EngArc - L - Mole

Mole

Think of the mole as a package that contains 6.022 × 10²³ molecules. The mole is the connection between the microscopic world of molecules and the real world of macroscopic samples.

The mole is defined as an amount of substance containing as many elementary entities as there are atoms in 0.012 kg of carbon-12. These elementary entities must be specified; they may be atoms, molecules, electrons, ions, or other particles or specific groups. For example, one mole of diatomic oxygen, having a molecular weight of 32 (compared to 12 for carbon), has a mass of 0.032 kg. So the mass of a substance in question equals the molecular weight of the substance multiplied by the number of the moles of the substance multiplied by 0.012 kg of carbon-12 all divided by the molecular weight of carbon (which is 12). Or,

mass for substance in question =

(molecular weight of substance in question)*(number of moles of substance in question)*(0.012 kg of carbon-12)

molecular weight of carbon (12)

Or,

m =

0.012nM

= 0.001nM

symbol	description
m	mass
n	number of moles
M	molecular weight

But make sure the correct units are used. The base unit for the mole is mol.

So to rewrite for the number of moles n,

n =

1000m

Where the units for n in this particular case are: [kg/(kg/mol)] = [mol]

But this can be simplified further, the 1000 can be eliminated by converting the units of mol to kmol by dividing by 1000, resulting in:

n =

(where the units are in kmol)

where the units were made to kmol by: [kg/(kg/mol)]*[kmol/(1000 mol)] = [kmol]

The mole is frequently used in thermodynamics.

Counting by weighing and Avogadro's number
The number of atoms or molecules in a lump of mass is so small that it is physically difficult if not impossible to directly count out atoms/molecules. But, atoms/molecules may be counted indirectly by weighing:

The number of nails in a bundle need to be estimated. The weight of the bundle is 1340 g. One nail is individually weighed and comes to be 0.450 g. Therefore, the number of nails = (1340 grams / bundle of nails)*(1 nail/ 0.450 grams ) ≅ 2978 nails.

Avogadro's number is the number of particles that delivers a mole of a substance. Avogadro's number = 6.022 x 10²³.
The mole is tied to the gram mass unit.

If the American system of units was used and amounts were measured in pound moles then Avogadro's number would be larger by a factor of 454. Remember 1 pound = 454 grams. A pound mole of hydrogen-1 (1 proton, 0 neutrons) would weigh 1 pound which would be 454 grams. A gram mole of hydrogen-1 weighs 1 gram and contains 6.022 x 10²³ ¹H atoms.

The average atomic mass for an element like carbon can be found from a periodic table. The average mass is 12.01 amu. This mass is a very tiny number of grams. The molar mass of carbon is defined as the mass in grams that is numerically equal to the average atomic weight. This means
1 gram mole carbon = 12.01 grams carbon.

This is commonly written:

1 mole carbon = 12.01 grams carbon.

This is the mass of carbon that contains 6.022 x 1023 carbon atoms.

Avogadro's number is 6.022 x 10²³ particles.

This same process gives us the molar mass of any element.

1 mole neon = 20.18 grams Ne

1 mole sodium = 22.99 grams Na

number of items in a mole = 6.02 x 10²³

one mole = 6.02 x 10²³ items

If it is asked how many grams are in a mole, it is the same as asking how many grams are in the total 6.02 x 10²³ parts that make up that mole. Well, what is a part? If a part is a particle, then the answer is 1 gram is in 1 mole, or 1 gram is in 6.02 x 10²³ particles.

So a mole can be anything, but, typically when moles are spoken of, it is with respect to the number of particles in something.

Atomic Mass

Unit Conversion