Problem 19 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;(\mathbf{b})\) barium carbonate decomposes into barium oxide and carbon dioxide gas when heated; \((\mathbf{c})\) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l),\) is combusted in air; \((\mathbf{d})\) dimethylether, \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(g),\) is combusted in air.

Step-by-Step Solution

Answer

(a) Mg (s) + Cl₂ (g) → MgCl₂ (s) (b) BaCO₃ (s) → BaO (s) + CO₂ (g) (c) C₈H₈ (l) + 11/2O₂ (g) → 8CO₂ (g) + 4H₂O (g) (d) CH₃OCH₃ (g) + 2O₂ (g) → 2CO₂ (g) + 3H₂O (g)

Step 1: (a) Reaction Between Magnesium and Chlorine

First, let's write the unbalanced chemical equation for the reaction between Magnesium (Mg) and Chlorine (Cl₂). In this reaction, Magnesium will react with Chlorine to form Magnesium Chloride (MgCl₂): Mg (s) + Cl₂ (g) → MgCl₂ (s) Now, let's balance the equation. We have one magnesium atom on both sides and two chlorine atoms on the left side with only one chlorine atom on the right side. To balance the number of chlorine atoms, we can add a coefficient of 2 to MgCl₂: Mg (s) + Cl₂ (g) → 1MgCl₂ (s) Now, the balanced chemical equation is: Mg (s) + Cl₂ (g) → MgCl₂ (s)

Step 2: (b) Decomposition of Barium Carbonate when Heated

First, write the unbalanced chemical equation for the decomposition of Barium Carbonate (BaCO₃) into Barium Oxide (BaO) and Carbon Dioxide (CO₂) when heated: BaCO₃ (s) → BaO (s) + CO₂ (g) Next, balance the equation. The numbers of Barium, Carbon, and Oxygen atoms on both sides are already balanced. Therefore the balanced chemical equation is: BaCO₃ (s) → BaO (s) + CO₂ (g)

Step 3: (c) Combustion of Styrene in Air

First, let's write the unbalanced chemical equation for the combustion of Styrene (\(C_8H_8\)) in air. In a combustion reaction, Styrene reacts with Oxygen (O₂) to produce Carbon Dioxide (CO₂) and Water (H₂O): C₈H₈ (l) + O₂ (g) → CO₂ (g) + H₂O (g) Next, balance the equation. There are 8 carbon atoms, 8 hydrogen atoms and 2 oxygen atoms in the unbalanced equation. To balance the carbon atoms, we need to add a coefficient of 8 to CO₂: C₈H₈ (l) + O₂ (g) → 8CO₂ (g) + H₂O (g) To balance the hydrogen atoms, we need to add a coefficient of 4 to H₂O: C₈H₈ (l) + O₂ (g) → 8CO₂ (g) + 4H₂O (g) Now, to balance the oxygen atoms, we need to add a coefficient of 11/2 to O₂: C₈H₈ (l) + 11/2O₂ (g) → 8CO₂ (g) + 4H₂O (g) The balanced chemical equation is: C₈H₈ (l) + 11/2O₂ (g) → 8CO₂ (g) + 4H₂O (g)

Step 4: (d) Combustion of Dimethyl Ether in Air

First, write the unbalanced chemical equation for the combustion of Dimethyl Ether (CH₃OCH₃) in air. In a combustion reaction, Dimethyl Ether reacts with Oxygen (O₂) to produce Carbon Dioxide (CO₂) and Water (H₂O): CH₃OCH₃ (g) + O₂ (g) → CO₂ (g) + H₂O (g) Now, balance the equation. There are 2 carbon atoms, 6 hydrogen atoms, and 1 oxygen atom in the unbalanced equation. To balance the carbon atoms, add a coefficient of 2 to CO₂: CH₃OCH₃ (g) + O₂ (g) → 2CO₂ (g) + H₂O (g) To balance the hydrogen atoms, add a coefficient of 3 to H₂O: CH₃OCH₃ (g) + O₂ (g) → 2CO₂ (g) + 3H₂O (g) Finally, to balance the oxygen atoms, add a coefficient of 2 to O₂: CH₃OCH₃ (g) + 2O₂ (g) → 2CO₂ (g) + 3H₂O (g) The balanced chemical equation is: CH₃OCH₃ (g) + 2O₂ (g) → 2CO₂ (g) + 3H₂O (g)

Key Concepts

Chemical Reactions

Chemical reactions are processes that lead to the transformation of one set of chemical substances into another. In a typical chemical reaction, bonds between atoms in the reactants are broken and new bonds form to create the products. This results in changes in chemical properties and energy. Chemical reactions are represented by balanced chemical equations, which show the equal number of atoms of each element involved in both sides of the reaction.

• Reactants are substances that start the reaction.
• Products are substances that are formed as the reaction proceeds.
• Balancing chemical equations ensures that the mass and charge are conserved, fulfilling the Law of Conservation of Mass.

The balancing process involves adding coefficients in front of molecules to ensure the same number of each type of atom appears on both sides of the equation. It's vital to remember that the coefficients represent moles of a substance, not individual molecules or atoms.

Combustion Reactions

Combustion reactions are a type of chemical reaction where a substance combines with oxygen, releasing energy in the form of light and heat. These reactions can occur with organic compounds, like hydrocarbons, which are composed of carbon and hydrogen or with other elements that can oxidize. In combustion reactions, oxygen (O₂) from the air is typically the reactant that manages to oxidize another substance.

• Complete Combustion produces carbon dioxide (CO₂) and water (H₂O).
• Incomplete Combustion could result in carbon monoxide (CO) or even solid carbon (soot) if there is not enough oxygen.
• The combustion of hydrocarbons is crucial in everyday energy production, such as in cars or power plants, due to the energy released.

A common task in chemistry is to balance combustion reactions, as seen with the combustion of styrene and dimethyl ether. Each involves adding coefficients to balance the atoms of carbon, hydrogen, and oxygen to reflect the conservation of mass.

Decomposition Reactions

Decomposition reactions are those where a single compound breaks down into two or more simpler substances. This process often requires an input of energy, such as heat, light, or electricity, to proceed. They are the opposite of combination reactions where two or more substances combine to form a single new substance.

• During decomposition, the compound breaks apart, releasing more stable forms of the elements or compounds involved.
• These reactions are common in both natural processes and industrial applications.
• An illustrative example is the decomposition of barium carbonate into barium oxide and carbon dioxide upon heating.

Balancing decomposition reactions involves ensuring that the total number of each type of atom on the reactant side is equal to that on the products side. This is straightforward for cases like the decomposition of barium carbonate, where atoms are already present in simple ratios.