Problem 56 - Chemistry: The Central Science

Question

Predict the chemical formulas of the compounds formed by the following pairs of ions: (a) \(\mathrm{Cu}^{2+}\) and \(\mathrm{Br}^{-}\), (b) \(\mathrm{Fe}^{3+}\) and \(\mathrm{O}^{2-}\), (c) \(\mathrm{Hg}_{2}^{2+}\) and \(\mathrm{CO}_{3}^{2-}\), (d) \(\mathrm{Ca}^{2+}\) and \(\mathrm{AsO}_{4}{\underline{\phantom{xx}}}^{3-}\), (e) \(\mathrm{NH}_{4}{\underline{\phantom{xx}}}^{+}\) and \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\).

Step-by-Step Solution

Answer

The chemical formulas for the given pairs of ions are: (a) \(\mathrm{CuBr_2}\), (b) \(\mathrm{Fe_2O_3}\), (c) \(\mathrm{Hg_2CO_3}\), (d) \(\mathrm{Ca_3(AsO_4)_2}\), and (e) \(\mathrm{(NH_4)_2CO_3}\).

Step 1: (a) Cu²⁺ and Br⁻

First, we will find the least common multiple (LCM) of the charges of both ions to balance them. For Cu²⁺ (Copper) and Br⁻ (Bromine), the LCM of 2 and 1 is 2. Multiply each ion by the required factor to reach the LCM: Cu x 1 and Br x 2, so we have one Cu²⁺ ion combined with two Br⁻ ions. The chemical formula is: \(\mathrm{CuBr_2}\)

Step 2: (b) Fe³⁺ and O²⁻

For Fe³⁺ (Iron) and O²⁻ (Oxygen), the LCM of 3 and 2 is 6. Multiply each ion by the necessary factor: Fe x 2 and O x 3. Combining two Fe³⁺ ions with three O²⁻ ions, we get the chemical formula: \(\mathrm{Fe_2O_3}\)

Step 3: (c) Hg₂²⁺ and CO₃²⁻

For Hg₂²⁺ (Mercury) and CO₃²⁻ (Carbonate), the charges are already balanced (²⁺ and ²⁻). Thus, we can directly combine them without any extra factor, resulting in the chemical formula: \(\mathrm{Hg_2CO_3}\)

Step 4: (d) Ca²⁺ and AsO₄³⁻

For Ca²⁺ (Calcium) and AsO₄³⁻ (Arsenate), the LCM of 2 and 3 is 6. Multiply each ion by the necessary factor: Ca x 3 and AsO₄ x 2. Combining three Ca²⁺ ions with two AsO₄³⁻ ions, the chemical formula is: \(\mathrm{Ca_3(AsO_4)_2}\)

Step 5: (e) NH₄⁺ and CO₃²⁻

For NH₄⁺ (Ammonium) and CO₃²⁻ (Carbonate), the LCM of 1 and 2 is 2. Multiply each ion by the necessary factor: NH₄ x 2 and CO₃ x 1. Combining two NH₄⁺ ions with one CO₃²⁻ ion, we arrive at the chemical formula: \(\mathrm{(NH_4)_2CO_3}\)

Key Concepts

Ion Combination

Creating a chemical formula involves understanding how ions with opposite charges combine. Ions are atoms or molecules with a net electric charge due to the loss or gain of one or more electrons. In a compound, cations (positively charged ions) and anions (negatively charged ions) are attracted to each other to form a neutral compound.
For instance, in the step involving Cu²⁺ and Br⁻, the ions combine to balance their charges, resulting in a neutral compound,

• Cu²⁺ (Copper ion with a +2 charge)
• Br⁻ (Bromine ion with a -1 charge)

The compound is two bromine ions being needed to balance the two positive charges of copper, leading to the formation of CuBr₂. This process of combining oppositely charged ions is essential for understanding how chemical compounds come together.

Balancing Charges

Balancing charges is a fundamental step in forming neutral chemical compounds from ions. The principle is that the total positive charge from the cations must equal the total negative charge from the anions.
When predicting the formula for a compound from ions, it's crucial to adjust the number of each type of ion to reach overall charge neutrality. In step (b) with Fe³⁺ and O²⁻, we multiply the Fe ion by 2 and the O ion by 3 to get

• 2 Fe³⁺ ions (total charge of +6)
• 3 O²⁻ ions (total charge of -6)

Thus, the charges balance to form Fe₂O₃. Balancing charges is central to deriving proper chemical formulas.

Least Common Multiple (LCM)

In chemistry, the Least Common Multiple (LCM) is used to determine the smallest number to balance opposing ionic charges. This ensures the compound's neutrality.
In step (d), involving Ca²⁺ and AsO₄³⁻, the LCM of 2 and 3 is calculated to be 6.
This tells us how to scale the ions:

• Ca²⁺ must be multiplied by 3, giving +6 charge in total
• AsO₄³⁻ must be multiplied by 2, giving -6 charge in total

The result is a balanced compound: Ca₃(AsO₄)₂. Recognizing the LCM allows us to accurately and efficiently figure out the ratios of ions needed for a neutral compound.

Inorganic Chemistry

Inorganic chemistry deals with compounds that are not based on a carbon-hydrogen structure. This field involves a wide range of compounds, including ionic compounds formed through the transfer of electrons between atoms.
The formation of ionic compounds like Fe₂O₃ and Ca₃(AsO₄)₂ in the exercises illustrates key principles of inorganic chemistry:

• Understanding how ions interact and form compounds
• Balancing charges to ensure neutral compounds

Inorganic compounds are vital, making up minerals, ores, and materials essential for technology and everyday life. Grasping the basics of ion combination and balancing charges is pivotal to mastering inorganic chemistry.

Compound Formation

Compound formation is the process by which elements come together to form chemical compounds. This involves the interaction of atoms or ions with opposite charges combining to create stable, neutral compounds.
In the exercise, compound formation is exemplified by NH₄⁺ and CO₃²⁻ to form (NH₄)₂CO₃, showing a typical example of ionic compound formation. The process includes:

• Identifying the ions involved – Knowing the type of ions is key to combination.
• Balancing the charges – Neutrality is achieved by ensuring the total charge is zero.
• Writing the chemical formula – Final step involves writing down the correct chemical formula based on the combination of ions.

Mastering compound formation helps understand the properties and reactions of diverse materials.