Determining oxidation states in magnesium and beryllium hydroxides

Charge and valence, rules for calculation oxidation state

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One of the key con­cepts that al­lows us to de­scribe the ox­i­da­tion and re­duc­tion prop­er­ties of mol­e­cules is the ox­i­da­tion state. This is only an aux­il­iary quan­ti­ty: it does not de­scribe the true charge on each of the atoms in the mol­e­cule, but helps to get an idea how the giv­ing up and ac­cep­tance of elec­trons takes place in ox­i­da­tion and re­duc­tion re­ac­tions. There is a cer­tain method that helps us to cal­cu­late cor­rect­ly the ox­i­da­tion states for each atom.

How to de­ter­mine the ox­i­da­tion state in a sim­ple sub­stance

Sub­stances are called sim­ple which con­sist of atoms of the same kind. For ex­am­ple, sim­ple sub­stances in­clude oxy­gen (O₂), hy­dro­gen (H₂), sodi­um (Na), beryl­li­um (Be), io­dine (I₂), ozone (O₃) and oth­ers.

Each of these sub­stances has a zero ox­i­da­tion state. This can be ex­plained by the fact that the elec­trons in mol­e­cules of this type do not shift any­where. In di­atom­ic mol­e­cules con­sist­ing of atoms of one el­e­ment, a co­va­lent non-po­lar bond is re­al­ized (Cl-Cl; H-H): as bond­ed atoms are equal, the dis­place­ment of elec­tron den­si­ty to any oth­er atom is not ob­served, and so the move­ment of elec­trons does not take place. In monoatom­ic mol­e­cules (for ex­am­ple he­li­um He, Ar­gon Ar), the ox­i­da­tion state is also zero.

How to de­ter­mine ox­i­da­tion states in com­plex sub­stances

Sub­stances are called com­plex which con­sist of two or more types of atoms.

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For ex­am­ple, ta­ble salt NaCl is a com­plex (or bi­na­ry, i.e. con­sist­ing of atoms of two types) com­pound, as it con­tains atoms of dif­fer­ent elec­tron con­fig­u­ra­tions that are chem­i­cal­ly con­nect­ed to each oth­er. In these com­pounds you can place the non-zero ox­i­da­tion states, as a move­ment of elec­tron den­si­ty is ob­served to the most elec­tri­cal­ly neg­a­tive el­e­ment. In sodi­um chlo­ride, the elec­tri­cal neg­a­tiv­i­ty is high­er in chlo­rine (this non-met­al is a strong ox­i­diz­er, and so its elec­tri­cal neg­a­tiv­i­ty is much high­er than sodi­um, which is a re­duc­er). The ox­i­da­tion state of sodi­um is +1, and the ox­i­da­tion state of chlo­rine is -1.

To es­tab­lish the cor­rect ox­i­da­tion state on an atom in a com­pound, we may use the fol­low­ing rules.

1. The ox­i­da­tion state of oxy­gen in com­pounds is usu­al­ly -2 (an ex­cep­tion is per­ox­ide (for ex­am­ple Na₂O₂) and su­per­ox­ides (KO₂), where the ox­i­da­tion state of oxy­gen is -1 and -1/2 re­spec­tive­ly; in ozonides such as KO₃ the ox­i­da­tion state of oxy­gen is -1/3; oxy­gen only has the pos­i­tive ox­i­da­tion state of +2 in the com­pound with flu­o­rine OF₂).

2. The ox­i­da­tion state of flu­o­rine is al­ways -1.

Beta-fluorine crystal structure.gif
By Giovani Rech - Own work, CC BY-SA 4.0, Link

An­i­ma­tion show­ing the crys­tal struc­ture of beta-flu­o­rine

3. The max­i­mum ox­i­da­tion state of an el­e­ment is fre­quent­ly equal to the num­ber of the group it is lo­cat­ed in; ex­cep­tions are oxy­gen (+2), flu­o­rine (-1), iron (+6), the sub­group of nick­el (+3, more rarely +4), and no­ble gas­es.

