Problem 45 - Chemistry and Chemical Reactivity

Question

Cobalt forms \(\mathrm{Co}^{2+}\) and \(\mathrm{Co}^{3+}\) ions. Write the formulas for the two cobalt oxides formed by these transition metal ions.

Step-by-Step Solution

Answer

The formulas for the cobalt oxides are \( \mathrm{CoO} \) and \( \mathrm{Co}_{2}\mathrm{O}_{3} \).

Step 1: Identify Possible Cations

Cobalt can form two types of cations: the divalent cation \( \mathrm{Co}^{2+} \) and the trivalent cation \( \mathrm{Co}^{3+} \).

Step 2: Determine the Charge of the Oxide Ion

The oxide ion \( \mathrm{O}^{2-} \) has a charge of \(-2\). Since only one type of oxide ion will combine with cobalt in both compounds, we need to balance the charges between cobalt and oxygen to form neutral compounds.

Step 3: Balance Charges for \\( \mathrm{Co}^{2+} \\) Oxide

For \( \mathrm{Co}^{2+} \), each cobalt ion has a charge of \( +2 \), which can be balanced by one oxide ion \( \mathrm{O}^{2-} \). Thus, the formula is \( \mathrm{CoO} \).

Step 4: Balance Charges for \\( \mathrm{Co}^{3+} \\) Oxide

For \( \mathrm{Co}^{3+} \), each cobalt ion has a charge of \( +3 \). Therefore, two \( \mathrm{Co}^{3+} \) ions with a total charge of \( +6 \) balance with three oxide \( \mathrm{O}^{2-} \) ions, each with a charge of \( -2 \), for a total charge of \( -6 \). Thus, the formula is \( \mathrm{Co}_{2}\mathrm{O}_{3} \).

Key Concepts

Transition Metal Ions

Transition metal ions are a fascinating topic in chemistry that deal with elements that have partially filled d orbitals. These elements are typically found in the d-block of the periodic table. One of the key characteristics of transition metals like cobalt is their ability to form ions with different charges. For example, cobalt can lose electrons to form either

• Co\(^{2+}\), a divalent cation, or
• Co\(^{3+}\), a trivalent cation.

The ability to form multiple oxidation states is due to the relatively similar energy levels of the 3d and 4s electrons, making it energetically feasible for these elements to lose varying numbers of electrons. This versatility is what makes transition metals so important in chemical reactions and compounds.

Charge Balancing

Charge balancing is an essential principle in chemistry that ensures compounds are electrically neutral. When forming compound formulas, it is crucial for the total positive charge from the cations to equal the total negative charge from the anions.For instance, when combining cobalt ions with oxide ions to form cobalt oxides, this principle comes into play.- The oxide ion \((\text{O}^{2-})\) has a charge of -2.- A cobalt ion can have charges of either +2 or +3.To balance these charges, we construct formulas where the sum of the charges equals zero. For the

• Co\(^{2+}\), one oxide ion balances one cobalt ion, resulting in CoO.
• Co\(^{3+}\), the charge balance requires two cobalt ions and three oxide ions, resulting in Co\(_2\)O\(_3\).

This ensures that the compound is stable and neutral.

Cation Formation

Cations are positively charged ions formed when atoms lose electrons. In transition metals, cation formation is a common occurrence due to the metals' ability to lose various numbers of electrons depending on their environment. For cobalt, cation formation happens as follows: - When a cobalt atom loses two electrons, it forms Co\(^{2+}\). - When it loses three electrons, it forms Co\(^{3+}\).The process of electron loss leads to the formation of different oxidation states and influences the metal's chemical properties. In the world of transition metals, these varying oxidation states enable cobalt to participate in a wide range of chemical reactions, forming compounds like cobalt oxides with different structures and properties.

Chemical Formulas

Chemical formulas represent the composition of compounds. They show the types and numbers of atoms involved in forming a compound. Understanding how to write chemical formulas is crucial for depicting accurately the interactions between ions. When writing formulas for transition metal compounds, it's important to account for the charge of the ions involved. Consider cobalt oxides:

• For Co\(^{2+}\) with O\(^{2-}\), the 1:1 charge ratio forms the simple formula CoO.
• For Co\(^{3+}\) with O\(^{2-}\), the charge difference necessitates a ratio of 2 cobalt ions to 3 oxide ions, resulting in Co\(_2\)O\(_3\).

These formulas not only convey the elements and their proportions but also hint at the structural and chemical behavior of the compound. Thus, chemical formulas are more than mere symbols; they are gateways to understanding chemical reactions and properties.