What is a mole?

[Ziggurat]

In addition to the above definitions of what a mole is, I want to add a note about why the concept is so important in chemistry.

If you combine oxygen and hydrogen and add a spark, then the hydrogen will burn, combining with oxygen to form water. But you can't just take an arbitrary amount of hydrogen and an arbitrary amount of oxygen and turn the whole mixture into water. If you have too much oxygen, you'll have leftover oxygen at the end, and if you have too little, you'll have leftover hydrogen. That's not hard to figure out from the chemical formula: water is always H₂O. It's not H_xO_y for arbitrary x and y. If you want a chemical reaction to take place with no leftovers, or if you want to know how much leftovers there will be, you need to count atoms and molecules. So for example:
2 H₂ + 1 O₂ -> 2 H₂O
10,000 H₂ + 5,000 O₂ -> 10,000 H₂O
But
2 H₂ + 2 O₂ -> 1 0₂ + 2 H₂O
etc, etc.

Of course, we typically measure the weight/mass of materials we work with, not the number of atoms directly, but you can of course calculate the number of atoms based on the weight. But the numbers get absurdly large. By using moles instead, you're basically scaling down ridiculously large numbers to something more manageable (and as Soapy Sam alluded to above, something you can do rough calculations on very easily in your head with pretty good accuracy for the lighter elements). So you would have, say:

2 mole H₂ + 1 mole O₂ -> 2 mole H₂O

I can look at this formula and know that the fractions are correct, that the reaction will be complete with no leftovers. I can also tell that this reaction is wrong:

1 mole H₂ + 1 mole O₂ -> 1 mole H₂O

Since I'm basically just counting the number of atoms, this works well even if the chemical formulas are complex. It's a little harder to look at a reaction like

1 gram H₂ + 16 gram O₂ -> 17 gram H₂O

and figure out if it's correct or not (hint: it's not). And it becomes even more difficult to check based on weights when the chemical formulas involved are complex, unless you check by converting to moles.

 

[Modified]

Try this: A Mole of Moles.

Do moles have moles on their skin? If so we could have a mole of mole moles.

 

[Madalch]

(The unit is the Dalton (da), but it is often expressed as grams per mole (g/mol).)

So 18.015 g/mol is the atomic mass (weight) of a single molecule of water.

NO!!!!!!!

The mass of a single molecule of water is 18.015 amu or 18.015 daltons. This is the same as saying the molecular weight of water is 18.015 amu (water doesn't come in atoms).

The molar mass of water is 18.015 g/mol. This means that a mole (not a single molecule) of water will have a mass of 18.015 g (not amu). Molar mass and atomic/molecular/formula weights are numerically equal (due to the convenient choice of definition of both the mole and the amu), but they are different concepts.

 

[Ziggurat]

NO!!!!!!!

Actually, he's right. Strictly speaking, a mole is a pure number, equal to Avogadro's number, N_A. So if you divide 18.015 grams by N_A, you will get 18.015 amu (assuming a conversion from grams to amu).

Molar mass and atomic/molecular/formula weights are numerically equal (due to the convenient choice of definition of both the mole and the amu), but they are different concepts.

But they don't simply have the same numerical value, they share the same units too. 1 amu = 1 gram/mole. The only purpose in distinguishing them is to make it more obvious the order of magnitude of quantity you're dealing with (macroscopic versus small number of molecule amounts), but that distinction, while useful in practical terms, is completely arbitrary from a mathematical perspective.

 

[jasonpatterson]

Actually, he's right. Strictly speaking, a mole is a pure number, equal to Avogadro's number, N_A. So if you divide 18.015 grams by N_A, you will get 18.015 amu (assuming a conversion from grams to amu).

No, that's not true, but for a different reason.

A single molecule of water will typically be made of 2 ¹H atoms and 1 ¹⁶O atom. The mass of that is not 18.015 amu. It's really really close, because both of those elements are almost exclusively populated by a single isotope, but the true mass of a single molecule is the sum of the masses of the atoms it is made from, most likely 18.011 amu. There is also a chance that an ²H (or two), ¹⁷O, or ¹⁸O isotope is in the molecule, in which case 18.015 is completely wrong. It's only when considering large numbers of atoms that we can generalize to the average atomic mass.

For a better example, consider the mass of hydrobromic acid, HBr. With the reasoning above, the mass would be 1.0079 + 79.904 = 80.912 amu. Any real molecule of hydrobromic acid is either 79.925 amu or 81.9241 amu because bromine comes in two isotopes, ⁷⁹Br and ⁸¹Br, in almost equal abundance. (I skipped deuterium isotopes in this consideration because there's only so much time to be pedantic in any one day.)

I probably wouldn't care about this in particular if I hadn't just finished a Beanium lab with my chemistry I students in which the distinction between the average mass of a bean is considered in comparison to the actual mass of a single bean. (Varieties of beans = isotopes in this activity.)

 

[fuelair]

No, that's not true, but for a different reason.

