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Section 1: Essentials (physical chemistry)

CHAPTER 1: ATOMIC STRUCTURE
(Introduction and some topics arising)
NB This chapter uses the following fonts: Tahoma, Symbol, wingdings and Windings 3.
Without Windings 3, arrows may appear as a 'D', an 'E' an 'f' a 'g' an 'h' or an 'i', depending on type of arrow.

QUICK SKIPS:
(Click on the 'back' arrow to get back to this quick skip section)

Mass number, atomic number etc
Moles, RAMs and Molar Mass
The Avogadro Constant
The importance of the Mole
More on RAM, RMM etc
Isotopes
Mass spectrometer
Molarity and other measures of concentration

1.1 ATOMIC QUANTITIES

1.1.1. Two numbers give a remarkable amount of information about an atom. They are shown here for sodium (symbol Na):

..mass number: 23
...........................Na
atomic number: 11

1.1.2. The mass number is the total number of protons and neutrons in

the nucleus of the atom. The connection with mass is that protons and neutrons both have relative atomic masses of 1. Since the electrons have negligible mass, the total number of protons and neutrons in a nucleus will be numerically equal to the relative atomic mass of the atom.

1.1.3. The atomic number is the number of protons in the nucleus of an atom, and even more information follows from this.

First, the number of neutrons in the nucleus can be simply calculated:

Mass number - Atomic number = number of neutrons

(12 in sodium)

Second, the number of electrons in the neutral atom can be deduced since it is equal to the number of protons. This makes sense because protons each have a charge of +1 and electrons each have a charge of -1 unit. Moreover, neutrons are (as the name implies) neutral.

1.1.4. The major characteristics of the atomic particles can be summarised:

......................R.A.M........Charge

neutron.............1.................0

proton...............1................+1 unit

electron.............0................-1 unit

The information which can be derived from mass number and atomic number for sodium can be summarised:

.....neutrons + protons = 23
.........................................Na
protons = 11 electrons = 11

.....difference neutrons = 12

1.2. MOLES, RAMS, AND MOLAR MASSES

1.2.1. At this stage it is sensible to sort out some terminology which causes confusion well beyond this level of chemistry. If you are happy with the concepts of moles, RAMS, and molar masses, and with the two main measures of concentration (molarity and gdm^-3), skip to the next chapter, but do so with caution.

The ultimate cause of the confusion is historical. Because of the way our understanding of atoms has evolved, we have been left with some very clumsy concepts. If the history of everyday language had been similar, we might have been left with these definitions:

1.2.2. One dozen of any substance is the amount of substance which contains as many elementary units as there are eggs in 2 British supermarket boxes (exactly) of chickens' eggs.

1.2.3. The yolk constant is the constant of proportionality between amount of substance and number of specified particles of that substance. It is represented by the symbol Y, and has a numerical value of 12; its unit is doz^-1.

Fortunately, dozen has always simply been regarded as a name for the number 12. There is no need for Yolk Constants.

For all practical purposes, you won't go far wrong at this level, if you consider mole as a name for the number 6.023 x 10²³, just as dozen is is another name for the number 12, and don't worry too much about Avogadro constants.

Strictly speaking this is a little risqué. You should remain aware of the following definitions:

1.2.4. One mole of any substance is the amount of substance which contains as many elementary units as there are atoms in 12 grams (exactly) of pure carbon-12.

1.2.5. The Avogadro Constant is the constant of proportionality between amount of substance and number of specified particles of that substance. It is represented by the symbol L, and has a numerical value of 6.023 x 10²³; its unit is mol^-1.

In this context "specified particles" means molecules, atoms, ions, electrons, etc. To work out the number of molecules in 2 moles of oxygen we need to multiply by the Avogadro Constant:

No. molecules in 2 moles = 2 x L

....................................= 2 x 6.023 x 10²³

....................................= 12.046 x 10²³.

