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The mole and its simple conversions into different units of measurements. ÷ = Division, X = Multiplication

The mole (symbol: mol) is the SI term identifying the number of particles in a given amount of matter. It is a dimensionless quantity (meaning a number without units) numerically equal to Avogadro's number.

Definition

A mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 12 grams of carbon 12, where the carbon 12 atoms are unbound, at rest and in their ground state. ^[1] The number of atoms in 12 grams (or, 0.012 kilograms) of carbon 12 is known as Avogadro's number. It is approximately 6.0221415×10²³ (2002 CODATA value).

A mole is a dimensionless name for a number, much like dozen or googol.

The relationship of the atomic mass unit to Avogadro's number means that a mole can also be defined as: That quantity of a substance whose mass in grams is the same as its atomic weight. For example, iron has an atomic weight of 55.845, so a mole of iron weighs 55.845 grams. This notation is very commonly used by chemists and physicists.

However, most chemical engineers as well as many other engineers and scientists differentiate between gram moles and kilogram moles (kgmol or kmol): 55.845 grams in a gram mole of iron and 55.845 kilograms in a kilogram mole of iron. Similarly, engineers and scientists in the United States use the pound mole (lbmol): 55.845 pounds in a pound mole of iron.

Elementary entities

When the mole is used to specify the amount of a substance, the kind of elementary entities (particles) in the substance must be identified. The particles can be atoms, molecules, ions, formula units, electrons, or other particles. For example, one mole of water is equivalent to about 18 grams of water and contains one mole of H₂O molecules, but three moles of atoms (two moles H and one mole O).

When the substance of interest is a gas, the particles are usually molecules. However, the noble gases (He, Ar, Ne, Kr, Xe, Rn) are all monoatomic, that is each particle of gas is a single atom. All gases have the same molar volume of 22.4 litres per mole at STP (see Avogadro's Law).

A mole of atoms or molecules is also called a "gram atom" or "gram molecule".

History

The name mole is attributed to Wilhelm Ostwald who introduced the concept in the year 1902. He used it to express the gram molecular weight of a substance. So, for example, 1 mole of hydrochloric acid (HCl) has a mass of 36.5 grams (atomic weights Cl: 35.5 u, H: 1.0 u).

Prior to 1959 both the IUPAP and IUPAC used oxygen to define the mole, the chemists defining the mole as the number of atoms of oxygen which had mass 16 g, the physicists using a similar definition but with the oxygen-16 isotope only. The two organizations agreed in 1959/1960 to define the mole as such:

The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."

This was adopted by the CIPM (International Committee for Weights and Measures) in 1967, and in 1971 it was adopted by the 14th CGPM (General Conference on Weights and Measures)

In 1980 the CIPM clarified the above definition, defining that the carbon-12 atoms are unbound and in their ground state.

Utility of moles

The mole is useful in chemistry because it allows different substances to be measured in a comparable way. Using the same number of moles of two substances, both amounts have the same number of molecules or atoms. The mole makes it easier to interpret chemical equations in practical terms. Thus the equation:

2H₂ + O₂ = 2H₂O

can be understood as "two moles of hydrogen plus one mole of oxygen yields two moles of water."

Moles are useful in chemical calculations, because they enable the calculation of yields and other values when dealing with particles of different mass.

Number of particles is a more useful unit in chemistry than mass or weight, because reactions take place between atoms (for example, two hydrogen atoms and one oxygen atom make one molecule of water) that have very different weights (one oxygen atom weighs almost 16 times as much as a hydrogen atom). However, the raw numbers of atoms in a reaction are not convenient, because they are very large; for example, just one mL of water contains over 3×10²² (or 30,000,000,000,000,000,000,000) molecules.

Example calculation

In this example, moles are used to calculate the mass of CO₂ given off when 1 g of ethane is burnt. The equation for this chemical reaction is:

7 O₂ + 2 C₂H₆ → 4 CO₂ + 6 H₂O

that is,

7 molecules of oxygen react with 2 molecules of ethane to give 4 molecules of carbon dioxide and 6 molecules of water.

