Question

Determine the oxidation numbers of all the elements in each of the following compounds. (Hint: Look at the ions present.) (a) \(\mathrm{Mn}\left(\mathrm{ClO}_{2}\right)_{2}\) (b) \(\mathrm{Fe}_{2}\left(\mathrm{CrO}_{4}\right)_{3}\) (c) \(\mathrm{HgCr}_{2} \mathrm{O}_{7}\) (d) \(\mathrm{Co}_{3}\left(\mathrm{PO}_{4}\right)_{2}\)

Short answer

(a) Mn = +6, Cl = +3, O = -2; (b) Fe = +3, Cr = +6, O = -2; (c) Hg = +2, Cr = +6, O = -2; (d) Co = +2, P = +5, O = -2.

Step-by-step solution

Understand the problem

We are tasked with determining the oxidation numbers of each element in the given compounds. The compounds are written in their empirical formulas, and we must find the individual oxidation states.

Determine oxidation numbers for (a) \(\mathrm{Mn(ClO_{2})_{2}}\)

For \(\mathrm{ClO_{2}^{-}}\), assign \(\mathrm{O}\) a typical oxidation number of \(-2\). Let \(x\) be the oxidation number of \(\mathrm{Cl}\). Thus, \(x + 2(-2) = -1\). Solving gives \(x = +3\). In \(\mathrm{Mn(ClO_{2})_{2}}\), as a neutral compound, the overall charge is zero. Let \(y\) be \(\mathrm{Mn}\)'s oxidation number. So, \(y + 2(+3) = 0\), giving \(y = -6\).

Determine oxidation numbers for (b) \(\mathrm{Fe_{2}(CrO_{4})_{3}}\)

For \(\mathrm{CrO_{4}^{2-}}\), \(\mathrm{O}\) has oxidation number \(-2\), making the total for four \(\mathrm{O}\) atoms \(-8\). Let \(x\) be \(\mathrm{Cr}\)'s oxidation number so that \(x - 8 = -2\). Solving gives \(x = +6\). Since \(\mathrm{Fe}\)'s oxidation state and \(\mathrm{CrO_{4}^{2-}}\) charge must sum to zero, let \(y\) be \(\mathrm{Fe}\)'s oxidation number: \(2y + 3(-2) = 0\). Solving: \(2y - 6 = 0\), gives \(y = +3\).

Determine oxidation numbers for (c) \(\mathrm{HgCr_{2}O_{7}}\)

\(\mathrm{O}\) has an oxidation number of \(-2\), so for \(\mathrm{O_{7}}\): \(7(-2) = -14\). Let \(x\) be \(\mathrm{Cr}\)'s and \(y\) be \(\mathrm{Hg}\)'s oxidation numbers. Since there's no charge, \(y + 2x - 14 = 0\). Assume typical \(\mathrm{Hg}\) as \(+2\), to solve: \(2 + 2x - 14 = 0\). Solving gives \(2x = 12; x = +6\).

Determine oxidation numbers for (d) \(\mathrm{Co_{3}(PO_{4})_{2}}\)

\(\mathrm{PO_{4}^{3-}}\) means each \(\mathrm{O}\) is \(-2\) (total \(-8\)), and let \(x\) be \(\mathrm{P}\)'s state. So \(x - 8 = -3\), giving \(x = +5\). Let \(y\) be \(\mathrm{Co}\)'s oxidation number so \(3y + 2(-3) = 0\). Solving \(3y - 6 = 0\) gives \(y = +2\).

Key concepts

Chemical Compounds

A chemical compound is a substance composed of two or more different elements that are chemically bonded together. These compounds are represented by chemical formulas which indicate the types and numbers of atoms in a compound. For example, in \( \text{Fe}_{2}(\text{CrO}_{4})_{3} \), Fe (iron), Cr (chromium), and O (oxygen) combine in a specific ratio to form a compound.

• The elements within a compound are held together by chemical bonds, which can be ionic, covalent, or metallic.
• Compounds can be classified by their properties and structures, such as ionic compounds, covalent compounds, and complexes which often involve transition metals.
• Chemical compounds have distinct formulas and follow specific rules for naming and writing chemical equations, focusing on the balance of charge and number of elements.

Understanding the nature of chemical compounds is essential for determining properties such as oxidation states, which can tell you a lot about a compound's reactivity and behavior in chemical reactions.

Oxidation States

Oxidation states, also known as oxidation numbers, are an important concept in chemistry that help to track the transfer of electrons in chemical reactions. They can be thought of as the "charge" of an atom within a compound, whether it's real or hypothetical.

• Generally, oxidation states are assigned based on a set of rules, such as assigning oxygen an oxidation state of \(-2\) and hydrogen \(+1\) in most compounds.
• The sum of oxidation states for all atoms in a compound must equal the overall charge of the compound, which is often zero for neutral compounds.
• For example, in the compound \(\text{Mn(ClO}_{2})_{2}\), manganese (Mn) requires oxidation state calculation by balancing the known states of chlorine (Cl) and oxygen (O) against the overall neutral charge.

Oxidation states allow chemists to identify changes in electron density and predict reaction pathways in redox reactions.

Redox Chemistry

Redox chemistry is a crucial part of chemistry that involves the study of oxidation-reduction reactions, commonly termed as redox reactions. These reactions describe processes in which oxidation states change, indicating a movement of electrons.

• An oxidation process is when an element loses electrons, thereby increasing its oxidation state, while reduction involves the gain of electrons and a decrease in oxidation state.
• Redox reactions are balanced when the total increase in oxidation state (due to oxidation) equals the total decrease (due to reduction).
• In practice, balancing these reactions involves identifying the oxidation and reduction half-reactions and ensuring the flow of electrons is even.

Understanding redox reactions is foundational for many real-world applications, including energy generation in batteries and metabolic processes in biology.

Transition Metals

Transition metals are elements found in the d-block of the periodic table, known for their ability to form multiple oxidation states. They play a critical role in complex chemical compounds and reactions.

• Transition metals include familiar elements such as iron (Fe), copper (Cu), and manganese (Mn), and they often exhibit variable oxidation states. This variability is due to the loss of electrons from both their outer s and d orbitals.
• These metals tend to form colored compounds and are critical in catalysis, where they speed up reactions without being consumed.
• In compounds like \( \text{Co}_{3}(\text{PO}_{4})_{2} \), understanding the transition metal oxidation state can help in predicting the compound's reactivity and stability.

Transition metals are essential in many industrial and biochemical applications, making them a vital area of study in chemistry.