Similarly, to work out the number of eggs in 2 dozen we need to multiply by the Yolk Constant (see above):

No. eggs in 2 dozen .......= 2 x Y

....................................= 2 x 12

....................................= 24.

Here, all we are doing is multiplying by the number of eggs in 1 dozen. Similarly, in the preceding molar calculation, we are multiplying by the number of molecules in 1 mole.

Fortunately, the controversy rarely arises. Moles are usually left as moles, and not just because the large numbers are unmanageable:

1.3. THE IMPORTANCE OF THE MOLE

1.3.1. The mole has not become important by chance. Its importance stems from the following fact. If an element has a relative atomic mass (RAM) of X, one mole of its atoms (i.e. 6.023 x 10²³ atoms) will have an actual mass of X grams. In other words, the molar mass is numerically equal to the relative atomic mass.

Thus oxygen has a relative atomic mass of 16, and 6.023 x 10²³ (one mole) of its atoms has an actual mass of 16g, i.e. a molar mass of 16g.

Note that relative atomic mass and molar mass are not the same thing. However, they are numerically equal. Here are the relevant definitions, plus a definition of relative molecular mass:

1.3.2. The relative atomic mass of an element is the ratio of the average mass of its atoms to 1/12 of the mass of a carbon-12 atom;

1.3.3. The relative molecular mass of a compound is the ratio of the average mass of its molecules to 1/12 of the mass of a carbon-12 atom;

1.3.4. Molar mass is the actual mass in grams of 6.023 x 10²³ (one mole of) specified particles of a substance (e.g. atoms of an element, molecules of a covalent compound etc.).

1.4. OTHER TERMS

1.4.1. Relative molecular mass is also used (loosely) for ionic compounds, but it is more correct to use the term, relative formula mass because ionic substances obviously do not contain molecules. They contain minimum groupings of ions, as specified by the chemical formula.

Thus it is the relative mass of an Na⁺/Cl^- ion pair which concerns us in sodium chloride (NaCl). Similarly, it is the relative mass of the 2Na⁺/SO₄^2- grouping in sodium sulphate (Na₂SO₄), and so on.

Certainly there is no shortage of terms and abbreviations used for these few concepts. Here are some of them:

1.4.2. Mole: gram atom, gram molecule (old names);

1.4.3. Relative atomic mass: RAM, A_r, atomic mass (sloppy), atomic weight (even worse);

1.4.4. Relative molecular mass: RMM, M_r, molecular mass (sloppy), molecular weight (even worse), relative formula mass (old but correct, and more correct than relative molecular mass when applied to ionic compounds);

1.4.5. Molar mass: MM, gram molecular mass (old name), gram formula mass (old name), atomic mass and molecular mass (bound to cause confusion), atomic weight and molecular weight (hopeless).

1.5 ISOTOPES

1.5.1. The relative atomic mass of chlorine is 35.5. This is because naturally occurring chlorine comprises two types of atom. Both types have 17 protons, as shown by the atomic numbers of 17. (In fact, it is the number of protons in an atom which ultimately determines its chemical properties and makes it the atom of a particular element.)

However, one type of chlorine atom has 18 neutrons and thus a relative atomic mass of 35, whereas the other type has 20 neutrons and thus a relative atomic mass of 37. Chlorine-35 and chlorine-37 occur naturally in a ratio of 3:1, so the average relative mass of the atoms is therefore 35.5.

The two forms of chlorine are known as isotopes.

1.5.2. Isotopes are different atoms of the same element, having the same numbers of protons, but different numbers of neutrons, and therefore different relative atomic masses.

1.6 THE MASS SPECTROMETER

The mass numbers of the isotopes of an element together with their relative abaundances may be found using a mass spectrometer (see fig1.1).

The vapourised element enters the ionisation chamber where it is bombarded by a stream of high energy electrons. The collision between atoms of the element and the high energy electrons causes one (or sometimes two) of the atoms electrons to be knocked out forming positive ions.

