Problem 14 - Chemistry and Chemical Reactivity

Question

Write balanced equations for the following reactions of alkanes. (a) the reaction of methane with excess chlorine (b) complete combustion of cyclohexane, \(\mathbf{C}_{6} \mathrm{H}_{12},\) with excess oxygen

Step-by-Step Solution

Answer

(a) \( \text{CH}_4 + \text{Cl}_2 \rightarrow \text{CH}_3\text{Cl} + \text{HCl} \), (b) \( \text{C}_6 \text{H}_{12} + 9 \text{O}_2 \rightarrow 6 \text{CO}_2 + 6 \text{H}_2\text{O} \).

Step 1: Identify the Reactants for Reaction (a)

In the reaction of methane with chlorine, the reactants are methane (\( \text{CH}_4 \)) and chlorine (\( \text{Cl}_2 \)). The reaction is a substitution reaction where chlorine replaces one or more hydrogens in methane.

Step 2: Write the Unbalanced Equation for Reaction (a)

Write the equation representing the substitution reaction between methane and chlorine: \( \text{CH}_4 + \text{Cl}_2 \rightarrow \text{CH}_3\text{Cl} + \text{HCl} \).

Step 3: Balance the Equation for Reaction (a)

Ensure that there are equal numbers of each type of atom on both sides of the equation. This equation is already balanced as written: \( \text{CH}_4 + \text{Cl}_2 \rightarrow \text{CH}_3\text{Cl} + \text{HCl} \). If further chlorination occurs to produce \( \text{CH}_2\text{Cl}_2, \text{CHCl}_3 \) or \( \text{CCl}_4 \), the process would continue with more chlorine and reactions.

Step 4: Identify the Reactants for Reaction (b)

In the complete combustion of cyclohexane, the reactants are cyclohexane (\( \text{C}_6 \text{H}_{12} \)) and oxygen (\( \text{O}_2 \)). Complete combustion results in carbon dioxide (\( \text{CO}_2 \)) and water (\( \text{H}_2\text{O} \)) as products.

Step 5: Write the Unbalanced Equation for Reaction (b)

Write the initial unbalanced equation for the complete combustion of cyclohexane: \( \text{C}_6 \text{H}_{12} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2 \text{O} \).

Step 6: Balance the Equation for Reaction (b)

Balance carbon and hydrogen first: \( \text{C}_6 \text{H}_{12} + \text{O}_2 \rightarrow 6 \text{CO}_2 + 6 \text{H}_2 \text{O} \). Next, balance oxygen: \( \text{C}_6 \text{H}_{12} + 9 \text{O}_2 \rightarrow 6 \text{CO}_2 + 6 \text{H}_2 \text{O} \). The equation is now balanced.

Key Concepts

Balanced Chemical Equations

In chemistry, a balanced chemical equation ensures that the number of each type of atom on both sides of the equation is equal. This is crucial because of the law of conservation of mass, which states that matter cannot be created or destroyed. For example, in the reaction of methane with chlorine, the equation is written as \[ \text{CH}_4 + \text{Cl}_2 \rightarrow \text{CH}_3\text{Cl} + \text{HCl} \].To balance this equation, make sure each element has the same number of atoms on both sides:

• 1 carbon on each side for carbon atoms
• 4 hydrogens on each side for hydrogen atoms
• 2 chlorines on each side for chlorine atoms

This balanced equation accurately represents the chemical transformation.

Substitution Reaction

A substitution reaction involves the replacement of one atom or group of atoms in a molecule with another atom or group. In the reaction of methane and chlorine, chlorine atoms substitute hydrogen atoms in methane.The basic substitution reaction for methane is expressed as:

• \( \text{CH}_4 + \text{Cl}_2 \rightarrow \text{CH}_3\text{Cl} + \text{HCl} \)

This substitution may continue, leading to products like \( \text{CH}_2\text{Cl}_2 \) or \( \text{CCl}_4 \), by further reacting methane derivatives with chlorine.

Complete Combustion

Complete combustion occurs when a hydrocarbon reacts with sufficient oxygen to produce carbon dioxide and water. This process releases energy in the form of heat and light and is common in engines and burners.For cyclohexane (\( \text{C}_6\text{H}_{12} \)), the complete combustion equation is:

• \( \text{C}_6\text{H}_{12} + 9\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} \)

Balancing involves adjusting coefficients to ensure equal numbers of each atom appear on both sides of the equation.

Methane and Chlorine Reaction

The reaction between methane and chlorine is a prime example of a substitution reaction and occurs under ultraviolet light or heat. It helps to visualize the process in stages:1. **Initiation:** Chlorine molecules absorb energy and split into radicals.
2. **Propagation:** Chlorine radicals react with methane, creating new radicals and continuing the chain reaction.
3. **Termination:** Radicals combine to form stable products, ending the reaction.This complex but fascinating chain reaction is summarized by the balanced equation:\[ \text{CH}_4 + \text{Cl}_2 \rightarrow \text{CH}_3\text{Cl} + \text{HCl} \].

Cyclohexane Combustion

Cyclohexane combustion is a classic example of complete combustion, where cyclohexane reacts with oxygen to produce carbon dioxide and water. This process can be expressed in the balanced equation:\[ \text{C}_6\text{H}_{12} + 9\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} \]In the combustion of cyclohexane:

• Carbon is converted to carbon dioxide.
• Hydrogen is converted to water.

Such reactions are exothermic, meaning they release heat, making them ideal for energy production.