4. The min­i­mum neg­a­tive ox­i­da­tion state is cal­cu­lat­ed ac­cord­ing to the for­mu­la: the num­ber of the group mi­nus 8 (in cal­cu­lat­ing the va­lence, the for­mu­la is cal­cu­lat­ed vice ver­sa – the num­ber of the group is sub­tract­ed from 8).

5. Ox­i­da­tion states of sim­ple monoatom­ic ions are equal to their charges (for ex­am­ple, Na(+) has both a charge of 1+ and an ox­i­da­tion state of +1; a sim­i­lar sit­u­a­tion ex­ists with Mg(2+), F(-) etc.).

6. In non-ion­ic com­pounds, the ox­i­da­tion de­gree of hy­dro­gen is +1 (an ex­cep­tion is com­pounds with sil­i­con and ar­senic SiH₄ и AsH₃; in hy­dro­gen hy­drides hy­dro­gen also has a neg­a­tive ox­i­da­tion state: in NaH sodi­um has an ox­i­da­tion state of +1, while hy­dro­gen has an ox­i­da­tion state of -1).

7. In com­pounds of non-met­als, which do not con­tain hy­dro­gen or oxy­gen, the atom with the neg­a­tive ox­i­da­tion state is the one with a high­er elec­tri­cal neg­a­tiv­i­ty (it can be seen in the cor­re­spond­ing ref­er­ence ta­ble): the val­ue of the ox­i­da­tion state in these com­pounds for a more elec­tri­cal­ly neg­a­tive non-met­al cor­re­sponds to the charge of its most wide­spread ion (in car­bon sul­fide CS₂ car­bon has the ox­i­da­tion state of +4, while sul­fur is a more elec­tri­cal­ly neg­a­tive atom, and its most com­mon ion has the charge of -2.

Carbon sulfide CS₂ [Wikimedia]

Ac­cord­ing to these rules, we can cal­cu­late the ox­i­da­tion states of atoms for any mol­e­cule.

Cal­cu­lat­ing ox­i­da­tion states in com­plex mol­e­cules

The sum­ma­ry ox­i­da­tion of a mol­e­cule should be zero, as the mol­e­cule is neu­tral.

Cal­cu­lat­ing val­ues for el­e­ments which can have sev­er­al ox­i­da­tion states

In cal­cu­lat­ing sum­ma­ry ox­i­da­tion states, at­ten­tion is al­ways paid to in­dices: in the per­chlo­ric acid mol­e­cule HClO₄ oxy­gen has the ox­i­da­tion state of -2. As there are 4 oxy­gen atoms in the mol­e­cule, its ox­i­da­tion state is mul­ti­plied by 4: -2*4 = -8.

This plays a role in de­ter­min­ing ox­i­da­tion states in el­e­ments in which this val­ue may vary. Chlo­rine has many pos­si­ble ox­i­da­tion states, so the val­ue for HClO₄ may be cal­cu­lat­ed math­e­mat­i­cal­ly, with the equa­tion:

+1 + х + (-2)*4 = 0

х = +7

The ox­i­da­tion state of chlo­rine in per­chlo­ric acid is +7, as each of the 4 oxy­gen atoms have an ox­i­da­tion state of -2, this val­ue is +1 for hy­dro­gen, and the mol­e­cule must have a zero ox­i­da­tion state in this sum).

Equa­tion of ox­i­da­tion states of el­e­ments in mag­ne­sium and beryl­li­um hy­drox­ides

Magnesium hydroxide [Wikimedia]

In mag­ne­sium hy­drox­ide Mg(OH)₂ there are two hy­dro­gen atoms with an ox­i­da­tion state of +1 and two oxy­gen atoms with ox­i­da­tion states of -2. If these ox­i­da­tion states are added tak­ing the in­dices into ac­count, we may re­ceive the val­ue of -2: (+1)*2+(-2)*2= -2.