A single molecule of water will typically be made of 2 ¹H atoms and 1 ¹⁶O atom. The mass of that is not 18.015 amu. It's really really close, because both of those elements are almost exclusively populated by a single isotope, but the true mass of a single molecule is the sum of the masses of the atoms it is made from, most likely 18.011 amu. There is also a chance that an ²H (or two), ¹⁷O, or ¹⁸O isotope is in the molecule, in which case 18.015 is completely wrong. It's only when considering large numbers of atoms that we can generalize to the average atomic mass.

For a better example, consider the mass of hydrobromic acid, HBr. With the reasoning above, the mass would be 1.0079 + 79.904 = 80.912 amu. Any real molecule of hydrobromic acid is either 79.925 amu or 81.9241 amu because bromine comes in two isotopes, ⁷⁹Br and ⁸¹Br, in almost equal abundance. (I skipped deuterium isotopes in this consideration because there's only so much time to be pedantic in any one day.)

I probably wouldn't care about this in particular if I hadn't just finished a Beanium lab with my chemistry I students in which the distinction between the average mass of a bean is considered in comparison to the actual mass of a single bean. (Varieties of beans = isotopes in this activity.)

We did that with isotopes of Candium or Mnmium (3 isotopes or 2 isotopes).

 

[Madalch]

But they don't simply have the same numerical value, they share the same units too. 1 amu = 1 gram/mole.

No, they are different units. An amu is a very small mass. A g/mol is a conversion factor for turning masses into moles.

As an analogy, consider those 1-oz. coins of precious metals. The mass of a single coin is 1 oz. If you want to know how many dozens of coins you have, you could weigh them in troy pounds, and use the "dozen mass" of 1 lb/dozen.

An ounce (weight of a single coin) is not the same thing as a pound per dozen (conversion between weight and dozens). They're just numerically equal, because someone wisely decided to make a troy pound a dozen ounces.

 

[Ziggurat]

No, they are different units. An amu is a very small mass. A g/mol is a conversion factor for turning masses into moles.

You're not listening. 1 mole = 1 N_A. Not 1 mole <-> 1 N_A. So 1 gram/1 N_A is a very, VERY small mass. It is, in fact, exactly equal to 1 amu.

An ounce (weight of a single coin) is not the same thing as a pound per dozen (conversion between weight and dozens). They're just numerically equal, because someone wisely decided to make a troy pound a dozen ounces.

Actually, those are not numerically equal, because there are 16 ounces per pound, not 12. But 1 pound/16 is in fact exactly equal to 1 ounce.

 

[Hellbound]

Actually, those are not numerically equal, because there are 16 ounces per pound, not 12. But 1 pound/16 is in fact exactly equal to 1 ounce.

Actually, he's right on that one. Troy weights, used for precious metals, have 12 ounces to the pound instead of 16. That's why a pound of gold (http://en.wikipedia.org/wiki/Troy_weight) weighs less than a pound of feathers (http://en.wikipedia.org/wiki/Avoirdupois).

 

[jasonpatterson]

We did that with isotopes of Candium or Mnmium (3 isotopes or 2 isotopes).

I've done that before, but I always have a problem with conservation of mass being violated, even with disturbingly heavily handled isotopes and additional samples of atoms for the students to examine on their own time. Some nuclides just disappear into the void every time; it's a chemystery... Shockingly enough, beanium seems remarkably stable in this environment.

 

[Hokulele]

I've done that before, but I always have a problem with conservation of mass being violated, even with disturbingly heavily handled isotopes and additional samples of atoms for the students to examine on their own time. Some nuclides just disappear into the void every time; it's a chemystery... Shockingly enough, beanium seems remarkably stable in this environment.

At least until one of the kids decides to stick it up his/her nose too far.

 

[Badly Shaved Monkey]

These are brilliant replies, even I now have a vague inkling of what it means. I can't see her signing up to International Mole Day somehow, maybe next year we'll be able to laugh about it, but things are a bit fraught for now. Excellent site though, I may get a T-shirt myself.

I'll show some of the replies to young Miss Nalyssus - this is a brilliant forum!

Many thanks folks,

Yuri

Having just read the page, I don't think this point has quite been made.

Our Avigadro's Number is what you get if you make what is actually an arbitrary and free choice to say it is the number of elements in an atomic weight's (or molecular weight's) worth in grams. The concept is useful because it gets to the underlying proportionally inherent in chemical reactions but the number itself is arbitrary and we could have had a different Avogadro's Number if we routinely worked in scruples, drachms or Troy ounces.

 

[fuelair]

I've done that before, but I always have a problem with conservation of mass being violated, even with disturbingly heavily handled isotopes and additional samples of atoms for the students to examine on their own time. Some nuclides just disappear into the void every time; it's a chemystery... Shockingly enough, beanium seems remarkably stable in this environment.

 

[barehl]

Not really a sceptical question, but does anyone have a simple definition of a mole, in chemistry for my daughter, who is very confused about what it means?

