Problem 17 - Chemistry: The Central Science

Question

Complete and balance the following equations: (a) \(\mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow\) (b) \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow\) (c) \(\mathrm{MnO}_{2}(s)+\mathrm{C}(s) \stackrel{\Delta}{\longrightarrow}\) (d) \(\mathrm{AlP}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow\) (e) \(\mathrm{Na}_{2} \mathrm{~S}(s)+\mathrm{HCl}(a q) \longrightarrow\)

Step-by-Step Solution

Answer

(a) \(3\mathrm{Mg}_{3}\mathrm{N}_{2}(s) + 6\mathrm{H}_{2}\mathrm{O}(l) \longrightarrow 3\mathrm{Mg(OH)}_2(s) + 6\mathrm{NH}_3(g)\) (b) \(\mathrm{C}_{3}\mathrm{H}_{7}\mathrm{OH}(l) + \cfrac{9}{2}\mathrm{O}_{2}(g) \longrightarrow 3\mathrm{CO}_{2}(g) + 4\mathrm{H}_2\mathrm{O}(g)\) (c) \(\mathrm{MnO}_{2}(s) + \mathrm{C}(s) \stackrel{\Delta}{\longrightarrow} \mathrm{Mn}(s) + \mathrm{CO}_2(g)\) (d) \(\mathrm{AlP}(s) + 3\mathrm{H}_{2}\mathrm{O}(l) \longrightarrow \mathrm{Al(OH)}_3(s) + \mathrm{PH}_3(g)\) (e) \(\mathrm{Na}_{2}\mathrm{S}(s) + 2\mathrm{HCl}(aq) \longrightarrow 2\mathrm{NaCl}(s) + \mathrm{H}_{2}\mathrm{S}(g)\)

Step 1: (a) Identifying Reaction and Balancing the Equation

For the given reaction: \(\mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow\) This is a synthesis reaction between magnesium nitride and water to produce magnesium hydroxide and ammonia gas. First, write the products: \(\mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Mg(OH)}_2(s) + \mathrm{NH}_3(g)\) Now, balance the equation: \(\mathrm{3 Mg}_{3} \mathrm{~N}_{2}(s)+\mathrm{6 H}_{2} \mathrm{O}(l) \longrightarrow 3 \mathrm{Mg(OH)}_2(s) + \mathrm{6 NH}_3(g)\)

Step 2: (b) Identifying Reaction and Balancing the Equation

For the given reaction: \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow\) This is a combustion reaction of propanol with oxygen to produce carbon dioxide and water. First, write the products: \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + \mathrm{H}_2 \mathrm{O}(g)\) Now, balance the equation: \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)+\cfrac{9}{2}\mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g) + \mathrm{4 H}_2 \mathrm{O}(g)\)

Step 3: (c) Identifying Reaction and Balancing the Equation

For the given reaction: \(\mathrm{MnO}_{2}(s)+\mathrm{C}(s) \stackrel{\Delta}{\longrightarrow}\) This is a reduction reaction of manganese dioxide with carbon to produce manganese and carbon dioxide. First, write the products: \(\mathrm{MnO}_{2}(s)+\mathrm{C}(s) \stackrel{\Delta}{\longrightarrow} \mathrm{Mn}(s) + \mathrm{CO}_2(g)\) Now, balance the equation: \(\mathrm{MnO}_{2}(s)+\mathrm{C}(s) \stackrel{\Delta}{\longrightarrow} \mathrm{Mn}(s) + \mathrm{CO}_2(g)\) (The equation is already balanced)

Step 4: (d) Identifying Reaction and Balancing the Equation

For the given reaction: \(\mathrm{AlP}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow\) This is a decomposition reaction of aluminum phosphide reacting with water to produce aluminum hydroxide and phosphine gas. First, write the products: \(\mathrm{AlP}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Al(OH)}_3(s) + \mathrm{PH}_3(g)\) Now, balance the equation: \(\mathrm{AlP}(\mathrm{s})+\\mathrm{3 H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Al(OH)}_3(s) + \mathrm{PH}_3(g)\)

