Problem 21 - Chemistry: The Central Science in SI Units, Global Edition

Question

Balance the following equations and indicate whether they are combination, decomposition, or combustion reactions: (a) \(\mathrm{C}_{7} \mathrm{H}_{16}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) (b) \(\mathrm{Li}_{3} \mathrm{~N}(s)+\mathrm{BN}(s) \longrightarrow \mathrm{Li}_{3} \mathrm{BN}_{2}(s)\) (c) \(\mathrm{Zn}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{ZnO}(s)+\mathrm{H}_{2} \mathrm{O}(I)\) (d) \(\mathrm{Ag}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Ag}(s)+\mathrm{O}_{2}(g)\)

Step-by-Step Solution

Answer

(a) \(C_{7}H_{16}(s) + 11O_{2}(g) \longrightarrow 7CO_{2}(g) + 8H_{2}O(l)\) (combustion) (b) \(3Li_{3}N(s) + 2BN(s) \longrightarrow 2Li_{3}BN_{2}(s)\) (combination) (c) \(Zn(OH)_{2}(s) \longrightarrow ZnO(s) + H_{2}O(l)\) (decomposition) (d) \(2Ag_{2}O(s) \longrightarrow 4Ag(s) + O_{2}(g)\) (decomposition)

Step 1: Identify the type of reaction

This reaction involves a hydrocarbon (C7H16) and oxygen, producing carbon dioxide and water, which are typical products of a combustion reaction. Therefore, it is a combustion reaction.

Step 2: Balance the equation

We will systematically balance the atoms in the equation. First, balance the carbon atoms: \(C_{7}H_{16} + 7CO_{2} \longrightarrow 7CO_{2} + H_{2}O\) Next, balance the hydrogen atoms: \(C_{7}H_{16} + 7CO_{2} \longrightarrow 7CO_{2} + 8H_{2}O\) Finally, balance the oxygen atoms: \(C_{7}H_{16} + 11O_{2} \longrightarrow 7CO_{2} + 8H_{2}O\) The balanced equation is: \(C_{7}H_{16}(s) + 11O_{2}(g) \longrightarrow 7CO_{2}(g) + 8H_{2}O(l)\) (b) \(\mathrm{Li}_{3} \mathrm{N}(s)+\mathrm{BN}(s) \longrightarrow \mathrm{Li}_{3} \mathrm{BN}_{2}(s)\)

Step 1: Identify the type of reaction

This reaction involves elements and compounds combining to form a single product, making it a combination reaction.

Step 2: Balance the equation

Balance the lithium, nitrogen, and boron atoms in the equation: \(3Li_{3}N + 2BN \longrightarrow 2Li_{3}BN_{2}\) The balanced equation is: \(3Li_{3}N(s) + 2BN(s) \longrightarrow 2Li_{3}BN_{2}(s)\) (c) \(\mathrm{Zn}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{ZnO}(s)+\mathrm{H}_{2} \mathrm{O}(I)\)

Step 1: Identify the type of reaction

This reaction involves a single reactant decomposing into two products, making it a decomposition reaction.

Step 2: Balance the equation

Balance the zinc, oxygen, and hydrogen atoms in the equation: \(Zn(OH)_{2} \longrightarrow ZnO + H_{2}O\) The balanced equation is already given: \(Zn(OH)_{2}(s) \longrightarrow ZnO(s) + H_{2}O(l)\) (d) \(\mathrm{Ag}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Ag}(s)+\mathrm{O}_{2}(g)\)

Step 1: Identify the type of reaction

This reaction involves a single reactant decomposing into two products, making it a decomposition reaction.

Step 2: Balance the equation

Balance the silver and oxygen atoms in the equation: \(2Ag_{2}O \longrightarrow 4Ag + O_{2}\) The balanced equation is: \(2Ag_{2}O(s) \longrightarrow 4Ag(s) + O_{2}(g)\)

Key Concepts

Combustion Reaction

A combustion reaction is a chemical process where a substance reacts with oxygen to produce energy in the form of light or heat. The classic example involves hydrocarbons reacting with oxygen, producing carbon dioxide and water. This kind of reaction is integral to processes such as burning fuel in engines and heating homes.
In the balanced equation for the combustion of \( \mathrm{C}_{7} \mathrm{H}_{16} \), we see how this hydrocarbon interacts with oxygen:

• The carbon atoms in heptane are balanced by producing seven molecules of \( \mathrm{CO}_{2} \).
• The hydrogen atoms are balanced to form eight molecules of \( \mathrm{H}_{2} \mathrm{O} \).
• Finally, oxygen molecules are adjusted to ensure the balance of all elements in the equation.

This systematic approach to balancing the equation helps us understand the basic principles of combustion reactions.

Combination Reaction

Combination reactions occur when two or more substances join to form a single compound. This type of reaction is also known as a synthesis reaction.
In the reaction where \( \mathrm{Li}_{3} \mathrm{N} \) and \( \mathrm{BN} \) combine to form \( \mathrm{Li}_{3} \mathrm{BN}_{2} \), we observe the following:

• Multiple reactants blend to produce a single product.
• All elements are accounted for to comply with the law of conservation of mass.

The balanced equation demonstrates how the atoms in the reactants are reorganized to create a product with different properties. Such reactions often showcase the creative nature of chemistry, forming new materials with unique characteristics.

Decomposition Reaction

Decomposition reactions involve a single compound breaking down into two or more simpler substances. These reactions often require an input of energy, such as heat, light, or electricity, to occur.
Examining the decomposition of \( \mathrm{Zn} \mathrm{(OH)}_{2} \) into \( \mathrm{ZnO} \) and \( \mathrm{H}_{2} \mathrm{O} \), we see:

• A single compound splits into distinct products.
• The balanced equation provides an equal number of each type of atom on both sides—ensuring mass conservation.

Likewise, the decomposition of \( \mathrm{Ag}_{2} \mathrm{O} \) into silver and oxygen is a classic example:

• This reaction illustrates the separation of metals from their oxides.
• Such decompositions are fundamental in extraction and recycling processes.

Decomposition reactions are vital in various applications, including the breakdown of organic materials and the preparation of elements. The clarity in balanced equations helps in visualizing these transformations.