Problem 13 - Chemistry: The Central Science

Question

Write balanced chemical equations to correspond to each of the following descriptions: (a) Solid calcium carbide, \(\mathrm{CaC}_{2}\), reacts with water to form an aqueous solution of calcium hydroxide and acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}\). (b) When solid potassium chlorate is heated, it decomposes to form solid potassium chloride and oxygen gas. (c) Solid zinc metal reacts with sulfuric acid to form hydrogen gas and an aqueous solution of zinc sulfate. (d) When liquid phosphorus trichloride is added to water, it reacts to form aqueous phosphorous acid, \(\mathrm{H}_{3} \mathrm{PO}_{3}(a q)\), and aqueous hydrochloric acid. (e) When hydrogen sulfide gas is passed over solid hot iron(III) hydroxide, the resultant reaction produces solid iron(III) sulfide and gaseous water.

Step-by-Step Solution

Answer

(a) \(\mathrm{CaC}_{2}(s) + 2\mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{Ca(OH)}_{2}(aq) + \mathrm{C}_{2} \mathrm{H}_{2}(g)\) (b) \(2\mathrm{KClO}_{3}(s) \rightarrow 2\mathrm{KCl}(s) + 3\mathrm{O}_{2}(g)\) (c) \(\mathrm{Zn}(s) + \mathrm{H}_{2}\mathrm{SO}_{4}(aq) \rightarrow \mathrm{H}_{2}(g) + \mathrm{ZnSO}_{4}(aq)\) (d) \(\mathrm{PCl}_{3}(l) + 3\mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{H}_{3}\mathrm{PO}_{3}(aq) + 3\mathrm{HCl}(aq)\) (e) \(3\mathrm{H}_{2}\mathrm{S}(g) + 2\mathrm{Fe(OH)}_{3}(s) \rightarrow \mathrm{Fe}_{2}\mathrm{S}_{3}(s) + 6\mathrm{H}_{2}\mathrm{O}(g)\)

Step 1: Write the unbalanced equation

The given reaction can be represented as: \(\mathrm{CaC}_{2}(s) + \mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{Ca(OH)}_{2}(aq) + \mathrm{C}_{2} \mathrm{H}_{2}(g)\)

Step 2: Balance the equation

Adjust the coefficients to balance the equation: \(\mathrm{CaC}_{2}(s) + 2\mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{Ca(OH)}_{2}(aq) + \mathrm{C}_{2} \mathrm{H}_{2}(g)\) (b) When solid potassium chlorate is heated, it decomposes to form solid potassium chloride and oxygen gas.

Step 1: Write the unbalanced equation

The given reaction can be represented as: \(\mathrm{KClO}_{3}(s) \rightarrow \mathrm{KCl}(s) + \mathrm{O}_{2}(g)\)

Step 2: Balance the equation

Adjust the coefficients to balance the equation: \(2\mathrm{KClO}_{3}(s) \rightarrow 2\mathrm{KCl}(s) + 3\mathrm{O}_{2}(g)\) (c) Solid zinc metal reacts with sulfuric acid to form hydrogen gas and an aqueous solution of zinc sulfate.

Step 1: Write the unbalanced equation

The given reaction can be represented as: \(\mathrm{Zn}(s) + \mathrm{H}_{2}\mathrm{SO}_{4}(aq) \rightarrow \mathrm{H}_{2}(g) + \mathrm{ZnSO}_{4}(aq)\)

Step 2: Balance the equation

The equation is already balanced. (d) When liquid phosphorus trichloride is added to water, it reacts to form aqueous phosphorous acid, \(\mathrm{H}_{3} \mathrm{PO}_{3}(aq)\), and aqueous hydrochloric acid.

