Mole concept & Avogadro’s constant
Mole concept & Avogadro’s constant;
1.1.1: Describe the mole concept and apply it to substances. The mole concept applies to all kinds of particles: atoms, molecules, ions, formula units etc. The amount of substance is measured in units of moles. The approximate value of Avogadro’s constant (L), 6.02 x 1023 mol-1, should be known.
Atoms and molecules are pretty small (understatement!) and, as scientists are interested in being able to describe quantities of matter in terms of the mass and number of particles contained per unit mass, this poses a problem.
Measuring the mass of individual atoms, we find that one hydrogen atom has a mass of about 1.66 x 10-27g
This number is far too small to be useful and so it makes sense to deal with quantities of atoms which can be measured in the laboratory.
Table of Contents
The hydrogen standard
Hydrogen is the smallest atom and it was originally used as the standard by which all the other atoms were compared. It was assigned a value of 1 unit and other atoms masses calculated compared to hydrogen atoms.
The 1H isotope has a mass assigned a value of exactly 1 atomic mass unit. This was the original reference.
 | The 1H isotope |
The carbon 12 standard
Nowadays the 12C isotope is used as a reference for comparison of relative atomic masses. This isotope has the assigned mass of 12.00000, all other atoms are measured relative to 12C.
.gif?resize=100%2C104&ssl=1) | The 12C isotope |
Measured on this scale hydrogen atoms (on average) have a relative mass of 1.00797
Carbon atoms have a relative mass of 12.01111 on average. Although this seems strange at first sight, it is because carbon has several isotopes 12C, 13C, and 14C and the relative mass of carbon is given as the weighted average of all of the isotopes in a naturally occurring sample. Clearly, the average must be greater than 12.0000.
Most tables use the relative atomic masses rounded up to one or two decimal places.
Carbon atoms have a mass approximately 12 times that of a hydrogen atom, therefore they have a RELATIVE mass of 12 (there are no units as it is a comparison – see relative measures)
| number of hydrogen atoms | number of carbon atoms | mass of hydrogen atoms | mass of carbon atoms | mass of carbon:mass of hydrogen ratio |
|---|---|---|---|---|
| 1 | 1 | 1 | 12 | 1:12 |
| 2 | 2 | 2 | 24 | 1:12 |
| 10 | 10 | 10 | 120 | 1:12 |
| 20 | 20 | 20 | 240 | 1:12 |
| 50 | 50 | 50 | 600 | 1:12 |
Provided the number of carbon atoms is equal to the number of hydrogen atoms the mass of carbon is always 12 times the mass of hydrogen.
Clearly there will be a specific number of hydrogen atoms that when weighed have a mass of 1g and that the same number of carbon atoms MUST have a mass of 12g. This number, named after its discoverer is called:
| Avogadro’s constant = 6.02 x 1023 |
Avogadro’s number
Avogadro’s number or constant is the number to which the mass of an atom must be multiplied to give a mass in grams numerically equal to its relative atomic mass.
| ExampleHydrogen has a relative atomic mass of 1 therefore 6.02 x 1023 hydrogen atoms have a mass of 1gCarbon has a relative mass of 12 therefore 6.02 x 1023 carbon atoms have a mass of 12gMagnesium has a relative atomic mass of 24 therefore 6.02 x 1023 magnesium atoms have a mass of 24g |
This gives rise to two important definitions
- The amount of any substance containing an Avogadro number of particles of that substance is called a mole.
- 1 mole of any substance has a mass equal to its relative mass expressed in grams
| Example1 mole of magnesium contains 6.02 x 1023 magnesium atoms1 mole of magnesium has a mass of 24g12g of magnesium is equivalent to 1/2 moles = 0.5 moles of magnesium12g of magnesium contains 1/2 moles of magnesium atoms = 0.5 x 6.02 x 1023 = 3.01 x 1023 magnesium atoms |
The relationship between moles, mass and number of particles can be expressed by simple formulae:
The structure of matter
It is now accepted that matter in all its forms is made up of indivisible particles that themselves have mass. These particles are called atoms, molecules and ions. The nature of the substance is dictated by the atoms elements that have bonded together to make the bulk substance. This may be an ionic structure, a covalent structre or a metallic structure.
