Problem 87 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write balanced chemical equations for \((\mathbf{a})\) the complete combustion of acetone \(\left(\mathrm{CH}_{3} \mathrm{COCH}_{3}\right),\) a common organic solvent; (b) the decomposition of solid mercury (I) carbonate into carbon dioxide gas, mercury, and solid mercury oxide; (c) the combination reaction between sulphur dioxide gas and liquid water to produce sulfurous acid.

Step-by-Step Solution

Answer

a) Balanced equation for the complete combustion of acetone: \(CH_3COCH_3 + 4O_2 → 3CO_2 + 3H_2O\) b) Balanced equation for the decomposition of solid mercury(I) carbonate: \(Hg_2CO_3 → CO_2 + 2Hg + 2HgO\) c) Balanced equation for the combination reaction between sulfur dioxide gas and liquid water: \(SO_2 + H_2O → H_2SO_3\)

Step 1: a) Combustion of acetone

Write the initial reaction equation: Acetone (CH₃COCH₃) reacts with oxygen gas (O₂) to produce carbon dioxide (CO₂) and water (H₂O). Unbalanced equation: CH₃COCH₃ + O₂ → CO₂ + H₂O Balancing the equation by adjusting the coefficients: 1. We have 6 hydrogen atoms on the left side of the equation, so we should have 3 H₂O molecules on the right side. 2. We have 3 carbon atoms on the left side of the equation, so we should have 3 CO₂ molecules on the right side. 3. Now, we need to balance the oxygen atoms. We have 4 oxygen atoms from the 2 O₂ molecules on the left and a total of 9 oxygen atoms on the right. Balanced equation: CH₃COCH₃ + 4O₂ → 3CO₂ + 3H₂O

Step 2: b) Decomposition of mercury(I) carbonate

Write the initial reaction equation: Solid mercury(I) carbonate (Hg₂CO₃) decomposes into carbon dioxide gas (CO₂), mercury (Hg), and solid mercury oxide (HgO). Unbalanced equation: Hg₂CO₃ → CO₂ + Hg + HgO Balancing the equation by adjusting the coefficients: 1. We need 2 mercury atoms on the right side of the equation, so we place a 2 in front of Hg. 2. This results in 3 mercury atoms on the right side, so we place a 2 in front of HgO to balance the equation. Balanced equation: Hg₂CO₃ → CO₂ + 2Hg + 2HgO

Step 3: c) Combination of sulfur dioxide and water

Write the initial reaction equation: Sulfur dioxide gas (SO₂) reacts with liquid water (H₂O) to produce sulfurous acid (H₂SO₃). Unbalanced equation: SO₂ + H₂O → H₂SO₃ There's no need to balance this particular reaction, as the coefficients in the unbalanced equation are already correct for balancing the atoms on both sides of the reaction. Balanced equation: SO₂ + H₂O → H₂SO₃

Key Concepts

Combustion Reaction

A combustion reaction is a type of chemical reaction where a substance combines with oxygen to produce heat and light. This kind of reaction can usually be observed in the form of a fire or flame. For a combustion reaction to occur, there must be a fuel (the substance that burns), oxygen, and an ignition source, like a spark or heat.
In the case of acetone, a common organic solvent, combustion involves reacting with oxygen to produce carbon dioxide and water. The balanced reaction for the combustion of acetone is:

• Unbalanced: \( \text{CH}_3\text{COCH}_3 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \)
• Balanced: \( \text{CH}_3\text{COCH}_3 + 4\text{O}_2 \rightarrow 3\text{CO}_2 + 3\text{H}_2\text{O} \)

Balancing a combustion reaction often involves matching the number of carbon, hydrogen, and oxygen atoms on both sides of the equation. This ensures the reaction follows the law of conservation of mass, meaning no atoms are created or destroyed.

Decomposition Reaction

A decomposition reaction is a chemical reaction where a single compound breaks down into two or more simpler substances. These types of reactions are the opposite of combination reactions and often require energy in the form of heat, light, or electricity to occur.
For the decomposition of mercury(I) carbonate, the compound Hg₂CO₃ decomposes into carbon dioxide, mercury, and mercury oxide. This reaction can be depicted as:

• Unbalanced: \( \text{Hg}_2\text{CO}_3 \rightarrow \text{CO}_2 + \text{Hg} + \text{HgO} \)
• Balanced: \( \text{Hg}_2\text{CO}_3 \rightarrow \text{CO}_2 + 2\text{Hg} + 2\text{HgO} \)

Balancing this reaction requires ensuring that the number of each type of atom is the same on both sides. In this case, it involves adjusting coefficients to account for two mercury atoms and balancing the mercury oxide produced.

Combination Reaction

A combination reaction, also known as a synthesis reaction, involves two or more simple substances combining to form a more complex compound. These reactions can be seen as the reverse of decomposition reactions and usually release energy, making them somewhat exothermic.
In the combination reaction between sulfur dioxide and water, these reactants form sulfurous acid as shown in the equation:

• Equation: \( \text{SO}_2 + \text{H}_2\text{O} \rightarrow \text{H}_2\text{SO}_3 \)

Interestingly, this particular reaction does not need any additional balancing, as all the atoms are already balanced in the given equation. This is because the simple addition of the reactants directly forms the product without any left-over atoms, perfectly adhering to the conservation of mass. Combination reactions like this indicate a straightforward path from reactants to products.