## Chemical Formulae & Valency

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# The Language of Chemistry - 02

## Chemical Formulae & Valency

### Chemical Formula

A chemical formula represents the chemical composition of a substance by depicting the number of atoms of different elements occurring in one fundamental "unit" of the substance. Subscripted numbers in the formula represent the number of atoms present if more than one.

In case of pure elements, the chemical formula is the symbol itself, such as C for carbon. If the element is in the form of molecules, the subscript denotes the number of atoms present in one molecule. Thus, the formula for the diatomic oxygen molecule is O2.

In case of covalent compounds (which consist of discrete molecules) the chemical formula represents a molecule, and so is also called molecular formula. For example, H2O (hydrogen monoxide) is the molecular formula for water, which consists of covalently bonded atoms of hydrogen and oxygen.

For ionic substances, the chemical formula not only represents its formula unit, but is also termed formula unit. Thus, NaCl is the formula unit (chemical formula) of common salt (sodium chloride).

##### Structural formula

In organic chemistry in particular, a molecule is represented by its structural formula, which is a 2-D diagram depicting the bonds between the atoms. A structural formula is more informative than the molecular formula alone.

Ethyl alcohol, whose molecular formula is C2H5OH, has the structural formula as depicted below: $H H | | H — C — C — O — H | | H H$ A structural formula uses lines to indicate the covalent bonds. Thus, in ethyl alcohol, (i) the two carbon atoms are bonded to each other (ii) the lone oxygen atom is bonded to one of the carbon atoms, and (iii) of the six hydrogen atoms, three bond with one carbon, two with the other carbon, and the last with the oxygen atom.

### Valency or Valence

When atoms of one element combine with the atoms of another element to form formula units, they do so in fixed numbers depending upon the capacities of the atoms to form bonds.

Valency of an element is a measure of the combining capacity of its atom to form chemical bonds.

Valency / Valence
Valency is defined as the number of hydrogen or chlorine atoms with which 1 atom of the element would combine.

As a general rule, if an atom participates in ionic bonding, the valency tells the charge on the ion formed. If the atom participates in covalent bonding, the valency tells the number of electrons the atom shares with its partner atom(s).

The following example will clarify the concept of valency:

(a) 1 atom of chlorine combines with 1 atom of hydrogen to form HCl (hydrogen chloride). The valency of chlorine is thus 1 (from the definition of valency).

(b) 1 atom of oxygen combines with 2 atoms of hydrogen to form H2O (water or hydrogen monoxide). The valency of oxygen is thus 2 (from the definition of valency).

(c) 1 atom of carbon combines with 4 atoms of hydrogen to form CH4 (methane). The valency of carbon is thus 4.

(d) 1 atom of magnesium combines with 1 atom of oxygen to form MgO (magnesium oxide). Since we know that oxygen has a valency of 2, i.e. its combining capacity is twice that of hydrogen, so the valency of magnesium also is 2.
##### Easy formula by balancing valencies

It is clear that if we know the valencies of elements, then we can work out the chemical formulae of their compounds by balancing the valencies of the different atoms which occur in the compound, i.e. the total of the valencies of one set of atoms should balance the total of the valencies of the other set.

To illustrate:

(a) Carbon dioxide is made up of carbon and oxygen. We know that the valency of carbon is 4 and that of oxygen is 2. In order for them to combine, we have to balance the valency of 4 of the carbon atom with 2 atoms of oxygen, each of valency 2. Thus, one atom of carbon will combine with two atoms of oxygen to form the molecule CO2 (carbon dioxide).

(b) From the chemical formula of the compound aluminium oxide Al2O3, the valency of aluminium can be determined. Since we know that the valency of oxygen is 2, and there are 3 oxygen atoms, this gives a total value 6 for the valencies of the oxygen atoms, which has to be matched by the 2 atoms of aluminium. Hence the valency of aluminium is 3.

Valency of an element is a whole number and varies from 1 to 8, and is 0 for an element that does not combine with any other element.

##### Elements with multiple valencies

Most elements have a fixed value of valency, but some exhibit two or more different valencies and hence can form two or more different compounds with another element.

There are two naming methods for distinguishing the names of the different compounds formed by the same multiple-valency element. In the older system, the latin name of the element was suffixed with -ous to indicate lower valence or -ic to indicate higher valence. In the newer Stock System, the element's name is followed by its valence in parentheses in Roman numerals.

(a) Iron forms two chloridesFeCl2 (ferrous chloride or iron(II) chloride) and FeCl3 (ferric chloride or iron(III) chloride. The valency of iron is 2 in the former compound and 3 in the latter compound.

(b) Similarly, tin is divalent in SnCl2 (stannous chloride or tin(II) chloride) and tetravalent in SnCl4 (stannic chloride or tin(IV) chloride).

(c) Valency of sulphur is 4 in SO2 (sulphur dioxide) and 6 in SO3 (sulphur trioxide).

As we know, a radical is a group of atoms which can combine with another element as a single unit. Each radical takes part as a whole in chemical reactions and has its own valency.

(a) In H2SO4(sulphuric acid), the radical SO4 combines with 2 atoms of hydrogen to exhibit a valency of 2.

(b) In H2CO3 (carbonic acid), the radical CO3 combines with 2 atoms of hydrogen to exhibit a valency of 2.

