Question

What is the oxidation state of \(\mathrm{Cl}\) in each ion? (a) \(\mathrm{ClO}^{-}\) (b) \(\mathrm{ClO}_{2}{ }^{-}\) (c) \(\mathrm{ClO}_{3}{ }^{-}\) (d) \(\mathrm{ClO}_{4}^{-}\)

Short answer

The oxidation states of Cl are +1, +3, +5, and +7 in \(\mathrm{ClO}^{-}\), \(\mathrm{ClO}_{2}{ }^{-}\), \(\mathrm{ClO}_{3}{ }^{-}\), and \(\mathrm{ClO}_{4}^{-}\) respectively.

Step-by-step solution

Conceptual Understanding - Oxidation States

Oxidation state refers to the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. The oxidation state of the oxygen is typically -2. For polyatomic ions, the sum of oxidation states of all the atoms must equal the charge of the ion.

Determine Oxidation State in \(\mathrm{ClO}^{-}\)

Let the oxidation state of Cl be represented as x. Since the ion's overall charge is -1 and the oxidation state of oxygen is -2, we can set up the equation: x + (-2) = -1, solving for x gives us the oxidation state of Cl. x = -1 + 2, thus the oxidation state of Cl is +1.

Determine Oxidation State in \(\mathrm{ClO}_{2}{ }^{-}\)

Letting the oxidation state of Cl be x, we have: x + 2(-2) = -1, since there are two oxygen atoms. Solving for x: x = -1 + 4, giving us that the oxidation state of Cl is +3.

Determine Oxidation State in \(\mathrm{ClO}_{3}{ }^{-}\)

With the oxidation state of Cl as x and considering three oxygen atoms: x + 3(-2) = -1. Solving for x: x = -1 + 6, means that the oxidation state of Cl is +5.

Determine Oxidation State in \(\mathrm{ClO}_{4}^{-}\)

Assuming the oxidation state of Cl to be x and having four oxygens: x + 4(-2) = -1. We find x by solving: x = -1 + 8, hence the oxidation state of Cl is +7.

Key concepts

Determining Oxidation Numbers

Understanding how to determine oxidation numbers is a fundamental skill in chemistry, particularly in redox reactions. An oxidation number, often referred to as an oxidation state, is a hypothetical charge that an atom in a molecule or an ion would have if all bonds to atoms of different elements were fully ionic.

Here are the basic rules to determine oxidation numbers:

• The oxidation number for any element in its standard state (uncombined form) is zero.
• For a monoatomic ion, the oxidation number is equal to the charge on the ion.
• Oxygen usually has an oxidation number of -2 in compounds and ions, except in peroxides like H₂O₂ where it's -1, or when it's bonded to fluorine.
• Hydrogen is usually +1 except when bonded to metals in binary compounds where it is -1.

To determine the oxidation number, we consider these rules and the fact that the sum of the oxidation numbers for atoms in a neutral molecule must equal zero, or for a polyatomic ion, the sum must equal the ion's charge. This principle helps us systematically calculate unknown oxidation numbers given the known values.

Balancing Charges in Ions

When determining oxidation numbers in ions, it's crucial to consider the overall charge balance. The sum of the oxidation numbers of all the atoms in a polyatomic ion must equal the charge of that ion. Let's say we have a polyatomic ion with a -1 charge. If one of the elements in the ion has a known oxidation number, we use algebra to solve for the unknown oxidation numbers.

For instance, if we have an ion that contains chlorine and oxygen, and we know oxygen has a typical oxidation state of -2, we set up an algebraic equation that represents the total charge. If the oxidation state of chlorine is 'x' and there are 'n' oxygens, our equation becomes:
\[ x + n(-2) = (\text{charge of the ion}) \]
By solving for 'x', we can determine the oxidation state of chlorine in that ion, ensuring that the charges balance out to the known charge of the ion.

Polyatomic Ion Oxidation States

Polyatomic ions are ions composed of more than one atom. Determining the oxidation states within polyatomic ions follows the same general rules, but it requires an understanding that the sum of the oxidation states must match the ion's overall charge. With multiple atoms, this creates a scenario where one must solve for one or more unknown oxidation states.

For example, in the polyatomic ion \(\mathrm{ClO}_{4}^{-}\), chlorine has an unknown oxidation state, and oxygen has a known oxidation state of -2. Since there are four oxygen atoms, their cumulative contribution to the charge is -8. The total charge of the ion is -1, so we can set up the equation:
\[ x + 4(-2) = -1 \]
By solving this equation, we find that 'x', the oxidation state of chlorine in this instance, is +7. This approach applies across various polyatomic ions, with the principle of charge balance guiding the process of finding each atom's oxidation state.