Problem 17 - Chemistry The Central Science

Question

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;\) (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; (d) dimethylether, \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(g)\), is combusted in air.

Step-by-Step Solution

Answer

a) \( \mathrm{Mg}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{MgCl}_{2}(s) \) b) \( \mathrm{BaCO}_{3}(s) \xrightarrow{\Delta} \mathrm{BaO}(s) + \mathrm{CO}_{2}(g) \) c) \( \mathrm{C}_{8} \mathrm{H}_{8}(l) + 6 \mathrm{O}_{2}(g) \rightarrow 8 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2}\mathrm{O}(l) \) d) \( 2 \mathrm{CH}_{3} \mathrm{OCH}_{3}(g) + 3 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2}\mathrm{O}(l) \)

Step 1: a) Magnesium reacts with chlorine gas

The reaction between magnesium (Mg) and chlorine gas (Cl2) will produce magnesium chloride (MgCl2). The balanced chemical equation is: \[ \mathrm{Mg}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{MgCl}_{2}(s) \]

Step 2: b) Barium carbonate decomposes into barium oxide and carbon dioxide gas when heated

Upon heating, barium carbonate (BaCO3) decomposes into barium oxide (BaO) and carbon dioxide gas (CO2). The balanced chemical equation for this reaction is: \[ \mathrm{BaCO}_{3}(s) \xrightarrow{\Delta} \mathrm{BaO}(s) + \mathrm{CO}_{2}(g) \]

Step 3: c) Combustion of styrene (C8H8) in air

The combustion of styrene (C8H8) in the presence of oxygen (O2) will produce carbon dioxide (CO2) and water (H2O). The balanced chemical equation for this reaction is: \[ \mathrm{C}_{8} \mathrm{H}_{8}(l) + 6 \mathrm{O}_{2}(g) \rightarrow 8 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2}\mathrm{O}(l) \]

Step 4: d) Combustion of dimethylether (CH3OCH3) in air

The combustion of dimethylether (CH3OCH3) in the presence of oxygen (O2) will produce carbon dioxide (CO2) and water (H2O). The balanced chemical equation for this reaction is: \[ 2 \mathrm{CH}_{3} \mathrm{OCH}_{3}(g) + 3 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2}\mathrm{O}(l) \]

Key Concepts

Chemical Reactions

Chemical reactions occur when substances known as reactants interact to form new substances called products. This process involves breaking and forming chemical bonds. Chemical equations represent these transformations using symbols to denote elements and compounds. They also use arrows to indicate the direction of the reaction. For example, consider the reaction

• between magnesium (\(\mathrm{Mg}(s)\)) and chlorine (\(\mathrm{Cl}_{2}(g)\)).

The resulting product is magnesium chloride (\(\mathrm{MgCl}_{2}(s)\)), expressed as: \[ \mathrm{Mg}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{MgCl}_{2}(s) \] Balancing chemical equations is crucial, ensuring the number of each type of atom in the reactants equals the number in the products. This satisfies the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.

Combustion Reactions

Combustion reactions are a type of chemical reaction where a substance combines with oxygen to release energy. This process is highly exothermic and usually produces heat and light. Combustion is common when organic compounds react in the presence of oxygen. For instance, burning hydrocarbons such as styrene and dimethyl ether results in complete combustion when they fully react with oxygen, producing carbon dioxide and water.In a balanced combustion reaction of styrene (\(\mathrm{C}_{8} \mathrm{H}_{8}(l)\)), styrene reacts with oxygen to form: \[ \mathrm{C}_{8} \mathrm{H}_{8}(l) + 6 \mathrm{O}_{2}(g) \rightarrow 8 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2}\mathrm{O}(l) \]Similarly, dimethyl ether (\(\mathrm{CH}_{3} \mathrm{OCH}_{3}(g)\)) undergoes combustion: \[ 2 \mathrm{CH}_{3} \mathrm{OCH}_{3}(g) + 3 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2}\mathrm{O}(l) \] These reactions emphasize the importance of understanding the reactivity of substances with oxygen and their potential to release significant energy.

Decomposition Reactions

Decomposition reactions involve a single compound breaking down into two or more simpler substances. Unlike combustion, they do not require oxygen and often occur when the compound is heated. These reactions can be understood best by considering the breakdown of barium carbonate (\(\mathrm{BaCO}_{3}(s)\)).When heated, barium carbonate decomposes into barium oxide (\(\mathrm{BaO}(s)\)) and carbon dioxide gas (\(\mathrm{CO}_{2}(g)\)): \[ \mathrm{BaCO}_{3}(s) \xrightarrow{\Delta} \mathrm{BaO}(s) + \mathrm{CO}_{2}(g) \]In decomposition, the compound absorbs energy, which causes it to break into fragments. This type of reaction is important in various industrial processes where specific materials or gases need to be produced from a compound.

Magnesium Chloride Production

The production of magnesium chloride is a straightforward chemical reaction between magnesium and chlorine. This reaction is exothermic, meaning it releases heat as magnesium atoms transfer electrons to chlorine atoms, forming ionic magnesium chloride. This simple synthesis reaction is represented by the equation: \[ \mathrm{Mg}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{MgCl}_{2}(s) \]Magnesium chloride is significant in industries due to its applications in producing magnesium metal and as a de-icing agent for roads. The ionic nature of magnesium chloride, which consists of positively charged magnesium ions (\(\mathrm{Mg}^{2+}\)) and negatively charged chloride ions (\(\mathrm{Cl}^-\)), accounts for its high solubility in water and suitability for these roles. Understanding this reaction shows the predictive power of chemical equations in anticipating product formation and energy changes.