's all clear.

yes that is all correct

If oxygen has an atomic mass of 16 and you have 16g of the substance, then you have a gram of substance per each unit of atomic mass.

According to you, what exactly is a unit of atomic mass? If you're referring to either a single neutron or proton, then what you're saying seems equivalent to saying: one proton weighs one gram. I hope I've misinterpreted. But I see no other way of interpreting what you've said.

I didn't say that it has one gram which equals each unit of atomic mass. I said that their is one gram per unit of atomic mass. I am referring to a ratio where you have one gram of the substance for each unit of atomic mass that is in it's molecular weight so that the ratio is of g to units is one 16/16. obviously if 1 gram equaled one atomic mass unit then in the examples you would have only one molecule and being 1g it would be visible. I said unit of atomic mass to differentiate from the amount: atomic mass unit. I'm just referring to the number of atomic mass units that make up one molecules atomic mass. I hope that makes sense. one molecule does not have a mass of 16g, but the molecule does have a mass of 16u. Many of these molecules make a mass of 18g. The amount of molecules of 16u in 16g would be the same as the amount of molecules of 19u in 19g. Because it is proportional, which is the point I was attempting to make, to the conversion factor from 1u to 1g.

If fluorine has an atomic mass of 19 and you have 19g of the substance, then you have a gram of substance per each unit of atomic mass.

Until I know what you mean by a unit of atomic mass, I don't know what you mean.

Thus in 19g of fluorine you have a gram per each atomic mass unit in the atomic mass of one molecule, which means that 19g of fluorine which has an atomic mass of 19u, has the conversion factor from 1u to 1g, it's that particular ratio.

Therefore you would have the same number of molecules in 16g of oxygen as you would in 19g of fluorine

This conclusion does not at all seem to follow from your premises at all. In fact, I can't make any sense out of the initial premises, therefore everything else you said only compounds the confusion.

the difference in atomic mass is the same ratio as the difference in mass, or because they contain the same gram to atomic mass ratio.

The only thing you seem to be demonstrating above is that 1 gram = 1 proton or neutron. Which seems extremely false. I'm sure you're probably getting at something else, but due to either you're erroneous explanation or due to my intellectual defects, I can't make any sense of what you're trying to say.

-----

[/quote]

Obviously you've misunderstood what i was saying and I apologize for any confusing terminology. But if you have a conversion from a particular weight in atomic mass units to grams, then the easiest way to measure the macro-scale amounts of the substance is not in atomic mass units, but in grams. Therefore using the number of atomic mass units a particular substance has will create a constant conversion factor. Therefore you use that number(not saying that it's equal, but that it creates a proportion) of grams, and you call that a mole. 1 mole of oxygen has 16 grams. 1 mole of fluorine has 19g. 1 atom of oxygen has 16u. 1 atom of fluorine has 19u. 1 mole of oxygen has 6.0221415 x 10^23 atoms. 1 mole of fluorine has 6.0221415 x 10^23 atoms.


I think using conversions and math avogadro's number becomes obvious:

This will come in handy: 1 atomic mass unit = 1.66053886 × 10-27 kilograms
O is oxygen
u is atomic mass unit

Lets try a conversion:
1 mole O x (16g O/1 mole of O) x (1kg/1000g) x (1 u/(1.66053886 x 10^-27kg)) x (1 atom/16u)=6.022141511 x 10^-23 atoms

again:
1 mole F x (19g F/1 mole of F) x (1kg/ 1000g) x (1 u/(1.66053886 x10^-27kg)) x (1atom/19u)= 6.022141511 x 10^-23

Because a mole is defined as having the same number of grams of substance as the u of the atomic mass for that substance, the g and u will always cancel out in a conversion from moles to atoms, giving you the same number of atoms of any substance in an equivalent amount of moles.

[cat10542]

oops i posted the same thing twice, sry

[vicdan]

mass and weight are practically the same thing. Weight is simply mass times the force of gravity. For example, you may weight 98 pounds, but your mass is only 10 pounds. As I said above, moles measure the number of parts of a substance (molecules, elements)

Erm, no. Pounds measure weight. Mass is measured in kilograms. The ratio between weight and mass is proportionate to gravity.

Your explanation confuses mass and weight in newtons. if an object has the mass of 10kg, then its weight is 98 newtons, because weight in newtons is mass times freefall acceleration, which on the surface of Earth is 9.8m/s^2.

[cat10542]

A gram is a unit of measure for mass.
A mole is a unit of measure that is proportional to the number of molecules.

A mole is clearly defined, but it's mass differs depending on what substance you have a mole of.
This is proportional to if you were to say you had five molecules and you wanted to know the mass, you would have no idea how much atomic mass units (or grams or any other mass measurement) that was unless you knew which substance you were talking about.

Why are moles so important?
Because they are proportional to the number of molecules.
Why is that important?
Because reactions occur between molecules not between masses.

ex.
2NaBr + H2SO4 -> 2HBr + NaSO4

In the example 2 molecules of NaBr reacts for each molecule of H2SO4 to form 2 molecules of HBr for each 1 molecule of NaSO4. When this reaction occurs in real life this happens many times over, but the proportion of 2:1 > 2:1 stays the same. This is because of the law of conservation of mass...which means that the equation must be balanced.