Step 5: (e) Identifying Reaction and Balancing the Equation

For the given reaction: \(\mathrm{Na}_{2} \mathrm{~S}(s)+\mathrm{HCl}(a q) \longrightarrow\) This is a double displacement reaction between sodium sulfide and hydrochloric acid to produce sodium chloride and hydrogen sulfide. First, write the products: \(\mathrm{Na}_{2} \mathrm{~S}(s)+\mathrm{HCl}(a q) \longrightarrow \mathrm{NaCl}(s) + \mathrm{H}_{2} \mathrm{S}(g)\) Now, balance the equation: \(\mathrm{Na}_{2} \mathrm{~S}(s)+2\mathrm{HCl}(a q) \longrightarrow 2\mathrm{NaCl}(s) + \mathrm{H}_{2} \mathrm{S}(g)\)

Key Concepts

Synthesis Reaction

In a synthesis reaction, two or more reactants combine to form a single product. A classic example of this type of reaction occurs when elements or compounds combine to form a complex compound. A synthesis reaction is often represented by the general formula:

\( A + B \rightarrow AB \)

These reactions are fundamental to the creation of many compounds. In the exercise provided, magnesium nitride reacts with water in a synthesis reaction to form magnesium hydroxide and ammonia:

\( \mathrm{3Mg_{3}N_{2}(s) + 6H_{2}O(l) \longrightarrow 3Mg(OH)_{2}(s) + 2NH_{3}(g)} \)

It is crucial to balance the equation to ensure that the same number of atoms of each element is present on both sides, adhering to the law of conservation of mass.

Combustion Reaction

A combustion reaction involves the burning of a substance in the presence of oxygen, releasing energy in the form of heat and light. This type of reaction is exothermic and typically involves hydrocarbons and oxygen to form carbon dioxide and water. The general equation for a combustion reaction with a hydrocarbon is:

\( C_xH_y + O_2 \rightarrow CO_2 + H_2O \)

In the given exercise, propanol (an alcohol) combusts in the presence of oxygen, producing carbon dioxide and water:

\( \mathrm{C_{3}H_{7}OH(l) + \cfrac{9}{2}O_{2}(g) \longrightarrow 3CO_{2}(g) + 4H_{2}O(g)} \)

Balancing a combustion reaction requires careful adjustment of coefficients to ensure that the number of atoms of each element is the same on both sides of the equation.

Reduction Reaction

A reduction reaction is a chemical reaction wherein a substance gains electrons, reducing its oxidation state. This process often involves a transfer of electrons between two substances. It's commonly associated with the reduction-oxidation (redox) reactions where one species is reduced and another is oxidized. The general form of a reduction reaction is:

\( A + e^- \rightarrow A^- \)

In the provided example, manganese dioxide is reduced to manganese by carbon (acting as a reducing agent) which is oxidized to carbon dioxide:

\( \mathrm{MnO_{2}(s) + C(s) \stackrel{\Delta}{\longrightarrow} Mn(s) + CO_{2}(g)} \)

This reaction is thermally driven, as indicated by the delta symbol (\(\Delta\)), and the equation is already balanced, demonstrating that one mole of manganese dioxide reacts with one mole of carbon to produce one mole of manganese and one mole of carbon dioxide.

Decomposition Reaction

During a decomposition reaction, a single compound breaks down into two or more simpler substances. This type of reaction can be caused by heat, light, or electricity. It follows the reverse pattern of a synthesis reaction and is typically represented by:

\( AB \rightarrow A + B \)

An example is the decomposition of aluminum phosphide with water as shown in the exercise, forming aluminum hydroxide and phosphine gas:

\( \mathrm{AlP(s) + 3H_{2}O(l) \longrightarrow Al(OH)_{3}(s) + PH_{3}(g)} \)

Balancing this reaction ensures that the reactants decompose to yield the correct amount of products without violating the law of conservation of mass.

Double Displacement Reaction

In a double displacement reaction, also known as a metathesis reaction, parts of two ionic compounds are exchanged and form two new compounds. This reaction typically occurs in aqueous solutions and can be represented by the formula:

\( AB + CD \rightarrow AD + CB \)

In the solution provided, sodium sulfide reacts with hydrochloric acid in a double displacement reaction to yield sodium chloride and hydrogen sulfide:

\( \mathrm{Na_{2}S(s) + 2HCl(aq) \longrightarrow 2NaCl(s) + H_{2}S(g)} \)

Balancing the equation ensures that the exchange between the ions is accurately represented and the reaction adheres to the law of conservation of mass.