Let's break down how to derive valencies for individual elements and then for compounds. Deriving Individual Valencies (for elements) Valency is primarily determined by an atom's desire to achieve a stable electron configuration, usually by having 8 electrons in its outermost shell (an octet), or 2 for hydrogen and helium (a duet). 1. For Main Group Elements (Groups 1, 2, 13-18): Metals (Groups 1, 2, 13): These elements tend to lose* electrons to achieve a stable configuration. Group 1 (Alkali Metals - e.g., Na, K): Have 1 valence electron. They lose 1 electron. So, their valency is 1*. Group 2 (Alkaline Earth Metals - e.g., Mg, Ca): Have 2 valence electrons. They lose 2 electrons. So, their valency is 2*. Group 13 (e.g., Al): Have 3 valence electrons. They lose 3 electrons. So, their valency is 3*. Non-metals (Groups 15, 16, 17): These elements tend to gain* electrons to achieve a stable octet. Group 17 (Halogens - e.g., F, Cl): Have 7 valence electrons. They gain 1 electron. So, their valency is 1* (8 - 7 = 1). Group 16 (e.g., O, S): Have 6 valence electrons. They gain 2 electrons. So, their valency is 2* (8 - 6 = 2). Group 15 (e.g., N, P): Have 5 valence electrons. They gain 3 electrons. So, their valency is 3* (8 - 5 = 3). Group 14 (e.g., C, Si): Have 4 valence electrons. They can either lose 4, gain 4, or more commonly, share 4 electrons. So, their common valency is 4*. Group 18 (Noble Gases - e.g., Ne, Ar): Have a full outer shell (8 valence electrons). They are already stable and generally do not gain, lose, or share electrons. So, their valency is 0*. 2. For Transition Metals (Groups 3-12): These elements often have variable valencies* because they can lose electrons from more than one electron shell. For example, iron can have a valency of 2 (Fe²⁺) or 3 (Fe³⁺). Their valency is usually indicated in the name of the compound (e.g., Iron(II) chloride, Iron(III) oxide) or needs to be determined from the other elements in the compound. Deriving Valencies in a Compound When elements combine to form a compound, their valencies must balance out to make the compound electrically neutral. Step 1: Identify Known Valencies Start with elements whose valencies are usually fixed (like Group 1, 2, 17 elements, or oxygen). Step 2: Use the "Criss-Cross" Method (for simple binary compounds) This method helps determine the formula of a compound given the valencies, or vice-versa. Write the symbols of the elements. Write their valencies above them. Criss-cross the valencies down to become subscripts for the other element. Simplify the ratio if possible. Example 1: Finding the formula of Aluminum Oxide Aluminum (Al) is in Group 13, so its valency is 3. Oxygen (O) is in Group 16, so its valency is 2. Al³ O² Criss-cross: Al₂O₃ The valency of Al is 3, and the valency of O is 2. Example 2: Finding the valency of an unknown element in a compound Let's say you have the compound Fe₂O₃ and you know oxygen's valency is 2. There are 3 oxygen atoms, each with a valency of 2. Total valency contributed by oxygen = 3 × 2 = 6. Since the compound is neutral, the two iron (Fe) atoms must collectively contribute a valency of 6. Therefore, each iron atom must have a valency of 6 / 2 = 3*. (This is Iron(III) oxide). Step 3: For Polyatomic Ions If a compound contains a polyatomic ion (like sulfate SO₄²⁻ or nitrate NO₃⁻), treat the entire ion as a single unit with its own charge (which represents its valency). For example, in Calcium Sulfate (CaSO₄): Calcium (Ca) is in Group 2, so its valency is 2 (Ca²⁺). The sulfate ion (SO₄) has a charge of 2- (SO₄²⁻), so its valency is 2. The valencies balance (2 and 2), so the formula is CaSO₄.