What exactly is a mole?

Upon coming back to University I've started studying basic chemistry again. I've always had trouble with the concept of "moles". According to my study book,

1 mole of any element or compound is equal to its molecular weight in grams.

I understand that part but later in the paragraph it also says:

One mole of any substance always contains exactly the same number of solute particles, that is, $6.02 \times 10^{23}$ (Avogadro's number). So whether you weigh out 1 mole of glucose (180 g) or 1 mole of water (18 g) or 1 mole of methane (16 g), in each case you will have $6.02 \times 10^{23}$ molecules of that substance.

If 1 mole equals the molecular weight of a compound, then how come 1 mole of glucose doesn't equate to 1 molecule of glucose? Basically, why is 1 mole of glucose $6.02\times10^{23}$ molecules instead of 1 molecule?

• one mole of glucose can not be equal to one molecule of glucose because one mole glucose weigh 180 gram while one molecule of glucose weigh 180u. Read the definition again. – Vidyanshu Mishra Oct 11 '16 at 17:02
• because the molecular weight of a compound is the weigth of one mole of compound. Also, could you imagine if a single molecule of O2 weighted 32g? how would you breath it? – njzk2 Oct 11 '16 at 19:57
• Why are there 12 eggs in a dozen eggs, and not 1? – BlueRaja - Danny Pflughoeft Oct 11 '16 at 22:30
• I can't believe nobody's pointed out that the definition is actually wrong. "a mole" is never equal to any weight. The definition should be "1 mole of any element or compound has a mass equal to its molecular weight in grams." – tex Oct 12 '16 at 13:37
• A type of rodent, maybe? – Oscar Lanzi Aug 9 '18 at 22:28

The first thing to realize is that "mole" is not a mass unit. It is simply a quantity - a number - like dozen or gross or score. Just as a dozen eggs is 12 eggs, a mole of glucose is $6.02 \times 10^{23}$ glucose molecules, and a mole of carbon atoms is $6.02 \times 10^{23}$ carbon atoms. "Moles" are only associated with mass because individual objects have mass, and thus a mole of objects also has a certain mass.

So why $6.02 \times 10^{23}$? What's so special about Avogadro's number? Well, nothing, really, it just makes calculations work out nicely. Avogadro's number is defined as the number of $\ce{^{12}C}$ atoms which weigh 12 g. So it's effectively a ratio: how many times larger is a gram than an atomic mass unit? If you have one atom of $\ce{^{12}C}$, it weighs 12 amu. If you have $6.02 \times 10^{23}$ of them, they weigh 12 g. If you have one molecule of glucose, it weighs 180 amu (or thereabouts). If you have $6.02 \times 10^{23}$ of them, they weigh 180 g (or thereabouts). -- This is just like if one egg weighs 60 g (on average), then a dozen of them weigh 720 g (on average), and if one cup of flour weighs 120 g (on average), then a dozen cups of flour weigh 1440 g (on average). The only difference is that dozen is defined forwards ("a dozen is twelve"), whereas a mole is defined "backwards" ("a dozen is the number of 60 g eggs that are in a collection of eggs that weighs 720 g.")

This convenience definition - pegging the value of Avogadro's number directly to the difference in scale between the amu and the gram - is what is probably throwing you. Moles are not a mass unit, but the definition is intimately tied to mass units. The equivalence in numbers at the atomic scale (amu) and at the macroscopic scale (grams) can also result in chemists playing fast and loose with terminology, quickly working back and forth from atomic to macroscopic scale, without a necessarily clear distinction between the two.

• Note that the SI definitions are to be revised with Avogadro’s number to be turned into a fixed-value constant. That would obsolete the ‘$12~\mathrm{g}\ \ce{^{12}C}$’ definition. Timeframe: Soon™. – Jan Oct 11 '16 at 20:45
• This was a brilliant explanation, thank you! I have a better grasp on the concept now. – teachmechemistry Oct 11 '16 at 21:42
• This also means you can have a mole of moles. what-if.xkcd.com/4 – JAB Oct 11 '16 at 23:13
• Following up on Jan's remark, you can read about the proposed SI changes in the Wikipedia article Proposed redefinition of SI base units – MaxW Oct 12 '16 at 17:23
• Please note that the atomic mass unit (amu) is the obsolete unit that referred to the relative atomic mass of oxygen which was taken as 16 (and unfortunately physicists used the atomic mass of the nuclide $\ce{^16O}$ whereas chemists used the average atomic mass of natural oxygen). The current unit (since 1961), which is defined as 1/12 of the mass of a neutral atom of the nuclide $\ce{^12C}$ in the ground state at rest, is the unified atomic mass unit (symbol: u). – Loong Oct 12 '16 at 18:21

Perhaps a hardware analogy might help. Let's say you're in the business of putting things together using nuts, bolts, and washers. For the sake of argument, let's say that whenever you join something you always need one bolt, two washers, and one nut. Oh, and you're going to be bolting together a lot of stuff.

So, you're going to need a lot of nuts, bolts, and washers, but that's okay, the hardware store sells them by the pound.