The ox­i­da­tion state of mag­ne­sium in the com­pound is +2 (as mag­ne­sium is a mem­ber of the sec­ond group of the pe­ri­od­ic ta­ble).

When we add the val­ues, we get zero: +2+(-2)=0.

This means that the ox­i­da­tion states have been cal­cu­lat­ed cor­rect­ly: for mag­ne­sium the val­ue is +2, for oxy­gen -2 and for hy­dro­gen +1.

All atoms in mag­ne­sium hy­drox­ide Mg(OH)₂ have fixed val­ues of ox­i­da­tion states, so this com­pound is a rather sim­ple case for de­ter­min­ing con­di­tion­al charges in atoms.

The sit­u­a­tion with beryl­li­um hy­drox­ide Be(OH)₂ is sim­i­lar: the ox­i­da­tion state of beryl­li­um al­ways cor­re­sponds to its charge and is +2, the ox­i­da­tion state of oxy­gen of com­pounds is -2, and of hy­dro­gen +1. If these val­ues are added tak­ing into ac­count the in­dices, we get zero:

+2 + (-2 + (+1))*2 = 0.

How the ox­i­da­tion state dif­fers from va­lence and charge

The ox­i­da­tion state, va­lence and charge of an el­e­ment are of­ten iden­ti­cal in val­ue. Nev­er­the­less, these con­cepts have a dif­fer­ent mean­ing. The ox­i­da­tion state is the con­di­tion­al charge on each atom in the com­pound (it is writ­ten above each atom, and first its al­ge­bra­ic sign must be in­di­cat­ed, and then the nu­mer­i­cal val­ue). The ion charge is writ­ten dif­fer­ent­ly: for sim­ple ions it is also writ­ten above the el­e­ment sym­bol, but first its val­ue is in­di­cat­ed, and then the al­ge­bra­ic sign (for ex­am­ple, 2+). For com­plex ions (such as the sul­fate ion SO₄²⁻), the charge is not in­di­cat­ed above the spe­cif­ic el­e­ment, as the ox­i­da­tion state, but above the en­tire com­plex ion. Click here to find out more about ox­i­da­tion states.

The charge is con­nect­ed with its ox­i­da­tion states: for ex­am­ple in Mg(OH)₂ two hy­drox­yl groups are present. The charge of the OH group is al­ways (1-). Ac­cord­ing to the rules, the sum of the ox­i­da­tion states of atoms in this group should be equal to its charge (for the OH group, which con­sists of oxy­gen and hy­dro­gen, this rule is ob­served, as -2+1=-1).

Giv­en that there are two OH groups in mag­ne­sium hy­drox­ide, we may say that their sum­ma­ry charge is (2-). The ox­i­da­tion state of mag­ne­sium (+2) co­in­cides with its charge (2+).

Va­lence is the abil­i­ty of atoms to form a cer­tain num­ber of chem­i­cal bonds. It can only have a pos­i­tive val­ue. Of­ten va­lence co­in­cides with the ox­i­da­tion lev­el in its nu­mer­i­cal val­ue, but there are also cer­tain ex­cep­tions – in ni­tric acid HNO₃ the va­lence of ni­tro­gen is IV, but the ox­i­da­tion state is +5.


In molec­u­lar ni­tro­gen a triple bond is re­al­ized be­tween atoms (so va­lence is III), but the ox­i­da­tion state is 0. Va­lence may be de­ter­mined by the struc­tural for­mu­la of the sub­stance.

The ox­i­da­tion state plays a key role in record­ing the ox­i­da­tion-re­duc­tion pro­cess­es by the method of elec­tron bal­ances. The elec­tron bal­ance is the sim­plest method of record­ing the move­ment of elec­trons in a re­ac­tion, in which not real par­ti­cles are ex­am­ined, which ex­ist in a so­lu­tion (for ex­am­ple ions), but only atoms in com­pounds, which change their ox­i­da­tion states, giv­ing and tak­ing elec­trons.