Problem 26 - 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, \(\mathrm{C}_{6} \mathrm{H}_{12}\) with excess oxygen.

Step-by-Step Solution

Answer

(a) CH₄ + 4 Cl₂ → CCl₄ + 4 HCl; (b) C₆H₁₂ + 9 O₂ → 6 CO₂ + 6 H₂O

Step 1: Understanding the reaction: Methane with chlorine

When methane reacts with excess chlorine, the reaction is a substitution reaction where one or more hydrogen atoms in methane are replaced by chlorine atoms. In such reactions, chlorine radicals replace hydrogen one-by-one potentially forming chloromethane, dichloromethane, trichloromethane, and carbon tetrachloride, depending on the availability of chlorine.

Step 2: Balancing the equation for Methane with chlorine

The general reaction can be represented as: CH₄ + Cl₂ → CH₃Cl + HCl. In the presence of excess chlorine, the reaction can continue to form: CH₄ + 4Cl₂ → CCl₄ + 4HCl. Ensure each atom type is balanced on both sides of the equation.

Step 3: Understanding the reaction: Combustion of cyclohexane

In complete combustion, an alkane like cyclohexane reacts with oxygen to form carbon dioxide and water. The general equation for combustion is: C₆H₁₂ + O₂ → CO₂ + H₂O. We need to balance this equation by ensuring that the number of atoms on each side is equal.

Step 4: Writing and balancing the equation for Combustion of cyclohexane

Start balancing from the number of carbon atoms: C₆H₁₂ + O₂ → 6CO₂ + H₂O. Next, balance the hydrogen atoms which are 12: C₆H₁₂ + O₂ → 6CO₂ + 6H₂O. Finally, you balance the oxygen, realizing you need 18 atoms: C₆H₁₂ + 9O₂ → 6CO₂ + 6H₂O.

Key Concepts

Alkanes

Alkanes are a group of hydrocarbons that consist solely of hydrogen and carbon atoms. They are also called saturated hydrocarbons because they have single bonds between carbon atoms. This means they hold the maximum number of hydrogen atoms possible.

• The simplest alkane is methane \((\text{CH}_4)\).
• Alkanes are generally stable substances, but they can participate in chemical reactions like combustion and substitution when the conditions are right.

Alkanes have a variety of uses, largely as fuels and as raw materials in the petrochemical industry. Their relatively stable nature makes them less reactive than other hydrocarbons, although they do react consistently in familiar patterns such as combustion.

Combustion Reactions

Combustion is a chemical reaction that occurs when a substance reacts with oxygen to produce energy in the form of light or heat. Complete combustion of alkanes produces carbon dioxide and water.

• In complete combustion, there is sufficient oxygen for all the fuel to react and burn, forming \({\text{CO}_2}\) and \(\text{H}_2\text{O}\).
• Partial combustion may occur when there is not enough oxygen, leading to carbon monoxide or even soot as byproducts.

For complete combustion of the alkane cyclohexane (\(\text{C}_6\text{H}_{12}\)), the balanced chemical equation is:\[\text{C}_6\text{H}_{12} + 9\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O}\]Here, nine molecules of oxygen are needed to fully oxidize the hydrocarbon completely.

Substitution Reactions

Substitution reactions are a type of chemical reaction where one atom in a molecule is replaced with a different atom or group of atoms. In alkanes, this is typically seen with halogens like chlorine or bromine in the presence of light or heat.

• Example: Methane \(\text{CH}_4\) reacting with chlorine gas \(\text{Cl}_2\) in excess.
• The hydrogen atoms in methane are replaced one-by-one by chlorine atoms, forming various chlorinated products.

The basic reaction of methane with chlorine could be:\[\text{CH}_4 + \text{Cl}_2 \rightarrow \text{CH}_3\text{Cl} + \text{HCl}\]With excess chlorine, further chlorination can occur until all hydrogen atoms are replaced, leading to products like carbon tetrachloride (\(\text{CCl}_4\)).

Balancing Equations

Balancing chemical equations is a process of ensuring that the number of atoms for each element involved in the reaction is the same on both sides of the equation. This reflects the law of conservation of mass, where matter is neither created nor destroyed.

• Start by counting the atoms of elements that appear in one reactant and one product first.
• Use coefficients to balance the number of atoms, starting from elements that appear in the least number of compounds.

For the combustion of cyclohexane, this process involves:

• Balancing the carbon atoms: \(\text{C}_6\text{H}_{12} + \text{O}_2 \rightarrow 6\text{CO}_2 + \text{H}_2\text{O}\)
• Balancing the hydrogen atoms: Now you have \(12\) hydrogen, so add \(6\) \(\text{H}_2\text{O}\)
• Balancing the oxygen atoms: Adjust the oxygen to \(9\text{O}_2\) for overall balance.

Balancing equations is crucial for understanding reaction stoichiometry and ensuring chemical reactions are represented accurately.