Question

Complete and balance the following equations: (a) \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \stackrel{\text { spark }}{\longrightarrow}\) (b) \(\mathrm{KAl}\left(\mathrm{SO}_{4}\right)_{2} \cdot 12 \mathrm{H}_{2} \mathrm{O}(s) \stackrel{\Delta}{\longrightarrow}\) (c) \(\mathrm{H}_{3} \mathrm{PO}_{4}(a q)+\mathrm{NaOH}(a q) \longrightarrow\)

Short answer

(a) \( ext{C}_4 ext{H}_9 ext{OH} + 6 ext{O}_2 ightarrow 4 ext{CO}_2 + 5 ext{H}_2 ext{O} \); (b) \( 2 ext{KAl(SO}_4 ext{)}_2 imes 12 ext{H}_2 ext{O} ightarrow ext{Al}_2 ext{O}_3 + ext{K}_2 ext{SO}_4 + 4 ext{SO}_2 + 12 ext{H}_2 ext{O} \); (c) \( ext{H}_3 ext{PO}_4 + 3 ext{NaOH} ightarrow ext{Na}_3 ext{PO}_4 + 3 ext{H}_2 ext{O} \).

Step-by-step solution

Identify Reactants and Products for (a)

For equation (a), identify the reactants: butanol (\[ ext{C}_4 ext{H}_9 ext{OH (l)} \]) and oxygen (\[ ext{O}_2 ext{ (g)} \]), and predict the products. This combustion reaction will yield carbon dioxide (\[ ext{CO}_2 \]) and water (\[ ext{H}_2 ext{O} \]).

Balance Equation (a)

To balance equation (a): 1. Balance carbon by ensuring 4 \[ ext{CO}_2 \]: \[ ext{C}_4 ext{H}_9 ext{OH} + ext{O}_2 ightarrow 4 ext{CO}_2 + ext{H}_2 ext{O} \].2. Balance hydrogen by having 5 \[ ext{H}_2 ext{O} \]: \[ ext{C}_4 ext{H}_9 ext{OH} + ext{O}_2 ightarrow 4 ext{CO}_2 + 5 ext{H}_2 ext{O} \].3. Finally, balance oxygen resulting in \[ 6 ext{O}_2 \]: \[ ext{C}_4 ext{H}_9 ext{OH} + 6 ext{O}_2 ightarrow 4 ext{CO}_2 + 5 ext{H}_2 ext{O} \].

Identify Reactants and Products for (b)

For equation (b), a thermal decomposition of \[ ext{KAl(SO}_4 ext{)}_2 imes 12 ext{H}_2 ext{O (s)} \] yields aluminum oxide (\[ ext{Al}_2 ext{O}_3 \]), potassium sulfate (\[ ext{K}_2 ext{SO}_4 \]), sulfur dioxide (\[ ext{SO}_2 \]), and water (\[ ext{H}_2 ext{O} \]).

Balance Equation (b)

Once decomposed, balance equation (b) noting the stoichiometry: - To match the formula weights: \[ 2 ext{KAl(SO}_4 ext{)}_2 ightarrow ext{Al}_2 ext{O}_3 + ext{K}_2 ext{SO}_4 + 4 ext{SO}_2 + 12 ext{H}_2 ext{O} \].

Identify Reactants and Products for (c)

For equation (c), phosphoric acid (\[ ext{H}_3 ext{PO}_4 \]) reacts with sodium hydroxide (\[ ext{NaOH} \]) to form sodium phosphate (\[ ext{Na}_3 ext{PO}_4 \]) and water (\[ ext{H}_2 ext{O} \]).

Balance Equation (c)

Start by balancing equation (c):1. Balance the phosphorous by having 1 \[ ext{Na}_3 ext{PO}_4 \]: \[ ext{H}_3 ext{PO}_4 + ext{NaOH} ightarrow ext{Na}_3 ext{PO}_4 + ext{H}_2 ext{O} \].2. Balance sodium by adding a coefficient of 3 to \[ ext{NaOH} \]: \[ ext{H}_3 ext{PO}_4 + 3 ext{NaOH} ightarrow ext{Na}_3 ext{PO}_4 + ext{H}_2 ext{O} \].3. Balance water by ensuring the reaction yields 3 \[ ext{H}_2 ext{O} \]: \[ ext{H}_3 ext{PO}_4 + 3 ext{NaOH} ightarrow ext{Na}_3 ext{PO}_4 + 3 ext{H}_2 ext{O} \].

Key concepts

Combustion Reaction

Combustion reactions are a type of chemical reaction where a substance combines with oxygen to release energy in the form of heat and light. This process is fundamental to many everyday reactions, such as burning fuel or lighting a candle.
One common example of a combustion reaction is the burning of a hydrocarbon. In the case of the provided exercise involving butanol, when \[\text{C}_4\text{H}_9\text{OH} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}\] it undergoes a spark-induced combustion with oxygen. This results in the formation of carbon dioxide \(\text{CO}_2\) and water \(\text{H}_2\text{O}\).
To correctly balance a combustion reaction:

• First, balance the elements that are present in only one reactant and one product — typically carbon.
• Next, move to hydrogen, which occurs in water as one of the products.
• Finally, balance oxygen, adjusting coefficients as necessary to match the oxygen atoms on both sides of the equation.

Understanding this sequence helps ensure the conservation of mass by making sure the number of atoms for each element is the same on both sides of the reaction equation.

Thermal Decomposition

Thermal decomposition refers to a chemical reaction in which heat causes a compound to break down into simpler substances. This type of reaction is also known as thermolysis and involves breaking chemical bonds within the molecule.
In the exercise, thermal decomposition is illustrated with \(\text{KAl(SO}_4\text{)}_2 \cdot 12 \text{H}_2\text{O}\) decomposing to form aluminum oxide \(\text{Al}_2\text{O}_3\), potassium sulfate \(\text{K}_2\text{SO}_4\), sulfur dioxide \(\text{SO}_2\), and water \(\text{H}_2\text{O}\). The balanced equation for this reaction is:\[2 \text{KAl(SO}_4\text{)}_2 \text{ } \rightarrow \text{ } \text{Al}_2\text{O}_3 + \text{K}_2\text{SO}_4 + 4 \text{SO}_2 + 12 \text{H}_2\text{O}\]
This reaction showcases how applying heat to hydrated salts can lead to the loss of water molecules and restructuring of the compound into salts and gases. Thermal decomposition is essential for applications such as recycling materials or understanding geological processes like the formation of rocks.
Balancing these reactions involves paying careful attention to the stoichiometry to ensure that each type of atom is accounted for on both sides of the reaction.

Acid-Base Reaction

Acid-base reactions, also known as neutralization reactions, occur when an acid and a base react to form water and a salt. These reactions are widespread in both laboratory settings and natural processes.
In the exercise, phosphoric acid \(\text{H}_3\text{PO}_4\) reacts with sodium hydroxide \(\text{NaOH}\) to produce sodium phosphate \(\text{Na}_3\text{PO}_4\) and water \(\text{H}_2\text{O}\). This reaction can be represented as:\[\text{H}_3\text{PO}_4 + 3\text{NaOH} \rightarrow \text{Na}_3\text{PO}_4 + 3\text{H}_2\text{O}\]
Key points to balance an acid-base reaction include:

• Start by balancing the atoms of the polyatomic ions as units. In this case, phosphate ions \(\text{PO}_4^{3-}\).
• Then, adjust the coefficients to balance the cation (sodium in this case) and hydrogen atoms.

These reactions are significant because they regulate pH in various systems, like human blood, and are foundational in the production of essential chemicals used in cleaning, agriculture, and industry.