For example, neon comprises two isotopes, neon-20 and neon-22 occuring in the ratio 9:1.

Thus considering 10 atoms of neon entering the ionisation chamber and being ionised we could write:

....20......................................................20
9...Ne..+. 9e^-.....g.....9..Ne⁺. +. 9e^-. +. 9e^-
....10...............bombarding .....................10.....................electrons........bombarding
........................electrons ...............................................knocked out.....electrons

....22................................................22
.....Ne. +. e^-.......g.... Ne^+. +. e^-. +. e^-
....10..............bombarding ................10....................electron........bombarding
................... ....electron .........................................knocked out....electron

The positive ions so formed then pass through holes in parallel plates across which an electric field is applied. The field accelerates the ions as a single stream which next passes through a magnetic field. The magnetic field deflects them according to their mass and charge.

It follows that the settings of the electric and magnetic fields can be adjusted so that only particles of a particular mass/charge ratio will hit the ion detector. (E.g. for neon, one combination of settings will send neon-20 to the ion detector and another setting will send neon-22 to the ion detector.)

The actual mass/charge ratio of a particular ion hitting the ion detector may be calculated from the strength of the electric field, the strength of the magnetic field and the arc of curvature. And, since most of the ions produced will be 1+ ions, the masses of the different isotopes present may be calculated.

Moreover, the relative proportions of different ions hitting the detector is measured by the ion detector. In the graph below (fig 1-2) the height of the peaks (or more correctly the areas under the peaks) gives a measure of the quantity.

As shown in the diagram, for neon the neon-20 and neon-22 isotopes are found to be in the ratio 9:1 and this emanbles the relative atomic mass of neon to be calculated as 20.2.

1.7 MOLARITY AND OTHER MEASURES OF CONCENTRATION

1.7.1. Having previously cleared up the mole, we can sort out molarity before returning to the subject of atomic structure. Molarity is a measure of concentration and should not be confused with the pure and simple mole. Nor should it be confused with another measure of concentration, gdm^-3 (grams per cubic decimetre). And, whilst sorting out confusion, be warned: molarity also goes by other names.

When dealing with solutions, we can easily measure volumes. So, if we want to know how much dissolved substance (solute) there is in a particular volume of solution, it is useful to know how much solute there is in a standard volume of solution. That is, we need a measure of concentration.

The standard volume of solution which has been chosen is 1dm³ (1 litre). The amount of solute dissolved in 1dm³ can be given in grams or moles. This gives rise to two different measures of concentration:

1.7.2. Concentration in gdm^-3 is the mass in grams of solute dissolved in 1dm³ of solution.

1.7.3. Concentration in moles dm^-3 (molarity) is the number of moles of solute dissolved in 1dm^-3 of solution.

Note also that a solution with a molarity of 2 (i.e. containing 2 mol dm^-3)is also known as a 2 molar, or 2M, solution.

The interrelationships amongst the measures of amount of substance (moles and grams) and the measures of concentration (molarity and gdm^-3) are summarised in FIG. 1.3.

FIG 1-3 (Click on diagram to enlarge on a new web page)

1.8. QUESTIONS

1) If an element, X, has an atomic number of 35, and one mole of its atoms has a mass of 80g, deduce the following quantities for the element:

i) relative atomic mass

ii) probable actual mass (in grams) of one of its atoms;

iii) probable mass number of one of its atoms;

iv) number of protons in each atom;

v) number of electrons in a neutral atom;

vi) mass of X₂ molecules which must be dissolved in 1dm³ of

of tetrachloromethane to produce a 1 molar solution.

2) Why has the word "probable" been used in parts ii and iii of question 1? (Clue: see section 1.5. if you get stuck.)

Unless otherwise stated, all materials in this web version of chapter 1 are © 2005 Adrian Faiers MA (Oxon) MCIPR