We've googled it but most of the definitions are complex (though correct, I'm sure) and difficult to understand for one who is just starting chemistry at this level and is struggling with basic concepts (and one (me!) who probably never fully grasped the concept and anyway hasn't done chemistry for very many years).

I can think of several times I used this concept, which is just a ratio of weight to the number of atoms or molecules.

When I took chemistry in college, we did titration. Basically, you are given an unknown acid or base solution. Then you mix up its complement, an acid for a base or a base for an acid. You know exactly what the concentration of your own solution is because you weigh it and you know exactly how much water you have. For example, let's say I had hydrochloric acid of unknown concentration. I could weigh out some baking soda on a lab scale and mix this with water to create a weak base. You measure out a quantity of the unknown solution and then add yours to it a little at a time until it just neutralizes (pH 7). Because you now know the two quantities and you know the concentration of yours, you can figure out the exact concentration of the unknown. You know the weight and that then requires Avogadro's number to convert to concentration like mols/liter. If you know the quantity and concentration then you can also figure out the weight of the acid. We used a concentration of hydrochloric acid about equal to stomach acid and then titrated with Tums antacid to see what the weight ratio was. If I recall correctly the makers of Tums claimed 47x its weight in acid.

This number fits into the Ideal Gas Law. If you know the quantity of gas, the pressure, and the temperature, you can figure out the number of molecules of gas and its weight. This can be an interesting concept because you can't weigh a volume of atmosphere while it is surrounded by atmosphere. You can do other things. You could figure out how much helium it might take to lift a blimp of a given empty weight. You could take the volume of a hot air balloon and figure out how much buoyancy you would have if you heated the air by a certain amount. You could combine this with the specific heat of the gas to see how much energy (BTUs, Calories, Ergs, or WattHours) it would take to raise it that amount. Then you could figure out how much fuel you might need for a flight. On small scale, you could get a garbage bag. The volume of these are normally listed on the box (like 49 liters). Then you estimate what the buoyancy would be if you heated up the air inside, say 20 degrees Fahrenheit. You can either weigh one garbage bag if you have a sensitive scale or you can weigh a number of them and divide. Then you find out how many BTUs petroleum has. You weigh a candle and figure out how much energy it can put off. You'll find out pretty quickly that one garbage bag can't lift a 16 ounce candle. But, maybe it could lift a tea candle. Things like this can be fun. It might be less exciting now in these days of hovering quadra-copters but you can actually make a small hot air balloon out of tissue paper or a larger one out of light, nylon fabric.

On another forum, I was looking at a model airplane engine. I explained the procedure for figuring out if the claimed power output was realistic. To do this, you start with the known volume of the engine and how many RPMs it has to turn. This tells you exactly how much air passes through the cylinders in a given amount of time. Since you can look up the typical percentage of oxygen in the atmosphere, this gives you a good estimate of how much oxygen was in that volume. From this you can use chemistry to see how many molecules of oxygen you need to fully burn a petroleum molecule like octane. This then gives you weight of octane. So, now you know roughly what your fuel burn would be. Air cooled engines tend to have a certain fuel burn for a given power output. Since you have estimated the fuel used, this gives you a rough estimate of power output and you can see if they match. This is of some importance in the experimental aircraft category because aircraft engines tend to be very expensive. However, you can trust their published power output. Engines that are used on RC aircraft are derived from chainsaw engines. They are much cheaper but the published power output is not nearly so reliable.

If you like rockets, you can use this number to figure out the weight ratio of hydrogen and oxygen. You can calculate how much oxygen it would take to rust all of the iron in the Earth's crust. You can calculate how much oxygen would have been produced to form a large oil or coal deposit from plant material. If you were ambitious, you could estimate the number of rubber tires on D-Day and then, knowing the chemical formulas for rubber and alcohol, figure out how much alcohol it took to make that rubber. Then you could estimate how much corn it took to make that much alcohol.

 

[fuelair]

Sooooo, have any of your students ever put the atoms of beanium in their ears? I ask as this seems to have occurred in the 60s for some young scientists as noted indirectly in this song from the folk era of that time: http://www.songlyrics.com/the-serendipity-singers/beans-in-my-ears-lyrics/ !!!!!:

 

[catsmate]

Actually, he's right on that one. Troy weights, used for precious metals, have 12 ounces to the pound instead of 16. That's why a pound of gold (http://en.wikipedia.org/wiki/Troy_weight) weighs less than a pound of feathers (http://en.wikipedia.org/wiki/Avoirdupois).

But an ounce of gold is likewise heavier than an ounce of feathers.

 

[Hellbound]

But an ounce of gold is likewise heavier than an ounce of feathers.

Well, yeah, if you really wanna go that far down the rabbit hole

 

[fuelair]

Well, yeah, if you really wanna go that far down the rabbit hole

Once the hole starts opening.........

 

[elgarak]

Once the hole starts opening.........

Mole hole?

 

[fuelair]

Mole hole?

Or, for those of us old enough to remember iirc IGY and Mohole..............