Molecules are made up of two or more atoms chemically bonded together.
Ions are specialised atoms or groups of atoms chemically combined together that have lost or gained electrons and posess an overall electrical charge.
The fundamental particle that is the building block of matter is therefore the atom. There are about 90 naturally occuring types of atoms each with a different arrangement of sub-atomic particles (protons, neutrons and electrons) and consequently different masses.
The structure of matter is one of the following:
- atoms —> molecules —> bulk compound or element
- atoms —> bulk element
- atoms —> ions —> bulk ionic compound
The masses that are measured in the laboratory are masses corresponding to vast numbers of tiny atoms or molecules. Logically atoms that are heavier will register larger masses for equal numbers of atoms.
Relative atomic mass
If one carbon atom has a mass of 12 atomic mass units and one magnesium atom has a mass of 24 atomic mass units, then as a magnesium atom is twice as heavy as a carbon atom it follows that this ratio will be maintained for any number of atoms.
On the atomic mass scale the carbon 12 isotope is designated a value of 12 atomic mass units and all other masses are measured relative to this (relative atomic mass)
The mole concept
It is convenient to consider the number of atoms needed to make 12g of carbon and for this number to be given a name – one mole of carbon atoms. This allows us to talk about relative quantities of substances in the macroscopic world and to know the relative number of atoms (or smallest particles) in each bulk substance.
The actual number of atoms that is needed to give the relative atomic mass expressed in grams is called Avogadro’s number (symbol L)
Avogadro’s number = 6,02 x 1023
Definition of a mole
There are two useful definitions.
- The relative atomic (molecular) mass of a substance expressed in grams
- An Avogadro number of particles of any substance
| Example 1:one mole of carbon = 12g magnesium atoms are twice as heavy as carbon atoms therefore 1 mole of magnesium = 24g Example 2. equal masses of carbon and magnesium contain different numbers of atoms.6g of carbon contains 6/12 moles of carbon =0,5 moles6g of magnesium contains 6/24 moles of magnesium =0,25 moles |
| Example: Sodium carbonate crystals (27.8230g) were dissolved in water and made up to 1.00 dm3. 25.0 cm3 of the solution were neutralised by 48.8 cm3 of hydrochloric acid of conc 0.100 mol dm-3. Find n in the formula Na2CO3.nH2O48.8 cm3 of 0.1M HCl = 0.00488molesNa2CO3 + 2HCl –> NaCl + CO2 + H2Otherefore moles of Na2CO3 = 0.00488/2 = 0.00244molesThis is in 25cm3 therefore the moles in 1000cm3 = 0.00244/0.025 =0.0976molesIf the formula = Na2CO3.nH2OThen the neutralisation has measured only the Na2CO3Therefore the mass of Na2CO3 = RMM x no of moles = 106 x 0.0976 = 10.3456gThe remaining mass must be due to water = 27.823 – 10.3456 = 17.4774gRMM of water = 18 therefore this is equivalent to 17.4774/18 moles = 0.971Thuus the mole ratio of Na2CO3 to water in the original compound = 0.096 : 0.971or approximately 1 :10The formula is therefore Na2CO3.10H2O |
| Example 3.How many atoms are there in 24g carbon24g of carbon = 24/12 moles = 2 moles1 mole of atoms = 6,02 x 1023therefore 2 moles of carbon contains 2 x 6,02 x 1023 atoms = 1,204 x 1024 atoms |
1.1.2: Calculate the number of particles and the amount of substance (in moles). Convert between the amount of substance (in moles) and the number of atoms, molecules or formula units
1 mole = 6.02 x 1023 formula units of that substance.
We can also talk about the atoms within molecules.
For example, 1 mole of water contains 2 moles of hydrogen atoms and 1 mole of oxygen atoms. It is a simple matter of multiplying the moles of the compound by the atoms or ions that make it up.
