Problem 45 - Chemistry Matter and Change

Question

Determine the oxidation number of the boldface element in these substances and ions. a. \(\mathrm{CaCrO}_{4}\) b. \(\mathrm{NaHSO}_{4}\) c. \(\mathrm{NO}_{2}^{-}\) d. \(\mathrm{BrO}_{3}^{-}\)

Step-by-Step Solution

Answer

Cr: +6 in \( \text{CaCrO}_4 \); S: +6 in \( \text{NaHSO}_4 \); N: +3 in \( \text{NO}_2^- \); Br: +5 in \( \text{BrO}_3^- \).

Step 1: Understanding Oxidation Number Rules

Oxidation numbers (or oxidation states) are assigned based on a set of rules. Key rules include: elements in their natural state have an oxidation number of zero, the oxidation number of a monatomic ion is equal to its charge, the sum of oxidation numbers in a neutral compound is zero, and for ions, it is equal to the ion charge. Recognize these rules before proceeding.

Step 2: Calculate Oxidation Number for Cr in \( \text{CaCrO}_4 \)

Let's denote the oxidation number of Cr as \( x \). Calcium has an oxidation number of +2, and each oxygen is -2. For \( \text{CaCrO}_4 \), the equation is: \[ +2 + x + 4(-2) = 0 \]Simplifying gives:\[ 2 + x - 8 = 0 \]\[ x = 6 \].Thus, the oxidation number of Cr is +6.

Step 3: Calculate Oxidation Number for S in \( \text{NaHSO}_4 \)

Let the oxidation number of S be \( y \). Sodium is +1, hydrogen is +1, and each oxygen is -2. Using the neutrality of \( \text{NaHSO}_4 \), the equation is:\[ +1 + 1 + y + 4(-2) = 0 \]Simplifying:\[ 1 + 1 + y - 8 = 0 \]\[ y = 6 \].Hence, the oxidation number of S is +6.

Step 4: Calculate Oxidation Number for N in \( \text{NO}_2^- \)

Let the oxidation number of N be \( z \). Each oxygen is -2. Since it's an ion \( \text{NO}_2^- \), the total should equal -1:\[ z + 2(-2) = -1 \]Simplifying this yields:\[ z - 4 = -1 \]\[ z = +3 \].Thus, the oxidation number of N is +3.

Step 5: Calculate Oxidation Number for Br in \( \text{BrO}_3^- \)

Let the oxidation number of Br be \( w \). Each oxygen is -2. For the ion \( \text{BrO}_3^- \), the sum should equal -1:\[ w + 3(-2) = -1 \]Simplifying:\[ w - 6 = -1 \]\[ w = +5 \].Thus, the oxidation number of Br is +5.

Key Concepts

Oxidation State Calculation

When calculating the oxidation state, remember that this is a way of keeping track of electrons in chemical reactions. The oxidation number is an assigned figure that helps in understanding how electrons are distributed among the atoms in molecules. Start by recognizing the oxidation state in the most basic elements and ions. For example:

• The oxidation state of any element in its natural form is zero. This is true for molecules like O₂ or N₂.
• For a monatomic ion, the oxidation number is equivalent to the ion’s charge. Thus, for Na⁺, the oxidation state is +1.

Remember, the sum of all oxidation states in a neutral compound must add up to zero, while for ions, it equals the ion charge. In complex molecules, tackle each element based on these basic rules to ascertain their oxidation states. This skill is crucial for understanding reaction mechanisms and balancing chemical equations.

Redox Reactions

Redox stands for reduction-oxidation reactions. These are chemical reactions where the oxidation state of atoms changes due to the transfer of electrons. In a redox reaction, one substance loses electrons (oxidation), and another gains electrons (reduction). Here are some key aspects:

• Oxidation is losing electrons, which increases the oxidation number.
• Reduction is gaining electrons, which decreases the oxidation number.

In the process, the substance that gets oxidized is known as the reducing agent, while the one that gets reduced acts as the oxidizing agent. Knowing how to identify which substances are oxidized or reduced in a reaction helps in understanding and predicting the reaction products. It’s important for anyone trying to grasp electrochemical cells, energy changes in chemistry, or corrosion of materials.

Chemical Compounds

Chemical compounds are combinations of two or more elements bonding together in fixed proportions. Depending on the type of chemical bond (ionic, covalent, or metallic), compounds exhibit different properties and reactions:

• Ionic compounds are formed when electrons are transferred from one atom to another, leading to a bond between oppositely charged ions, like in NaCl.
• Covalent compounds occur when atoms share electrons, resulting in a strong bond, as seen in H₂O.
• Metallic compounds, while less discussed, involve a "sea" of electrons moving freely between metal atoms, leading to properties like conductivity and malleability.

Understanding the structure of chemical compounds, including their molecular geometry and polarity, helps predict how they behave in different chemical reactions. This foundation is key for exploring topics like synthesis, reactivity, and material properties in advanced chemistry.

Ion Charge

The concept of ion charge is essential in understanding how atoms combine to form compounds. Ions are atoms or molecules that have gained or lost electrons, resulting in a net charge:

• Cations are positively charged ions formed when an atom loses electrons, like Ca²⁺.
• Anions are negatively charged ions created when an atom gains electrons, such as Cl^-.

The charge of an ion is significant in chemical reactions as it dictates how ions attract or repel each other, and how they combine to form ionic compounds. For instance, in Na⁺ + Cl^- → NaCl, the charges must balance, leading to the formation of neutral compounds. Mastery of ion charges leads to a better understanding of stoichiometry, solubility, and ionic equilibria in solutions, enabling successful predictions in various chemical contexts.