The bolts have a mass of 20 carats, the nuts are 5 carats and the washers are 2 carats. What's a carat? Doesn't matter really because you don't know how much stuff you're going to be joining - just "a lot".

So, you go to the hardware store and you buy 20 pounds of bolts, 5 pounds of nuts and 4 pounds of washers.

Now, you have no idea how many nuts, bolts and washers you have, but you do know that you have the same number of nuts as you have bolts and you have twice as many washers. So long as you convert the mass of the item in carats to the weight you buy in pounds, you can always make sure you get the items in the proportions you want.

Down the track a bit, you find out that there are 6,000 carats to the pound. That means 20 pounds of bolts is actually 6,000 bolts, and 5 pounds of nuts is also 6,000 nuts, and 4 pounds of washers is 12,000 washers.

So, in this analogy, a lot (aka a "mole") of items is 6,000 or 6 x 103

If you relocate to a country with a metric system and their hardware stores sell the same bolts, nuts, and washers but by the kilogramme (heresy!), are you in the least bit phased? Nah. You buy 20 kg of bolts, 5 kg of nuts and 4 kg of washers. Now you have 2.2 x 6,000 lots of joiner uppers. So, you're still in business.

The idea with atoms is basically the same, when you convert the mass in amu (or the dalton as I believe is preferred now) to grammes, then the mole is NA or Avogadro's number 6.02 x 1023.

The precise definition of exactly what is an amu (Da) is a fine point, important, but tangential to the concept of the mole which is what you're struggling with. Interestingly, and equally tangentially, Avogadro's number may well be used to redefine what a kilogramme is: https://www.youtube.com/watch?v=ZMByI4s-D-Y

• Analogies should be banned as answers – Ubaid Hassan Apr 21 at 18:25

The first point is that it is a definition. In practical terms it enables us to have a convenient unit to express concentrations as $\pu{mol dm^{-3}}$ without having to use huge numbers. More importantly it allows us to know how many atoms molecules etc. are in a given mass of substance.

A mole is defined as the amount of substance, n, that contains as many objects (atoms, molecules, ions for example) as there are atoms in 12 grammes of carbon-12. This number has been determined by experiment and is approximately $6.02214~10^{23}$. This is Avogadro's number.

If a sample has N atoms or molecules then the amount of substance it contains is $n=N/N_A$ where $N_A$ is Avogadro's constant and is $6.02214~10^{23} \pu { mol^{-1}}$. Thus $\pu {1 mol}$ contains $6.02214~10^{23}$ atoms , molecules or ions etc.

It follows that

The mass of one mole of a substance equals its relative molecular mass expressed in grams,

thus 18 g of water (for simplicity using O = 16; H = 1 instead of exact masses) or 78 g of benzene contains Avogadro's number of molecules, similarly 32 g of sulphur, 200g of mercury, all have Avogadro's number of atom.

Atoms combine on a particle by particle basis. That is, by numbers of particles.

Laboratory and industrial operations rely on measuring masses.

The mole is the bridge between these. It allows us to "count out" a particular number of atoms by massing the substance.

A mole is a quantity of discrete objects, not a dimension for measuring one thing. In the same way that a dozen objects is 12 or a score of objects is 20, a mole of objects is about $6.02214 \times 10^{23}$.

Technically, we shouldn't say "1 mole of glucose". We should instead say "1 mole of glucose molecules". The same goes for any other object: "1 mole of water" should be "1 mole of water molecules", and so on. If we want to speak of raw elements, then we'd be talking about a mole of atoms of that element, rather than a mole of molecules, but the principle is the same. By convention, we usually omit that "molecules" part, but if we really want to be strict about things we should say it.

Avogadro's Number was chosen so that the mass of a mole of molecules (of the same thing) happens to equal $x$ grams, where $x$ is the molecular mass of that thing. Originally, it was defined so that 1 mole of hydrogen (which, remember, is really "1 mole of hydrogen atoms") weighs 1 gram. Nowadays, we define it so that one mole of Carbon-12 (again, "1 mole of Carbon-12 atoms") weighs 12 grams, but the proportions still work out, more or less. The folks behind SI are working on pinning this to a mathematical constant.

Since I rely on my chemistry textbook,so I am gonna provide you the knowledge about one mole I have gained through it.

Mole just indicate the amount of substance,it is SI unit of measurement of amount of substance.Three definitions can be given to a mole;

1. A mole is defined as that amount of substance which has mass equal to the gram atomic mass if substance is atomic or gram molecular mass if the substance is molecular.

For example,$H_2O$ have molecular mass of $18u$ thus its gram molecular mass is $18gram$. So you can say that $18$ gram of $H_2O$ is equivalent to $1$ mole of $H_2O$.

2.A mole is defined as that amount of substance which contains Avogadro's number $(6.022140857×10^{23})$ number of atoms if the substance is atomic or Avogadro's number of molecules if the substance is molecular.

For example, $6.022140857×10^{23}$ molecules of $H_2O$ will form $1$ mole of $H_2O$.

3.In case of gases, a mole is defined as that amount of the gas which has a volume of $22.4$ litres at S.T.P ($101.3kPa$ and $273.15 K$).