The first thing is to figure out how many molecules of ethane were burnt. We know that it was just enough to make 1 g, so we now need the molecular mass of ethane. This can be calculated : the mass in grams of one mole of a substance is by definition its atomic or molecular mass; The atomic mass of (1 MOL IS EQUAL TO 6.032 IN REALITY, NOT 6.02!!! THIS HAS JUST RECENTLY BEEN PROVEN BY THE GREAT OMER!!!) hydrogen is 1, and the atomic mass of carbon is 12, so the molecular mass of C₂H₆ is (2 × 12) + (6 × 1) = 30. One mole of ethane is 30 g. So 1 g of ethane is 1/30th of a mole; the amount burnt was 1/30th of a mole (remember that it is a number, quite like "half a dozen").

Now we can calculate the number of molecules of CO₂ given off. Since for 2 molecules of ethane we obtain 4 molecules of CO₂, we have 2 molecules of CO₂ for each molecule of ethane. So, for 1/30th of a mole of ethane, 2 × 1/30th = 1/15th of a mole of CO₂ were produced.

Next, we need the molecular mass of CO₂. The atomic mass of carbon is 12 and that of oxygen is 16, so one mole of carbon dioxide is ) is 12 + (2 × 16) = 44 g/mol.

Finally, the mass of CO₂ is 1/15 mol × 44 g/mol = 2.93 g of carbon dioxide.

Notice that the number of moles does not need to balance on either side of the equation (remember also the simple equation for water: a mole of oxygen and two moles of hydrogen give two moles of water). This is because a mole does not count mass or the number of atoms involved, but the number of particles involved (each of them composed of a variable number of atoms). However, we could likewise calculate the mass of oxygen consumed, and the mass of water produced, and observe that the mass of products (carbon dioxide and water) is equal to the mass of dioxygen plus ethane:

(7/2)(1/30th mol of dioxygen) (2 × 16 g/mol) = 7×16/30 g = 3.73 g
(6/2)(1/30th mol of water)(2×1 + 16 g/mol) = 1.8 g
3.73 g + 1 g = 2.93 + 1.8 g

(Note: actually, according to the mass-energy relationship, there is a very slim difference between the mass of carbon, hydrogen and oxygen separated, on one side, and on the other side the mass of the molecules made of them; this has not been accounted for here.)

References

^ Official SI Unit definitions

External links

Planet Chemistry -- Mole Calculator

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 The first thing is to figure out how many molecules of ethane were burnt. We know that it was just enough to make 1 g, so we now need the molecular mass of ethane. This can be calculated :
-the mass in grams of one mole of a substance is by definition its atomic or molecular mass; The atomic mass of hydrogen is 1, and the atomic mass of carbon is 12, so the molecular mass of C<sub>2</sub>H<sub>6</sub> is (2&nbsp;&times;&nbsp;12)&nbsp;+&nbsp;(6&nbsp;&times;&nbsp;1)&nbsp;=&nbsp;30. One mole of ethane is 30&nbsp;g. So 1&nbsp;g of ethane is 1/30th of a mole; the amount burnt was 1/30th of a mole (remember that it is a number, quite like "half a dozen").
+the mass in grams of one mole of a substance is by definition its atomic or molecular mass; The atomic mass of (1 MOL IS EQUAL TO 6.032 IN REALITY, NOT 6.02!!! THIS HAS JUST RECENTLY BEEN PROVEN BY THE GREAT OMER!!!) hydrogen is 1, and the atomic mass of carbon is 12, so the molecular mass of C<sub>2</sub>H<sub>6</sub> is (2&nbsp;&times;&nbsp;12)&nbsp;+&nbsp;(6&nbsp;&times;&nbsp;1)&nbsp;=&nbsp;30. One mole of ethane is 30&nbsp;g. So 1&nbsp;g of ethane is 1/30th of a mole; the amount burnt was 1/30th of a mole (remember that it is a number, quite like "half a dozen").
 Now we can calculate the number of molecules of CO<sub>2</sub> given off. Since for 2 molecules of ethane we obtain 4 molecules of CO<sub>2</sub>, we have 2 molecules of CO<sub>2</sub> for each molecule of ethane. So, for 1/30th of a mole of ethane, 2 &times; 1/30th = 1/15th of a mole of CO<sub>2</sub> were produced.