Oxidation state and hydration energy: small and charged wins

The problem

Sulphur is +6 in sulphuric acid and −2 in hydrogen sulphide. Same atom, two opposite numbers. Is the book contradicting itself? No: the number simply depends on whether sulphur is counting its electrons or its empty places.

The second idea is about water. Drop a tiny, highly charged ion like Al³⁺ into water and a huge amount of heat comes out. A big ion with a single charge, like K⁺, gives out far less.

Oxidation state is the charge, with its sign, that an atom would carry in a compound. It is zero for an element in its free state, and it is directly or indirectly related to the element's valence electrons, which its group tells you.

Key terms

Groups 1, 2, 13 and 14 (IA to IVA)

These elements show an oxidation state equal to their valence electrons: +1 in group 1, +2 in group 2, +3 in group 13 and +4 in group 14. Boron, aluminium and gallium in group 13 (IIIA) always show +3.

Groups 15 to 18 (VA to VIIIA)

Here the oxidation state is either the number of valence electrons or the number of vacancies. Sulphur is +6 in H₂SO₄ and −2 in H₂S. Halogens are mostly −1; noble gases, with no vacancy, are usually zero.

Transition elements

Transition elements (groups 3 to 12, the old B subgroups) can show their old group number, as in Cu(I), Zn(II), V(V), Cr(VI) and Mn(VII). But partly filled d orbitals make more electrons available, so they usually show more than one oxidation state.

Hydration energy

The heat absorbed or evolved when one mole of gaseous ions dissolves in water to give an infinitely dilute solution. It depends mainly on the ion's charge-to-size ratio.

Short questions with model answers

1. Q1. Find the oxidation state of sulphur in H₂SO₄ and in H₂S.

   • H₂SO₄: 2(+1) + x + 4(−2) = 0
   • x = 8 − 2 = +6
   • H₂S: 2(+1) + x = 0 → x = −2

   H₂SO₄: +6 · H₂S: −2

2. Q2. Explain why hydration energies follow the order Al³⁺ > Mg²⁺ > Na⁺.

   • Na⁺ −390 · Mg²⁺ −1891 · Al³⁺ −4613 kJ mol⁻¹
   • Across period 3 the charge rises (+1, +2, +3) while the ions get smaller.

   The charge-to-size ratio increases from Na⁺ to Al³⁺, so the hydration energy does too.

3. Q3. SnCl₄ is a covalent compound. Find the oxidation state of tin.

   • Chlorine is more electronegative, so it takes −1.
   • x + 4(−1) = 0 → x = +4

   Sn: +4

Common mistakes

• ✗ Writing that the oxidation state of an element is related to its period number.

  ✓ It is related to the group number. That is why it stays almost constant down a group and changes along a period.

• ✗ Saying Na⁺ has the higher hydration energy because −390 is a bigger number than −4613.

  ✓ The minus sign only says heat is given out. Compare the sizes: Al³⁺ gives out 4613 kJ mol⁻¹, far more than Na⁺'s 390.

• ✗ Writing that halogens usually show +7 because they are in group 17 (VIIA).

  ✓ In group 17 (VIIA) the oxidation state is mostly −1: the number of vacancies, not the number of electrons.

MCQs

1. 1. The oxidation state of an element in its free state is:

   1. (a) +1
   2. (b) −1
   3. (c) 0
   4. (d) equal to its group number
   Show answer

   (c) Zero: an uncombined atom has neither gained nor lost electrons.

2. 2. The oxidation state of sulphur in H₂S is:

   1. (a) +6
   2. (b) +2
   3. (c) −2
   4. (d) 0
   Show answer

   (c) 2(+1) + x = 0, so x = −2: the two vacancies in sulphur's outer shell.

3. 3. Which ion in Table 1.2 has the highest hydration energy?

   1. (a) Li⁺
   2. (b) Mg²⁺
   3. (c) Al³⁺
   4. (d) F⁻
   Show answer

   (c) Al³⁺ at −4613 kJ mol⁻¹: the highest charge on a small ion.

4. 4. Down group 1 (IA: Li⁺ → Na⁺ → K⁺), hydration energy:

   1. (a) increases
   2. (b) decreases
   3. (c) stays the same
   4. (d) becomes positive
   Show answer

   (b) It decreases (499 → 390 → 305 kJ mol⁻¹ given out) because the ions grow while the charge stays +1.

5. 5. Transition metals usually show variable valency because of their:

   1. (a) complete outer shells
   2. (b) partly filled d orbitals
   3. (c) single valence electron
   4. (d) large atomic size
   Show answer

   (b) Partly filled d orbitals make extra electrons available for bonding, so several oxidation states are possible.

Quick revision

• Groups 1, 2, 13 and 14 (IA to IVA): oxidation state = valence electrons (+1, +2, +3, +4). Groups 15 to 18 (VA to VIIIA): valence electrons or vacancies (S: +6 in H₂SO₄, −2 in H₂S). Free elements: zero.
• Transition elements usually show more than one oxidation state because of partly filled d orbitals.
• Hydration energy depends on charge-to-size ratio: it falls down group 1 (IA) and rises across period 3 (Al³⁺ > Mg²⁺ > Na⁺).