For example, At S.T.P $22.4$ litres of $CO_2$ gas will be said $1$ mole of $CO_2$.

• Please note that you are using the old definition of STP ($T=273.15\ \mathrm K$ and $p=1\ \mathrm{atm}=101\,325\ \mathrm{Pa}$) and the corresponding molar volume of an ideal gas of about $V_\mathrm m=22.4\ \mathrm{l/mol}$. This is acceptable since you explicitly mention the temperature and the pressure. However, the value of the standard pressure was changed in 1982 to $p=1\ \mathrm{bar}=100\,000\ \mathrm{Pa}$. At this pressure, the molar volume of an ideal gas actually is $V_\mathrm m=22.710\,947(13)\ \mathrm{l/mol}$. – Loong Oct 12 '16 at 18:50
• YEah a agree,i suppose it was SATP right.Should i edit it. – Vidyanshu Mishra Oct 12 '16 at 18:53
• No, I guess, you do not have to edit that. It’s ok since you explicitly define what STP is supposed to mean in your answer. – Loong Oct 12 '16 at 18:59
• Okay Thanks,i will keep it in mind while writing answers in future – Vidyanshu Mishra Oct 12 '16 at 19:03

Mole is a measure of number. "Mole"-concept helps us to weigh or count definite-numbers of atoms (excluding the minute errors) just using a macroscopic pan-balance. If I know it is glucose, and take 180 gram of it ( since C6 H12 O6 has molecular weight 180); the sample contain 1 moles or avogadro numbers (N.A) or 6.023 * 10 ^ 23 molecules of glucose. Similarly, 18 gram H2O must contain 1 mole or 6.023 * (10 ^ 23) water molecules.

But how?

If we take 1 truck full of bricks and another truck full of brick-chips; the second truck would contain many times more brick chips than bricks in first one. Simple.

But if we took 1 truck brick (total mass of brick very heavy); and 1 bucket brick-chips (total mass of brick-chips much lighter than truckful bricks)... then? Perhaps the both will contain same (at least almost) number of particles.

I.e. if we take heavy objects in massive-amount, and lightweight objects in lighter amount; the number of objects of both cases, would tend to same.

In Quantitative terms:

 Say each brick-chip= 1 gram. 1 brick= 1000 gram.


Now, if we take 1234 * 1 gram brick-chips and 1234 * 1000 gram bricks; we'll get the same number of unit-particles in both case.

 Or if we take   X  *  1 gram brick-chips at a place,
and  X * 1000 gram bricks at another place;
in both case we would get the same number.


Molecular scale

1 atom of hydrogen (H) weigh 1 a.m.u. 1 molecule of Glucose ( C6 H12 O6 ) weighs 180 a.m.u. 1 molecule of H20 weighs 180 a.m.u.

  Now, 1 gram = 6.023 * (10 ^ 23) Dalton or N.A a.m.u.    (  *  )


So just like our above mentioned brick example;

1 gram of hydrogen (H) atom (or N.A amu H) , or 180 gram glucose (i.e. N.A * 180 amu glucose ), or 18 gram water ( N.A * 18 amu water) would contain the same number of particle (Which is here 6.023 * (10 ^ 23) pieces or N.A. pieces due to relationship between gram and amu). This way 1 mole of any substance would contain NA number of molecules

Avogadro number (N.A.) in this example working the same way as X in previous brick example.

Here is a simplified diagram comparing real-life example and chemistry-example.

We're given

1 C6 H12 O6 + 6 O2 = 6 CO2 + 6 H2O

The numbers at left side of compound's formula, or the stoichiometric coefficient; is smallest possible number of molecules to complete a reaction.

we're given certain amount of glucose, and asked for amount of CO2 evolved after complete combustion in O2 ?

We can calculate that freshly from a.m.u. Larger calculation.

But mole concept help a lot since we can determine quantities of reactants and products directly in gram, from molecular formula and stoichiometric coefficients, without using any unit conversion between gram and a.m.u.

If we could multiply the whole reaction

(180 amu + 6 * 32 amu = 6 * 44 amu + 6 * 18 amu for respective compound)

with NA (could run NA numbers of such reactions at a time)

i. e.

180 amu * NA + 6 * 32 amu * NA = 6 * 44 amu * NA + 6 * 18 amu * NA (respective compound)

or

1 mole glucose + 6 mole O2 = 6 mole CO2 + 6 mole H2O.

or

180 gram + 6 * 32 gram = 6 * 44 gram + 6 * 18 gram (respective compound).

once we knew the fact instead molecule we could use mole; and we could easily write reaction for a mole parallel reactions. Then we convert between moles to gram using the chemical formula, we can easily determine the required or obtained amount of certain reactant or product. For a certain given value of 1 reactant or product

for say 2 H2 + O2 = 2 H2O. From this reaction we easily conclude 2 mole of H and 1 mole of O2 forms 2 moles of H2O; or 2 * 2 g H2 and 32 g O2 makes 2 * 18 g H20. Now using unitary method we could find an asked amount of reactant or product from some given amount of reactant or product.

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