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.

Short answer

(a) Chlorination: \(\mathrm{CH}_4 + \mathrm{Cl}_2 \rightarrow \mathrm{CH}_3\mathrm{Cl} + \mathrm{HCl}\). (b) Combustion: \(\mathrm{C}_{6}\mathrm{H}_{12} + 9\mathrm{O}_{2} \rightarrow 6\mathrm{CO}_{2} + 6\mathrm{H}_{2}\mathrm{O}\).

Step-by-step solution

Identify the Reaction Type for Methane

Methane (\(\mathrm{CH}_4\)) reacts with chlorine (\(\mathrm{Cl}_2\)) in a substitution reaction. In this case, chlorine atoms replace hydrogen atoms in methane, producing chloromethane (\(\mathrm{CH}_3\mathrm{Cl}\)) and hydrogen chloride (\(\mathrm{HCl}\)).

Write the Initial Equation for Methane Reaction

The general equation for the reaction of methane with excess chlorine is:\[ \mathrm{CH}_4 + \mathrm{Cl}_2 \rightarrow \mathrm{CH}_3\mathrm{Cl} + \mathrm{HCl} \]Since the reaction involves excess chlorine, it can proceed further to form more highly chlorinated products, which we will address next.

Consider Further Chlorination Steps

Excess chlorine allows further reactions, leading to products like dichloromethane (\(\mathrm{CH}_2\mathrm{Cl}_2\)), chloroform (\(\mathrm{CHCl}_3\)), and carbon tetrachloride (\(\mathrm{CCl}_4\)). Here is the step for dichloromethane:\[ \mathrm{CH}_3\mathrm{Cl} + \mathrm{Cl}_2 \rightarrow \mathrm{CH}_2\mathrm{Cl}_2 + \mathrm{HCl} \]And similar steps continue for further chlorination.

Write the Reaction for Complete Combustion of Cyclohexane

The complete combustion of cyclohexane (\(\mathrm{C}_{6} \mathrm{H}_{12}\)) with excess oxygen (\(\mathrm{O}_2\)) produces carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)). The unbalanced equation is:\[ \mathrm{C}_{6} \mathrm{H}_{12} + \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O} \]

Balance the Combustion Reaction Equation

Start by balancing the carbon atoms. There are 6 carbon atoms in \(\mathrm{C}_6\mathrm{H}_{12}\), requiring 6 \(\mathrm{CO}_2\):\[ \mathrm{C}_{6} \mathrm{H}_{12} + \mathrm{O}_{2} \rightarrow 6\mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O} \]Next, balance hydrogen: 12 hydrogen atoms require 6 \(\mathrm{H}_2\mathrm{O}\):\[ \mathrm{C}_{6} \mathrm{H}_{12} + \mathrm{O}_{2} \rightarrow 6\mathrm{CO}_{2} + 6\mathrm{H}_{2}\mathrm{O} \]Finally, balance the oxygen: there are 18 oxygen atoms needed (12 from \(\mathrm{CO}_{2}\) and 6 from \(\mathrm{H}_{2}\mathrm{O}\)), so 9 \(\mathrm{O}_2\) molecules are needed:\[ \mathrm{C}_{6} \mathrm{H}_{12} + 9\mathrm{O}_{2} \rightarrow 6\mathrm{CO}_{2} + 6\mathrm{H}_{2}\mathrm{O} \]

Key concepts

Substitution Reaction

Substitution reactions involve the replacement of one atom or a group of atoms in a molecule with a different atom or group. In organic chemistry, this often occurs in alkanes, which are saturated hydrocarbons with single bonds. Alkanes can undergo substitution reactions with halogens, such as chlorine, to form haloalkanes.

The basic process starts when a chlorine molecule (\(\mathrm{Cl}_2\)) interacts with an alkane, like methane (\(\mathrm{CH}_4\)). Ultraviolet light or heat is typically required to initiate the reaction, breaking the \(\mathrm{Cl}_2\) bond to form two \(\mathrm{Cl}\) radicals. These highly reactive radicals replace hydrogen atoms in the methane molecule, forming chloromethane (\(\mathrm{CH}_3\mathrm{Cl}\)) and hydrogen chloride (\(\mathrm{HCl}\)).

With excess chlorine, further chlorination can occur, leading to the formation of products like dichloromethane (\(\mathrm{CH}_2\mathrm{Cl}_2\)), chloroform (\(\mathrm{CHCl}_3\)), and eventually carbon tetrachloride (\(\mathrm{CCl}_4\)). Each step involves the substitution of another hydrogen atom with a chlorine atom. This series results from the highly reactive nature of chlorine radicals and the availability of hydrogen atoms in methane.

Combustion Reaction

Combustion reactions are a type of chemical process where a substance reacts with oxygen, releasing energy in forms such as heat and light. In the context of alkanes, combustion can be either complete or incomplete. Complete combustion typically involves an alkane reacting with an excess of oxygen to produce carbon dioxide and water.

For example, cyclohexane (\(\mathrm{C}_{6} \mathrm{H}_{12}\)) undergoes complete combustion when mixed with an abundance of oxygen. The resultant products of this reaction are carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)). The energy released in this process is significant, which is why alkanes like cyclohexane are used as fuels in engines and heating systems.

The visible signs of complete combustion are a clean flame with no soot. If there's not enough oxygen, incomplete combustion occurs, potentially producing carbon monoxide (\(\mathrm{CO}\)) or even carbon (\(\mathrm{C}\)), contributing to pollution and being hazardous to health.

Chemical Equation Balancing

Balancing chemical equations is an essential skill in understanding chemical reactions. It ensures the law of conservation of mass is upheld, meaning the mass of reactants equals the mass of the products.

When balancing a chemical equation, the number of each type of atom on the reactant side must match the number on the product side. For instance, in the combustion of cyclohexane, start by balancing carbon atoms: \(\mathrm{C}_{6} \mathrm{H}_{12} + \mathrm{O}_{2} \rightarrow 6 \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O}\). Cyclohexane contains 6 carbon atoms, so we'll need 6 molecules of \(\mathrm{CO}_{2}\).

Next, balance the hydrogen atoms. Since there are 12 in cyclohexane, we need 6 molecules of water to provide 12 hydrogen atoms: \(\mathrm{C}_{6} \mathrm{H}_{12} + \mathrm{O}_{2} \rightarrow 6 \mathrm{CO}_{2} + 6 \mathrm{H}_{2}\mathrm{O}\). Finally, balance the oxygen atoms. The 6 \(\mathrm{CO}_{2}\) and 6 \(\mathrm{H}_{2}\mathrm{O}\) require a total of 18 oxygen atoms, hence 9 \(\mathrm{O}_{2}\) molecules are needed for balance: \(\mathrm{C}_{6} \mathrm{H}_{12} + 9\mathrm{O}_{2} \rightarrow 6 \mathrm{CO}_{2} + 6 \mathrm{H}_{2}\mathrm{O}\). Balancing is crucial for predicting the quantities of reactants and products involved in the chemical reaction.