Question

Complete and balance the following equations: (a) \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \stackrel{\text { spark }}{\longrightarrow}\) (b) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s) \stackrel{\Delta}{\longrightarrow}\) (c) \(\mathrm{H}_{2} \mathrm{CO}_{3}(a q)+\mathrm{KOH}(a q) \longrightarrow\)

Short answer

(a) \(2 \mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH} + 9 \mathrm{O}_{2} \rightarrow 6 \mathrm{CO}_{2} + 8 \mathrm{H}_{2} \mathrm{O} \); (b) \(\mathrm{Ca}(\mathrm{NO}_{3})_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CaO} + 2 \mathrm{NO}_{2} + \mathrm{O}_{2} + 4 \mathrm{H}_{2} \mathrm{O} \); (c) \(\mathrm{H}_{2} \mathrm{CO}_{3} + 2 \mathrm{KOH} \rightarrow \mathrm{K}_{2} \mathrm{CO}_{3} + 2 \mathrm{H}_{2} \mathrm{O} \)."}

Step-by-step solution

Identify the Type of Reactions

For equation (a), we recognize this as a combustion reaction. For (b), it is a thermal decomposition reaction, and for (c), it is a neutralization reaction between an acid and a base.

Write the Products for Equation (a)

Combustion of alcohols usually yields carbon dioxide and water. Thus, the products for the reaction of \( \mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH} + \mathrm{O}_{2} \) should be \( \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O} \).

Balance Equation (a)

The balanced equation is \[ \mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH} + \frac{9}{2} \mathrm{O}_{2} \rightarrow 3 \mathrm{CO}_{2} + 4 \mathrm{H}_{2} \mathrm{O} \].To clear the fraction, multiply all coefficients by 2: \[ 2 \mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH} + 9 \mathrm{O}_{2} \rightarrow 6 \mathrm{CO}_{2} + 8 \mathrm{H}_{2} \mathrm{O} \].Now, the equation is balanced.

Write the Products for Equation (b)

In thermal decomposition, the compound breaks down into its constituents. Heating \( \mathrm{Ca}(\mathrm{NO}_{3})_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O} \) will produce \( \mathrm{Ca} \mathrm{NO}_{2} \), \( \mathrm{NO}_{2} \), oxygen, and water, the latter as steam. The initial hydrated compound decomposes to calcium nitrite, nitrogen dioxide, and oxygen.

Balance Equation (b)

The balanced decomposition equation is \[ \mathrm{Ca}(\mathrm{NO}_{3})_{2} \cdot 4\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CaO} + 2 \mathrm{NO}_{2} + \mathrm{O}_{2} + 4 \mathrm{H}_{2} \mathrm{O} \].

Write the Products for Equation (c)

In acid-base neutralization, \( \mathrm{H}_{2} \mathrm{CO}_{3} \) reacts with \( \mathrm{KOH} \) to form salt and water. The products will be \( \mathrm{K}_{2} \mathrm{CO}_{3} \) and \( \mathrm{H}_{2} \mathrm{O} \).

Balance Equation (c)

Balance by ensuring the number of atoms on both sides of the equation is equal. The balanced equation is \[ \mathrm{H}_{2} \mathrm{CO}_{3} + 2 \mathrm{KOH} \rightarrow \mathrm{K}_{2} \mathrm{CO}_{3} + 2 \mathrm{H}_{2} \mathrm{O} \].

Key concepts

Combustion Reaction

In a combustion reaction, a substance reacts rapidly with oxygen, often producing heat and light in the form of a flame. Let’s look at the common example involving alcohols. When an alcohol like propanol

• is ignited, it reacts with oxygen to produce carbon dioxide (\[\mathrm{CO}_{2}\]) and water (\[\mathrm{H}_2\mathrm{O}\]).
• In a balanced combustion equation, it's crucial to have the same number of each type of atom on both sides of the reaction.Getting this balance right ensures that matter is conserved, reflecting the Law of Conservation of Mass.
• In our exercise, the balanced reaction for the combustion of 2 moles of propanol with 9 moles of oxygen forms 6 moles of carbon dioxide and 8 moles of water.

Breaking down complex organic compounds requires attention to detail to balance atoms like carbon, hydrogen, and oxygen

Thermal Decomposition

Thermal decomposition is a type of chemical reaction where a compound breaks down into simpler compounds or elements when heated. This process requires an input of energy, usually in the form of heat.
Let's consider the decomposition of hydrated calcium nitrate:

• Upon heating, the water in the compound converts to steam, and the original compound separates into calcium nitrite, nitrogen dioxide, and oxygen gas.
• This reaction illustrates how substances can break down when thermal energy is applied, a common process in both industrial and natural settings.
• The challenge often lies in accurately predicting the products, as these can sometimes include a mixture of gasses and solids.

The balanced decomposition equation reflects the change in states of matter, showcasing conservation of mass through meticulous balancing of products and reactants.

Acid-Base Neutralization

In acid-base neutralization reactions, an acid reacts with a base to form a salt and usually water. In our example, carbonic acid \[\left(\mathrm{H}_2\mathrm{CO}_3\right)\] reacts with potassium hydroxide \[\left(\mathrm{KOH}\right)\], a base.

• The result of this reaction is the production of potassium carbonate \[\left(\mathrm{K}_2\mathrm{CO}_3\right)\], a salt, and water, which is common in these types of reactions.
• In balancing such reactions, care must be taken to ensure that the number of atoms for each element involved, especially hydrogen and oxygen, matches. This showcases the exchange of ions between the acid and base.
• Neutralization reactions have wide applications, including in digestion, chemical manufacturing, and environmental management.

This specific balancing act illustrates the simplicity and elegance of neutralization, where an acid efficiently cancels the effect of a base.