Question

Identify the group number in the periodic table of \(\mathrm{X}\), a representative element, in each of the following ionic compounds: a. \(\mathrm{X}_{2} \mathrm{O}_{3}\) b. \(\mathrm{X}_{2} \mathrm{SO}_{3}\) c. \(\mathrm{Na}_{3} \mathrm{X}\)

Short answer

a. Group 13 (III A), b. Group 1 (I A), c. Group 15 (V A)

Step-by-step solution

Determine the oxidation state of oxygen in each compound

In ionic compounds, oxygen typically has an oxidation state of -2. For compounds involving oxygen, we identify the oxidation states of other elements assuming oxygen is always -2.

Calculate the oxidation state of X in \(X_2O_3\)

In \(X_2O_3\), each \(O\) has an oxidation state of -2. There are 3 oxygen atoms which contribute a total of \(3 \times -2 = -6\) to the compound. Let \(x\) be the oxidation state of \(X\). From the formula, namely \(2x + 3(-2) = 0\), solving the equation gives \(2x - 6 = 0\) or \(2x = 6\), hence \(x = 3\). The oxidation state of \(X\) is +3, indicating it belongs to Group 13 (III A).

Calculate the oxidation state of X in \(X_2SO_3\)

In \(X_2SO_3\), the sulfur atom (\(S\)) typically has an oxidation state of +4 and each oxygen atom (\(O\)) has an oxidation state of -2. With 3 oxygens contributing -6 and 1 sulfur contributing +4, we need the two \(X\) ions to balance this charge. Let \(x\) be the oxidation state of \(X\). From the equation \(2x + 4 + 3(-2) = 0\), solving this gives \(2x + 4 - 6 = 0\), hence \(2x - 2 = 0\) or \(x = 1\). Therefore, the oxidation state of \(X\) is +1, indicating it belongs to Group 1 (I A).

Calculate the oxidation state of X in \(Na_3X\)

In \(Na_3X\), sodium (\(Na\)) has an oxidation state of +1. Together 3 sodium atoms contribute +3. Let \(x\) be the oxidation state of \(X\). From the equation \(3(+1) + x = 0\), solving this gives \(3 + x = 0\), hence \(x = -3\). The oxidation state of \(X\) is -3, indicating that \(X\) belongs to Group 15 (V A).

Key concepts

Representative Elements

Representative elements are those found in the first two groups and the last six groups of the periodic table. They include groups 1 (I A), 2 (II A), and groups 13 (III A) through 18 (VIII A). These elements are characterized by having their outermost electrons in the s or p orbitals, which makes them highly reactive, especially in forming compounds.
Studying these elements is crucial because they exhibit a wide range of chemical properties and oxidation states. For example, in the exercise above:

• Element X in \(X_2O_3\) belongs to Group 13 (III A).
• Element X in \(X_2SO_3\) belongs to Group 1 (I A).
• Element X in \(Na_3X\) belongs to Group 15 (V A).

Understanding representative elements help us predict their behavior in chemical reactions, which is essential for problem-solving in chemistry.

Oxidation State Determination

Determining the oxidation state of an element in a compound is a vital skill in chemistry. The oxidation state, or oxidation number, is the charge an atom would have if all bonds were 100% ionic. This concept helps us understand how electrons are transferred in reactions.
Here's a systematic approach to determine the oxidation states:

• Identify the oxidation state of commonly known elements. For instance, oxygen is usually -2.
• Set up an equation based on the fact that the sum of oxidation states in a neutral compound is zero.
• Solve for the unknown oxidation state.

This method was used in the exercise:

• For \(X_2O_3\), we found \(X\) by knowing oxygen's state (-2).
• For \(X_2SO_3\), we included sulfur's state (+4).
• For \(Na_3X\), sodium's state (+1) was crucial.

Practicing this process enriches your understanding of chemical reactions and compound formation.

Periodic Table Group Identification

The periodic table is a powerful tool that organizes elements based on their properties. Identifying the group number of an element helps predict its chemical behavior and its interactions with other elements.
In the problem, we identified the group number of \(X\) by determining its oxidation state:

• Elements in Group 13 (III A) typically have an oxidation state of +3.
• Elements in Group 1 (I A) have an oxidation state of +1.
• Elements in Group 15 (V A) often have an oxidation state of -3.

Using the periodic table, we placed \(X\) accordingly:

• For \(X_2O_3\), \(X\) with +3 corresponds to Group 13.
• For \(X_2SO_3\), the +1 oxidation state places \(X\) in Group 1.
• For \(Na_3X\), an oxidation state of -3 places \(X\) in Group 15.

Understanding the groups in the periodic table is essential for learning chemistry, as it relates directly to the element's oxidation state and properties.