Problem 68 - Chemistry

Question

Write the formula for each of the following compounds: a. chromium(III) hydroxide c. lead(IV) carbonate b. magnesium cyanide d. ammonium acetate

Step-by-Step Solution

Answer

The chemical formulas for the given compounds are: a. Chromium(III) hydroxide: \(Cr(OH)_3\) b. Magnesium cyanide: \(Mg(CN)_2\) c. Lead(IV) carbonate: \(Pb(CO_3)_2\) d. Ammonium acetate: \(NH_4CH_3COO\) (or \(NH_4C_2H_3O_2\))

Step 1: 1. chromium(III) hydroxide formula

First, identify the constituent ions and their charges. Chromium(III) indicates that chromium has a charge of +3. Hydroxide is a polyatomic ion with the chemical formula OH^- and a charge of -1. To balance the charges, we need three hydroxide ions (OH^-) for every chromium(III) ion (Cr^3+): Cr^(3+) + 3(OH^-) → Cr(OH)₃ So, the formula for chromium(III) hydroxide is Cr(OH)₃.

Step 2: 2. lead(IV) carbonate formula

Identify the ions and their charges. Lead(IV) means that lead has a charge of +4. Carbonate is a polyatomic ion with the formula CO₃²⁻ and a charge of -2. To balance the charges, we need two carbonate ions (CO₃²⁻) for every lead(IV) ion (Pb^4+): Pb^(4+) + 2(CO₃²⁻) → Pb(CO₃)₂ So, the formula for lead(IV) carbonate is Pb(CO₃)₂.

Step 3: 3. magnesium cyanide formula

Identify the ions and their charges. Magnesium is in group 2 of the periodic table, which means it forms a divalent cation with a charge of +2 (Mg²⁺). Cyanide is a polyatomic ion with the formula CN^- and a charge of -1. To balance the charges, we need two cyanide ions (CN^⁻) for every magnesium ion (Mg²⁺): Mg^(2+) + 2(CN⁻) → Mg(CN)₂ So, the formula for magnesium cyanide is Mg(CN)₂.

Step 4: 4. ammonium acetate formula

Identify the ions and their charges. Ammonium is a polyatomic ion with the formula NH₄⁺ and a charge of +1. Acetate is also a polyatomic ion with the formula CH₃COO⁻ (or C₂H₃O₂⁻) and a charge of -1. In this case, the charges of the ammonium and acetate ions balance each other perfectly, so we can combine them directly: NH₄^+ + CH₃COO^⁻ → NH₄CH₃COO (or NH₄C₂H₃O₂) So, the formula for ammonium acetate is NH₄CH₃COO (or NH₄C₂H₃O₂).

Key Concepts

Ionic Compounds

Ionic compounds are formed when metals transfer electrons to non-metals, resulting in the formation of positive and negative ions. These ions attract each other due to opposite charges and create a stable compound through ionic bonding. A classic example is sodium chloride (table salt), consisting of sodium ions

• In ionic compounds, metals typically lose electrons becoming cations with a positive charge.
• Non-metals gain electrons to become anions, carrying a negative charge.

To determine the formula of an ionic compound:

• Identify the metal (cation) and its charge based on its group in the periodic table. Elements in Group 1 have a +1 charge, Group 2 have a +2 charge, etc.


• Identify the non-metal (anion) and its charge using standard oxidation states, often found in reference tables.


• Balance the overall charge by adjusting the number of cations and anions until the total positive charge equals the total negative charge.

Polyatomic Ions

Polyatomic ions are ions that consist of more than one atom, acting as a single charged entity. Unlike monatomic ions, polyatomic ions comprise a group of atoms bonded together that collectively carry a charge. Examples of polyatomic ions include:

• Hydroxide (OH⁻): A negative ion with oxygen and hydrogen, often seen in bases like sodium hydroxide (NaOH).
• Carbonate (CO₃²⁻): A carbonate group bonded to metals in compounds like calcium carbonate (CaCO₃), prevalent in rocks and shells.
• Ammonium (NH₄⁺): A positive ion formed by nitrogen and hydrogen, common in fertilizers.

When writing the chemical formula for compounds containing polyatomic ions, treat these ions as discrete units. If multiple polyatomic ions are needed to balance the charge, they should be enclosed in parentheses with a subscript indicating the number needed, such as in magnesium cyanide, Mg(CN)₂.

Charge Balancing

Charge balancing is a crucial concept in chemistry to ensure that a compound is electrically neutral. The sum of positive and negative charges in a compound must equal zero. Steps to balance charges in formulas:

• Calculate the total positive charge from all cations.


• Calculate the total negative charge from all anions.


• Adjust the number of ions to balance these charges.

For instance, in lead(IV) carbonate, the lead has a +4 charge, and the carbonate has a -2 charge. To balance these, two carbonate ions are needed for each lead ion, resulting in the formula Pb(CO₃)₂. It's also important to consider the use of parentheses in formulas when multiple units of a polyatomic ion are present. This ensures clarity in indicating how many of each ion is part of the compound, as seen in compounds like Cr(OH)₃, where three hydroxide ions are balanced with one chromium ion.