Problem 21 - Chemistry The Central Science In Si Units

Question

Balance the following equations and indicate whether they are combination, decomposition, or combustion reactions: (a) \(\mathrm{C}_{7} \mathrm{H}_{16}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) (b) \(\mathrm{Li}_{3} \mathrm{~N}(s)+\mathrm{BN}(s) \longrightarrow \mathrm{Li}_{3} \mathrm{BN}_{2}(s)\) (c) \(\mathrm{Zn}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{ZnO}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (d) \(\mathrm{Ag}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Ag}(s)+\mathrm{O}_{2}(g)\)

Step-by-Step Solution

Answer

(a) Combustion, balanced: \(\mathrm{C}_{7}\mathrm{H}_{16} + 11\mathrm{O}_{2} \rightarrow 7\mathrm{CO}_{2} + 8\mathrm{H}_{2}\mathrm{O}\). (b) Combination, balanced as is. (c) Decomposition, balanced as is. (d) Decomposition, balanced: \(2\mathrm{Ag}_{2}\mathrm{O} \rightarrow 4\mathrm{Ag} + \mathrm{O}_{2}\).

Step 1: Analyze Reaction (a)

Equation (a) is a combustion reaction because it involves a hydrocarbon reacting with oxygen to form carbon dioxide and water. Combustion reactions typically have the form of a hydrocarbon (or similar) plus oxygen producing CO₂ and H₂O.

Step 2: Balance Equation (a)

The unbalanced equation is \(\mathrm{C}_{7} \mathrm{H}_{16}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\). First, balance carbon atoms: 7 carbon atoms from \(\mathrm{C}_7\mathrm{H}_{16}\) gives 7 \(\mathrm{CO}_2\). Next, balance hydrogen: 16 hydrogens give 8 \(\mathrm{H}_2\mathrm{O}\). Finally, balance oxygen with 11 \(\mathrm{O}_2\): 7 CO₂ needs 14 O and 8 H₂O needs 8 O, totaling 22 O in products, equivalent to 11 O₂. The balanced equation is: \(\mathrm{C}_{7}\mathrm{H}_{16}(s) + 11\mathrm{O}_{2}(g) \longrightarrow 7\mathrm{CO}_{2}(g) + 8\mathrm{H}_{2}\mathrm{O}(l)\).

Step 3: Analyze Reaction (b)

Equation (b) is a combination reaction because two reactants, \(\mathrm{Li}_{3} \mathrm{~N}\) and \(\mathrm{BN}\), are combining to form a single product, \(\mathrm{Li}_{3} \mathrm{BN}_{2}\).

Step 4: Balance Equation (b)

The unbalanced equation is \(\mathrm{Li}_{3} \mathrm{~N}(s)+\mathrm{BN}(s) \longrightarrow \mathrm{Li}_{3} \mathrm{BN}_{2}(s)\). Balance the equation by ensuring each type of atom is present in equal quantities on both sides: 1 \(\mathrm{Li}_{3} \mathrm{~N} + 1\mathrm{BN} \rightarrow 1 \mathrm{Li}_{3} \mathrm{BN}_{2}\). The equation is already balanced as written.

Step 5: Analyze Reaction (c)

Equation (c) is a decomposition reaction because a single compound, \(\mathrm{Zn(OH)}_2\), breaks down into two products, \(\mathrm{ZnO}\) and \(\mathrm{H}_2\mathrm{O}\).

Step 6: Balance Equation (c)

The unbalanced equation is \(\mathrm{Zn(OH)}_2(s) \longrightarrow \mathrm{ZnO}(s) + \mathrm{H}_2\mathrm{O}(l)\). To balance, note that each side already contains the same numbers of each type of atom: 1 Zn, 2 H, and 2 O from \(\mathrm{Zn(OH)}_{2}\) match those in \(\mathrm{ZnO}\) and \(\mathrm{H}_2\mathrm{O}\). The equation is already balanced.

Step 7: Analyze Reaction (d)

Equation (d) is a decomposition reaction because \(\mathrm{Ag}_2\mathrm{O}\) is breaking down into two products, \(\mathrm{Ag}\) and \(\mathrm{O}_2\).

Step 8: Balance Equation (d)

The unbalanced equation is \(\mathrm{Ag}_2\mathrm{O}(s) \longrightarrow \mathrm{Ag}(s) + \mathrm{O}_2(g)\). To balance, note there are 2 silver atoms in \(\mathrm{Ag}_2\). Add 2 \(\mathrm{Ag}\) to products: \(2\mathrm{Ag}_2\mathrm{O} \longrightarrow 4\mathrm{Ag} + \mathrm{O}_2\). This balances both sides: 4 Ag and 2 O in reactants and products.

Key Concepts

Combustion Reactions

Combustion reactions are a common type of chemical reaction where a substance reacts with oxygen to release energy in the form of heat or light. These reactions usually involve hydrocarbons—compounds made of hydrogen and carbon—and result in the formation of carbon dioxide and water. A typical example can be seen in reaction (a):
\[\mathrm{C}_{7} \mathrm{H}_{16}(s)+11 \mathrm{O}_{2}(g) \longrightarrow 7 \mathrm{CO}_{2}(g)+8 \mathrm{H}_{2} \mathrm{O}(l)\]
Here's what happens in steps:

• Identify the Reactants and Products: In combustion reactions, identify the hydrocarbon and oxygen as reactants, and carbon dioxide and water as products.
• Balance the Carbon: Adjust coefficients to balance the number of carbon atoms on both sides of the equation.
• Balance the Hydrogen: Then balance the hydrogen atoms, typically by adjusting the water molecules produced.
• Balance the Oxygen: Finally, count the oxygen molecules required from the products and adjust the \( \mathrm{O}_2 \) molecules in the reactants accordingly.

These stepwise balances ensure that the mass and atom count are equal on both sides of the equation, sticking to the law of conservation of mass.

Combination Reactions

In combination reactions, also known as synthesis reactions, two or more simple substances combine to form a more complex compound. This is exemplified in reaction (b):
\[\mathrm{Li}_{3} \mathrm{~N}(s)+\mathrm{BN}(s) \longrightarrow \mathrm{Li}_{3} \mathrm{BN}_{2}(s)\]
Here's a breakdown of the steps involved:

• Identify the Reactants and Product: Identify the reactants that merge to form a single compound.
• Balancing the Equation: Since synthesis reactions usually become balanced naturally as they form one simple compound, you often find the equation balanced with equal counts of each atom on both reactants and product sides from the start.

Understanding these reactions is crucial, as they appear in many practical applications, such as the formation of compounds like salts or combining elements to form compounds with desired properties.

Decomposition Reactions

Decomposition reactions involve breaking down one compound into two or more simpler substances. Reaction (c) and (d) illustrate this process:
(c) \(\mathrm{Zn(OH)}_{2}(s) \longrightarrow \mathrm{ZnO}(s)+\mathrm{H}_{2} \mathrm{O}(l)\)
(d) \(\mathrm{Ag}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Ag}(s)+\mathrm{O}_{2}(g)\)
The process of decomposition usually involves a single reactant yielding multiple products. Steps to balance include:

• Identify the Breakdown: Recognize when a compound splits into simpler components.
• Balancing the Products: Ensure the number of atoms for each element in the reactants matches those in the products. Adjust coefficients as needed.
• Special Considerations: Sometimes, decomposition requires energy like heat, light, or electricity to proceed.

This type of reaction is quite common, especially in laboratory settings and industrial processes where compounds need to be broken down into more useful forms.