Question

What must be the sum of the oxidation states of all the atoms in a polyatomic ion? For example, the sum of all the oxidation states of all the atoms in \(\mathrm{PO}_{4}^{3-}\) is .

Short answer

The sum of the oxidation states of all the atoms in a polyatomic ion must be equal to the charge of the ion. In the case of the polyatomic ion \(PO_{4}^{3-}\), the sum of the oxidation states is -3. This is determined by finding the oxidation state of each element (phosphorus +5 and oxygen -2), multiplying by the number of atoms, and adding them together: (+5) × 1 (Phosphorus) + (-2) × 4 (Oxygen) = +5 - 8 = -3.

Step-by-step solution

Identify the polyatomic ion

We are given the polyatomic ion PO4³⁻ as an example. This ion consists of one phosphorus atom (P) and four oxygen atoms (O).

Determine the oxidation state of the individual elements

In order to find the sum of the oxidation states for all the atoms in PO4³⁻, we must first determine the oxidation state of each element. For oxygen (O), the oxidation state is usually -2, except in peroxides and superoxides. In this case, since there are no peroxide or superoxide bonds, the oxidation state of oxygen is -2. For phosphorus (P), we can use the rule that the sum of the oxidation states of all the atoms in an ion must be equal to the charge of the ion. Let the oxidation state of phosphorus be x. Since there are four oxygen atoms, each with an oxidation state of -2, the sum of their oxidation state is -8. We can set up an equation to find x: x + (-8) = 3⁻ (the charge of the polyatomic ion)

Solve for the oxidation state of phosphorus

We have the equation x - 8 = -3. Solving for x, we get: \(x = -3 + 8\) \(x = 5\) Thus, the oxidation state of phosphorus (P) in the polyatomic ion PO4³⁻ is +5.

Calculate the sum of the oxidation states

Now we have found the oxidation states of both phosphorus (+5) and oxygen (-2). To find the sum of the oxidation states of all the atoms in the polyatomic ion, we multiply the oxidation state of each element by the number of atoms for that element and then add them together: Sum of oxidation states = (+5) × 1 (Phosphorus) + (-2) × 4 (Oxygen) Sum of oxidation states = +5 - 8 Sum of oxidation states = -3 The sum of the oxidation states of all the atoms in the polyatomic ion PO4³⁻ is -3, which is equal to the charge of the ion.

Key concepts

Polyatomic Ions

In the realm of chemistry, polyatomic ions are clusters of atoms that are bonded together and possess an overall charge. These ions act as individual charged species in chemical reactions and are key to understanding a variety of compounds. For instance, the sulfate ion (SO₄^2-), ammonium ion (NH₄⁺), and the example from our exercise, the phosphate ion (PO₄^3-), are all polyatomic ions.

Polyatomic ions carry either a positive or negative charge, which occurs from having a surplus or deficit of electrons compared to the total number of protons across all atoms in the ion. This charge is not arbitrarily assigned; it is the direct result of the chemical bonding characteristics within the ion and must be balanced when these ions engage in chemical reactions.
A fundamental principle to grasp is that the sum of the oxidation states in a polyatomic ion equals its overall charge. The challenge often lies in determining the individual oxidation states of the different atoms within the ion, as not all atoms have obvious oxidation states.

Chemical Oxidation Numbers

Chemical oxidation numbers, also referred to as oxidation states, are a conceptual tool used to keep track of electrons in chemical reactions, particularly in the context of oxidation-reduction (redox) reactions. Each atom in a compound is assigned an oxidation number that reflects its electronegativity or the tendency of an atom to attract electrons toward itself.

In most cases, the more electronegative element in a binary compound has a negative oxidation state, while the less electronegative element has a positive oxidation state. There are rules that help assign these oxidation numbers: for instance, oxygen usually has an oxidation state of -2, hydrogen is generally +1, and alkali metals in compounds carry a +1 state. In our polyatomic ion example, (PO₄^3-), oxygen, being more electronegative, has a -2 oxidation state, and by balancing the overall charge, phosphorus was determined to have an oxidation state of +5.

Importance of Oxidation Numbers

Oxidation numbers are crucial for balancing chemical equations, understanding redox reactions, and predicting the formation of compounds. For example, reactions like combustion can only be correctly balanced if the oxidation states of each element are accurately determined.

Balancing Charges in Ions

Balancing charges in ions is tantamount to establishing equilibrium among the participating atoms. It is a core tenet of chemical science that in an ion or compound, the sum of the oxidation states must be balanced with the total charge of the species. This balance is an expression of the conservation of charge, a principle that states that the total charge in a closed system remains constant.

In polyatomic ions like (PO₄^3-), this principle guides us to uncover the individual oxidation numbers of the constituent atoms. As demonstrated in the exercise, the oxidation state of phosphorus in the ion was calculated to be +5 when balanced against the -2 oxidation states of each of the four oxygen atoms, resulting in an overall charge of -3, the same as the charge of the ion itself.

Application in Chemical Reactions

Charges must be balanced when polyatomic ions participate in chemical reactions. In precipitation reactions, for example, where two aqueous solutions form a solid precipitate, the charge balance ensures that the precipitate is neutrally charged, with the sum of positive charges equaling the sum of negative charges. Additionally, when writing the formula of a compound containing a polyatomic ion, the charge balance helps in determining the correct ratio of atoms, maintaining electric neutrality of the compound.