Question

Write a balanced equation for each of the following decomposition reactions: (a) Chromium(III) carbonate decomposes with heat to give solid chromium(III) oxide and carbon dioxide gas. (b) Lead(IV) carbonate decomposes with heat to give solid lead(IV) oxide and carbon dioxide gas.

Short answer

(a) \( \text{Cr}_2(\text{CO}_3)_3 \rightarrow \text{Cr}_2\text{O}_3 + 3\text{CO}_2 \); (b) \( \text{Pb(CO}_3)_2 \rightarrow \text{PbO}_2 + 2\text{CO}_2 \)."}

Step-by-step solution

Write the Chemical Formula of Reactants

For each decomposition reaction, we need to start by writing the formula of the reactants. (a) Chromium(III) carbonate is represented as \( \text{Cr}_2(\text{CO}_3)_3 \).(b) Lead(IV) carbonate is represented as \( \text{Pb(CO}_3)_2 \).

Identify the Decomposition Products

Identify the products when each carbonate decomposes. Typically, metal carbonates decompose into a metal oxide and carbon dioxide gas. (a) Chromium(III) carbonate decomposes to form chromium(III) oxide (\( \text{Cr}_2\text{O}_3 \)) and carbon dioxide (\( \text{CO}_2 \)).(b) Lead(IV) carbonate decomposes to form lead(IV) oxide (\( \text{PbO}_2 \)) and carbon dioxide (\( \text{CO}_2 \)).

Write Unbalanced Equations

Write the unbalanced decomposition equations based on the reactants and products identified. (a) \[ \text{Cr}_2(\text{CO}_3)_3 \rightarrow \text{Cr}_2\text{O}_3 + \text{CO}_2 \](b) \[ \text{Pb(CO}_3)_2 \rightarrow \text{PbO}_2 + \text{CO}_2 \]

Balance the Equations

Balance each equation by ensuring the same number of each type of atom appears on both sides.(a) Chromium(III) carbonate: - Balance carbon first by adding a coefficient 3 in front of \( \text{CO}_2 \): \[ \text{Cr}_2(\text{CO}_3)_3 \rightarrow \text{Cr}_2\text{O}_3 + 3\text{CO}_2 \] - The equation is now balanced.(b) Lead(IV) carbonate: - Balance the equation by ensuring there are the same number of oxygen and carbon atoms: \[ \text{Pb(CO}_3)_2 \rightarrow \text{PbO}_2 + 2\text{CO}_2 \] - The equation is now balanced.

Key concepts

Chemical Equation Balancing

Balancing chemical equations is crucial because it follows the law of conservation of mass, ensuring that atoms are neither created nor destroyed in a chemical reaction. To effectively balance equations, follow a series of steps: Identify the compounds involved and write their unbalanced chemical formulas. It helps to list each type of atom in the reactants and products to keep things organized.

• Compare the number of atoms of each element on both sides of the equation.
• Add coefficients to the species that need adjustment, focusing on one element at a time.
• Re-check your work to ensure that all elements have been balanced.

In the context of decomposition reactions, this method allows you to accurately reflect the breaking down of a compound into its constituent parts while maintaining the balance of atoms throughout the process. By balancing equations, you're representing a realistic depiction of the reaction occurring at the molecular level.

Metal Carbonates

Metal carbonates are special compounds consisting of a metal ion combined with carbonate ions (\( ext{CO}_3^{2-}\)). These compounds are quite common in chemistry and play a significant role in various reactions. In decomposition reactions, they are particularly known for breaking down into metal oxides and carbon dioxide gas when subjected to heat. This process can be expressed generally as:

• \( ext{MCO}_3\) decompose to form \( ext{MO}\) and \( ext{CO}_2\).

Common examples include Chromium(III) carbonate (\( ext{Cr}_2( ext{CO}_3)_3\)) decomposing to form Chromium(III) oxide and Lead(IV) carbonate (\( ext{Pb(CO}_3)_2\)) decomposing to form Lead(IV) oxide. These types of reactions illustrate the fundamental behaviors of metal carbonates under thermal conditions.Understanding these properties helps in predicting the products of decomposition reactions involving other metal carbonates.

Thermal Decomposition

Thermal decomposition is a type of chemical reaction where a single compound breaks down into simpler substances when heated. It is an endothermic process, meaning it requires heat to occur. In the case of metal carbonates, thermal decomposition typically results in the formation of a metal oxide and the release of carbon dioxide gas, a common gaseous product. Highlights of thermal decomposition include:

• This reaction often requires specific temperature conditions to initiate and sustain the breakdown.
• The process is crucial in industrial applications, especially in material processing and extraction of metals.

For instance, heating Chromium(III) carbonate results in the production of Chromium(III) oxide and carbon dioxide, while Lead(IV) carbonate will yield Lead(IV) oxide and carbon dioxide under similar thermal conditions. Recognizing these patterns aids in predicting the outcomes of chemical processes involving decomposition through heat.