Step 1: Write the unbalanced equation

The given reaction can be represented as: \(\mathrm{PCl}_{3}(l) + \mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{H}_{3}\mathrm{PO}_{3}(aq) + \mathrm{HCl}(aq)\)

Step 2: Balance the equation

Adjust the coefficients to balance the equation: \(\mathrm{PCl}_{3}(l) + 3\mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{H}_{3}\mathrm{PO}_{3}(aq) + 3\mathrm{HCl}(aq)\) (e) When hydrogen sulfide gas is passed over solid hot iron(III) hydroxide, the resultant reaction produces solid iron(III) sulfide and gaseous water.

Step 1: Write the unbalanced equation

The given reaction can be represented as: \(\mathrm{H}_{2}\mathrm{S}(g) + \mathrm{Fe(OH)}_{3}(s) \rightarrow \mathrm{Fe}_{2}\mathrm{S}_{3}(s) + \mathrm{H}_{2}\mathrm{O}(g)\)

Step 2: Balance the equation

Adjust the coefficients to balance the equation: \(3\mathrm{H}_{2}\mathrm{S}(g) + 2\mathrm{Fe(OH)}_{3}(s) \rightarrow \mathrm{Fe}_{2}\mathrm{S}_{3}(s) + 6\mathrm{H}_{2}\mathrm{O}(g)\)

Key Concepts

Chemical Reactions

Chemical reactions are processes that involve the transformation of substances through the breaking and forming of chemical bonds. In a chemical reaction, the starting materials, known as reactants, undergo a chemical change to produce one or more new substances, called products. The properties of the reactants are different from those of the products, which might be gases, liquids, solids, or solutions.

• Every chemical reaction is represented by a chemical equation, indicating the substances used and those produced.
• Chemical changes are usually accompanied by observable indicators such as color change, temperature change, gas evolution, or precipitation of a solid.

Understanding chemical reactions is crucial for predicting the outcomes of various processes, from simple laboratory experiments to complex industrial production.

Stoichiometry

Stoichiometry is the area of chemistry that involves quantifying the amount of reactants and products in a chemical reaction. It is based on the principle of the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.

• Stoichiometry helps in determining the proportions of elements and compounds involved in a chemical reaction.
• It's used extensively in calculating yields, determining limiting reactants, and scaling reactions to support practical applications like manufacturing.

For instance, in the reaction of zinc with sulfuric acid: \[\text{Zn}(s) + \text{H}_2\text{SO}_4(aq) \rightarrow \text{H}_2(g) + \text{ZnSO}_4(aq)\]this reaction uses stoichiometry to ensure that the amounts of hydrogen gas and zinc sulfate formed are predictable from given amounts of reactants.

Chemical Balancing

Chemical balancing is the process of equalizing the number of atoms of each element in the reactants and products of a chemical equation. A balanced chemical equation complies with the law of conservation of mass.

• This ensures that the mass and charge are the same before and after a reaction occurs.
• Chemical balancing involves adding coefficients before chemical formulas, which multiply the formulas without altering the compounds themselves.

For instance, in the decomposition of potassium chlorate:\[2\text{KClO}_3(s) \rightarrow 2\text{KCl}(s) + 3\text{O}_2(g)\]adding coefficients ensures that the number of each type of atom is conserved.

Reaction Stoichiometry

Reaction stoichiometry refers to the quantitative relationships or ratios between the amounts of reactants and products involved in a chemical reaction. These ratios are derived from the coefficients of a balanced chemical equation.

• It provides insight into how much product will form from a given amount of reactant, as well as how much of one reactant is needed to react with a given amount of another.
• A classic application is in determining the theoretical yield of a product, which is the maximum amount of product expected based on stoichiometric calculations.

For example, in the combustion of acetylene gas:\[\text{CaC}_2(s) + 2\text{H}_2\text{O}(l) \rightarrow \text{Ca(OH)}_2(aq) + \text{C}_2\text{H}_2(g)\]reaction stoichiometry tells us that 1 mole of calcium carbide reacts with 2 moles of water to produce specific amounts of calcium hydroxide and acetylene gas.