Problem 20 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write a balanced chemical equation for the reaction that occurs when (a) titanium metal reacts with \(\mathrm{O}_{2}(g) ;(\mathbf{b})\) silver(I) oxide decomposes into silver metal and oxygen gas when heated; (c) propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)\) burns in air; \((\mathbf{d})\) methyl tert-butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l),\) burns in air.

Step-by-Step Solution

Answer

The balanced equations for the given reactions are: a) \(Ti(s) + O_{2}(g) \rightarrow TiO_{2}(s)\) b) \(2 Ag_{2}O(s) \rightarrow 4Ag(s) + O_{2}(g)\) c) \(2 C_{3}H_{7}OH(l) + 9 O_{2}(g) \rightarrow 6 CO_{2}(g) + 8 H_{2}O(l)\) d) \(C_{5}H_{12}O(l) + 8 O_{2}(g) \rightarrow 5 CO_{2}(g) + 6 H_{2}O(l)\)

Step 1: Write the basic unbalanced equation

In this reaction, Titanium (Ti) reacts with oxygen gas (O2) to form Titanium dioxide (TiO2). The unbalanced equation is: Ti(s) + O2(g) -> TiO2(s)

Step 2: Balance the equation

As the equation is already balanced with coefficients 1:1:1, the final balanced equation is: Ti(s) + O2(g) -> TiO2(s) #b) Silver(I) oxide decomposes into silver metal and oxygen gas when heated#

Step 1: Write the basic unbalanced equation

In this reaction, Silver(I) oxide (Ag2O) decomposes into silver metal (Ag) and oxygen gas (O2) when heated. The unbalanced equation is: Ag2O(s) -> Ag(s) + O2(g)

Step 2: Balance the equation

To balance the equation, introduce the coefficients 2 for Ag and 1/2 for O2: Ag2O(s) -> 2Ag(s) + 1/2 O2(g)

Step 3: Remove fractional coefficients

To remove the fractional coefficients, multiply all coefficients by 2: 2 Ag2O(s) -> 4Ag(s) + O2(g) #c) Propanol C3H7OH(l) burns in air#

Step 1: Write the basic unbalanced equation

In this reaction, Propanol (C3H7OH) reacts with oxygen gas (O2) to form carbon dioxide (CO2) and water (H2O). The unbalanced equation is: C3H7OH(l) + O2(g) -> CO2(g) + H2O(l)

Step 2: Balance the equation

To balance the equation, introduce coefficients for each species: C3H7OH(l) + 4.5 O2(g) -> 3 CO2(g) + 4 H2O(l)

Step 3: Remove fractional coefficients

To remove the fractional coefficients, multiply all coefficients by 2: 2 C3H7OH(l) + 9 O2(g) -> 6 CO2(g) + 8 H2O(l) #d) Methyl tert-butyl ether C5H12O(l) burns in air#

Step 1: Write the basic unbalanced equation

In this reaction, Methyl tert-butyl ether (C5H12O) reacts with oxygen gas (O2) to form carbon dioxide (CO2) and water (H2O). The unbalanced equation is: C5H12O(l) + O2(g) -> CO2(g) + H2O(l)

Step 2: Balance the equation

To balance the equation, introduce coefficients for each species: C5H12O(l) + 8 O2(g) -> 5 CO2(g) + 6 H2O(l) The balanced equations for the given reactions are: a) Ti(s) + O2(g) -> TiO2(s) b) 2 Ag2O(s) -> 4Ag(s) + O2(g) c) 2 C3H7OH(l) + 9 O2(g) -> 6 CO2(g) + 8 H2O(l) d) C5H12O(l) + 8 O2(g) -> 5 CO2(g) + 6 H2O(l)

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is a crucial skill in chemistry that ensures the law of conservation of mass is followed. It requires having the same number of each type of atom on both sides of the equation. Here is how you can get started:

• First, write down the unbalanced equation with all reactants and products.
• Next, count the number of atoms for each element in the reactants and products.
• Then, adjust the coefficients (the numbers in front of the chemical formulas) to balance the atoms for each element, making sure to start with the least common element and save hydrogen and oxygen for last.
• Remember, never change the subscripts inside a chemical formula; only adjust the coefficients.
• After balancing, ensure the equation remains balanced as you multiply coefficients, particularly when dealing with fractional coefficients.

By doing this accurately, you’ll be able to predict the correct proportions of reactants and products involved in any chemical reaction.

Combustion Reactions

Combustion reactions are a type of chemical reaction where a substance combines with oxygen, releasing energy in the form of heat or light. These reactions are most famously harnessed in engines and energy production. Here are some key points:

• Combustion typically involves hydrocarbons (compounds made of hydrogen and carbon) reacting with oxygen to produce carbon dioxide and water.
• For example, when propanol combusts as shown in the exercise, the balanced equation is:
  \[2 ext{ C}_3 ext{H}_7 ext{OH}(l) + 9 ext{ O}_2(g) ightarrow 6 ext{ CO}_2(g) + 8 ext{ H}_2 ext{O}(l)\]
• Combustion reactions must be properly balanced due to their role in calculating the energy produced in a reaction.
• These reactions often appear exothermic as they release more energy than they consume.

By understanding combustion, you gain insights into both the chemical and energy aspects of these important reactions.

Decomposition Reactions

Decomposition reactions involve a single compound breaking down into two or more simpler substances. These reactions are opposite to synthesis reactions and are crucial for understanding chemical breakdown processes:

• A common example is the decomposition of silver(I) oxide upon heating, as written in the balanced equation:
  \[2 ext{ Ag}_2 ext{O}(s) ightarrow 4 ext{ Ag}(s) + ext{ O}_2(g)\]
• This involves a single reactant decomposing to form multiple products, often requiring an input of energy such as heat, light, or electricity.
• Decomposition reactions are used in various applications, including the decomposition of binary ionic compounds, like carbonates, hydroxides, and nitrates.
• In practical settings, understanding these reactions helps in waste management and material recycling through controlled break down processes.

These reactions are key to unlocking insights into more complex chemical processes that occur in nature and industry.

Synthesis Reactions

Synthesis reactions are fundamental in chemistry where simpler substances combine to form more complex compounds. They contrast decomposition and are pivotal in material creation:

• An example from the exercise is the reaction of titanium with oxygen gas to form titanium dioxide, represented as:
  \[ ext{Ti}(s) + ext{O}_2(g) ightarrow ext{TiO}_2(s)\]
• These involve multiple reactants and rely on proper collision of molecules to form a single product, often requiring energy input, such as heat or pressure.
• Synthesis reactions are prominently used in manufacturing, where they form the backbone for creating many industrial and consumer products.
• The principles of stoichiometry are crucial in optimizing these reactions to prevent excess waste and manage resource use efficiently.

By mastering synthesis reactions, students are well-positioned to understand processes that are essential to both natural and synthetic chemistry.