Measurements can be made by mass, but it would be impossible to measure the amount of molecules in a sample. Therefore it is useful to measure the mass, and convert it moles which is proportional to the number of molecules (which dictates how the reaction is balanced 2:1 > 2: 1 in this case). Moles is a more useful conversion than molecules because you don't have to deal with 10^20smthg power which can be tedious and lead to mistakes. Also, a mole is a very, very common unit of measure in chemistry, so it's not outlandish to use, and you need it to calculate molarity, and molality, and other things later.

Here is a case when moles are more useful than mass.

You have 1.5g NaBr, and 3.0g H2SO4. What is the limiting reactant? How much HBr will theoretically be formed?
Atomic weights=
H-1.01
S-32.06
O-16.00
Na-22.99
Br-79.90

To answer these questions you must first convert to moles:
1.5g NaBr x (1 mole NaBr/ 102.98g NaBr) = .0146 mole NaBr
3.0g H2S04 x (1 mole H2SO4/ 98.08 H2SO4) = .0306 mole H2SO4

Now you need to convert one of the figure into moles of the other using the 2:1 proportion (since you need 2 moles of NaBr for each mole H2SO4) This ratio will put both values of starting materials into the same substance so you can tell which one will limit the reaction.

.0146 mole of NaBr needs how many moles of H2S04 to react completely?
.0146mole NaBr (1 mole H2SO4/ 2 mole NaBr) = .0073 mole H2SO4 needed to fully react with the NaBr given.

Since .0306 mole is larger than .0073 moles of H2SO4 needed, you can conclude that NaBr is the limiting reactant, and there is excess H2S04 that will be left over after the reaction completes. (To figure out how much excess subtract .0306-.0073 and then convert from moles to grams)

Then to figure out how much HBr would form you would start with your limiting reactant and convert to HBr.

.0146mole NaBr x (2 mole HBr/2 mole NaBr) (80.91g HBr/1 mole HBr) = 1.18g HBr

Thus, using moles becomes very important in chemical equations because they deal with molecular proportions. Conversion from grams to moles is easy, which makes moles better than molecules. Also, mass is an easy unit of measurement, but doesn't work well for reactions. Therefore being able to convert between grams and moles is important.

I hope this answers some of your questions about moles. :)

[Cory Duchesne]

Ok, but are we talking molecules or are we talking atoms?

A molecule is composed of atoms. For example, water has two atoms of hydrogen that combine with one atom of oxygen to form one molecule of water. A mole measures the number of complete parts of a substance you have. The substance could be a molecule, like water, or an element(single atom) like Helium.

Ok, that's very clear. Although, one of my driving curiosities is how Johann Josef Loschmidt computed the number of particles in one cubic centimetre of gas - in 1865

I'm sure there is an enlightening story behind that one.

The mole is useful since it provides an easy way to figure out the number of molecules you have based on the mass you have.

How certain can a person be about the number of molecules had in a given mass? How on earth did they calculate it? That's really what I've been driving at. I don't want to know what, I want to know how.

And since chemical reactions occur using ratios between the number of reactants and products, that number is necessary to prepare reactions.

I don't follow you here. Look, consider this:

As you probably know, if you take 0.24g of magnesium, put it in a crucible, and heat it up to 2000 degrees, the magnesium turns into a substance that weighs a total of 0.40g. In other words, the weight of the substance increases 66.6666% (due to oxidation). Furthermore, no matter how much magnesium you start with, the weight will always increase by 66.6666% (that is, as long as oxygen is made available to the magnesium, the oxidation will result in an increase of 66.6666%)

Ok, so there you have it. The mole, as a number, was not necessary to do a chemical reaction.

I'm hoping you or someone else will show me why the mole as a concept is useful. As it stands I can't see how it's useful.

The reason the number is what it is (6.02 x 10^23) is because that is the number that allows the atomic mass (in atomic mass units) to be the same number for a mole of the substance (in grams.)

Man, I'm sorry, it's probably intelligible to better minds, but I don't understand what you're trying to say.

Ok, am I correct to say that moles measure mass, while grams measure weight?

No, mass and weight are practically the same thing. Weight is simply mass times the force of gravity. For example, you may weight 98 pounds, but your mass is only 10 pounds.

I respectfully decline to accept that piece of reasoning. Seems false to me.

As I said above, moles measure the number of parts of a substance (molecules, elements)

But HOW is this measurement made? Look, the act of measuring is pretty clear when it comes to grams or centimeters. Why is the issue so opaque when it comes to moles?

[brokenhead]

Ok, so there you have it. The mole, as a number, was not necessary to do a chemical reaction.

I'm hoping you or someone else will show me why the mole as a concept is useful. As it stands I can't see how it's useful.

It's not necessary, it's just terminology that chemists or chemical engineers use as a shorthand. It scales things up to human proportions because the theoretical proportions are impracticably small in a laboratory setting. A mole is atomic weight of an atom in grams. Atomic weight is too small for discussion. A chemist would say "We take two moles of Hydrogen and one mole of Oxygen to make one mole of water." He is giving mass amounts in a human scale, and at the same time expressing the 2-to-1 ratio of the reactant molecules, making theory clear in the sentence. If he gave the weight in grams, the molecular structure would not be as evident. Obviously, he's not going to say something like "We will take two atoms of Hydrogen and one of Oxygen..." because you can't physically work with individual atoms or molecules.

The Avogadro Number is just a scaling factor.