(c) In HNO3 (nitric acid), the radical NO3 combines with 1 atom of hydrogen to exhibit a valency of 1.

(d) In H3PO4, (phosphoric acid) the radical PO4 combines with 3 atoms of hydrogen to exhibit a valency of 3.

(e) In NH4Cl (ammonium chloride), the radical NH4 combines with 1 atom of chlorine to exhibit a valency of 1.
##### Easy formula by valency interchange

Notice how while writing the chemical formula for a compound, the subscripts of the constituent elements/radicals are obtained by interchanging the values of valencies (a subscript of 1 is not written by convention), and if there happens to be a common factor between the subscripts, it is factored out.

The following exemplifies this "interchanging" of valencies.

(a) Na (valency 1) + Cl (valency 1) gives NaCl (interchange, but 1 need not be written).
(b) Al (valency 3) + O (valency 2) gives Al2O3 (interchange).
(c) Mg (valency 2) + O (valency 2) gives MgO (interchange; common factor 2 cancels out).
(d) Ba (valency 2) + CO3 (valency 2) gives BaCO3.
(e) Fe (valency 3) + SO4 (valency 2) gives Fe2(SO4)3.

#### Valencies of common elements & radicals

Table gives a list of valencies of some common elements and radicals.

Table 1: Some commonly used valencies
Valency 1: Monovalent
bromine Br acetate CH3COO *
chlorine Cl ammonium NH4+
cuprous or copper(I) Cu bicarbonate (hydrogencarbonate) HCO3
fluorine F bisulphate (hydrogensulphate) HSO4
hydrogen H bisulphite (hydrogensulphite) HSO3
iodine I chlorate ClO3
mercurous or mercury(I) Hg2 chlorite ClO2
potassium K cyanide CN
silver Ag hydroxide (hydroxyl) OH
sodium Na hypochlorite ClO
nitrate NO3
nitrite NO2
perchlorate ClO4
permanganate Mn4
* CH3COO is another way of writing C2H3CO2, as it is easier to remember. This radical falls under organic chemistry, where complex formulae are often written in ways easy to memorise.
Valency 2: Divalent
barium Ba carbonate CO32
calcium Ca dichromate Cr2O72
cobalt Co peroxide O22
cupric or copper(II) Cu silicate Si4O32
ferrous or iron(II) Fe sulphate SO42
magnesium Mg
manganous or manganese(II) Mn
mercuric or mercury(II) Hg
oxygen O
stannous or tin(II) Sn
sulphur S
zinc Zn
Valency 3: Trivalent
aluminium Al ferricyanide Fe(CN)63
auric or gold(III) Au phosphate PO43
chromic or chromium(III) Cr phosphite PO33
ferric or iron(III) Fe
nitrogen N
phosphorus(III) P
Valency 4: Tetravalent
carbon C ferrocyanide Fe(CN)64
silicon Si
stannic or tin(IV) Sn
Valency 5: Pentavalent
nitrogen N
phosphoric or phosphorus(V) P

### Rules for writing chemical formula

There are some basic rules that should be known for writing a chemical formula.

#### Ionic compounds

In general, the entity forming the cation is written first, and then the entity forming the anion. Once the entities are positioned correctly, the subscripts are obtained by interchanging their valencies.

For the case of an ionic compound consisting of a metal and non-metal, the metal is written first (since it forms cations), and then the non-metal (as it forms anions). Thus, we have the formula for common salt as NaCl, not ClNa.

When polyatomic ions, or radicals, are involved, they are treated the same way but as a single unit. The ammonium (NH4+) cation is one of the few polyatomic cations. Most other polyatomic ions are anions.

#### Binary covalent compounds

Except for binary compoundsBinary pertains to "two." A binary compound consists of two kinds of elements. of hydrogen, the formula is written with the first element being the one which is either farther to the left, or lower in the periodic table, unless that element is oxygen or fluorine. Oxygen is always named last, except in its compounds with fluorine. Also, remember that the position towards the left has a higher priority than a position lower in the periodic table.

Once the elements are positioned correctly, the subscripts are obtained by interchanging their valencies.

(a) For a compound of sulphur and chlorine, sulphur will be written first because it is to the left of chlorine in the periodic table.

(b) For a compound of sulphur and iodine, sulphur is written first even though it is lower in the periodic table, since it is to the left of iodine, and the left position has a higher priority than the lower position.

(c) For a compound of oxygen and chlorine, even though oxygen lies to the left of chlorine, chlorine is written first since oxygen is an exception.
##### Hydrogen-based covalent compounds

Binary compounds of hydrogen that are not acids have the hydrogen written last such as in NH3 (ammonia), except for the case of H2O (water) and H2O2 (hydrogen peroxide).

AcidsAcids are hydrogen based compounds which are capable of releasing hydrogen cations in water solution. are a special type of hydrogen containing compounds (some of which are binary) that will be covered later. In the formula for acids, hydrogen is written first, such as in the binary acid HCl (hydrochloric acid).

# Bibliography

Goldberg, DE, Fundamentals of Chemistry, 5th edn, USA: McGraw Hill, 2006.
McMurray, J & Fay, RC, Chemistry, 4th edn, USA: Prentice Hall, 2003.
Mustoe, F et al, Chemistry 11, Canada:McGraw-Hill Reyerson, 2005.