Question

Write a balanced equation for the complete combustion of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\), and for the incomplete combustion of benzene to \(\mathrm{CO}\) and \(\mathrm{H}_{2} \mathrm{O}\).

Short answer

Complete combustion: \( 2\mathrm{C}_{6} \mathrm{H}_{6} + 15\mathrm{O}_2 \rightarrow 12\mathrm{CO}_{2} + 6\mathrm{H}_{2}\mathrm{O} \). Incomplete combustion: \( 2\mathrm{C}_{6} \mathrm{H}_{6} + 9\mathrm{O}_2 \rightarrow 12\mathrm{CO} + 6\mathrm{H}_{2} \mathrm{O} \).

Step-by-step solution

Identify Reactants and Products

In the complete combustion of benzene (\(\mathrm{C}_{6} \mathrm{H}_{6}\)), the reactants are benzene and oxygen (\(\mathrm{O}_2\)), while the products are carbon dioxide (\(\mathrm{CO}_{2}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)). In incomplete combustion, the products are carbon monoxide (\(\mathrm{CO}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)).

Write the Unbalanced Equation for Complete Combustion

For complete combustion, write the unbalanced equation: \[ \mathrm{C}_{6} \mathrm{H}_{6} + \mathrm{O}_2 \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O} \].

Balance Carbon Atoms

In complete combustion, each benzene molecule has 6 carbon atoms, requiring 6 CO2 molecules as products: \[ \mathrm{C}_{6} \mathrm{H}_{6} + \mathrm{O}_2 \rightarrow 6\mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O} \].

Balance Hydrogen Atoms

Each benzene molecule has 6 hydrogen atoms, needing 3 water molecules to balance the hydrogens: \[ \mathrm{C}_{6} \mathrm{H}_{6} + \mathrm{O}_2 \rightarrow 6\mathrm{CO}_{2} + 3\mathrm{H}_{2}\mathrm{O} \].

Balance Oxygen Atoms for Complete Combustion

Now, balance the oxygen atoms: there are 12 oxygen atoms from the 6 CO2 and 3 oxygen atoms from the 3 H2O, totaling 15 oxygen atoms. Therefore, we need 15/2 = 7.5 O2 molecules. To balance, the equation becomes: \[ 2\mathrm{C}_{6} \mathrm{H}_{6} + 15\mathrm{O}_2 \rightarrow 12\mathrm{CO}_{2} + 6\mathrm{H}_{2}\mathrm{O} \].

Write the Unbalanced Equation for Incomplete Combustion

For incomplete combustion, write the unbalanced equation: \[ \mathrm{C}_{6} \mathrm{H}_{6} + \mathrm{O}_2 \rightarrow \mathrm{CO} + \mathrm{H}_{2} \mathrm{O} \].

Balance Carbon Atoms for Incomplete Combustion

Each benzene molecule again has 6 carbon atoms, requiring 6 CO molecules to balance carbon atoms: \[ \mathrm{C}_{6} \mathrm{H}_{6} + \mathrm{O}_2 \rightarrow 6\mathrm{CO} + \mathrm{H}_{2} \mathrm{O} \].

Balance Hydrogen Atoms for Incomplete Combustion

As before, each benzene molecule has 6 hydrogen atoms requiring 3 molecules of water: \[ \mathrm{C}_{6} \mathrm{H}_{6} + \mathrm{O}_2 \rightarrow 6\mathrm{CO} + 3\mathrm{H}_{2} \mathrm{O} \].

Balance Oxygen Atoms for Incomplete Combustion

For the incomplete reaction, there are 6 oxygen atoms in 6 CO and 3 oxygen atoms in 3 H2O, totaling 9 oxygen atoms, requiring 4.5 O2. To balance: \[ 2\mathrm{C}_{6} \mathrm{H}_{6} + 9\mathrm{O}_2 \rightarrow 12\mathrm{CO} + 6\mathrm{H}_{2} \mathrm{O} \].

Key concepts

Balanced Chemical Equation

A balanced chemical equation is a mathematical representation of a chemical reaction where the number of atoms for each element in the reactants equals the number of atoms in the products. This is crucial since atoms cannot be created or destroyed in a chemical reaction. For example, in the complete combustion of benzene (\(\mathrm{C}_6 \mathrm{H}_6\)), the equation must show an equal count of carbon, hydrogen, and oxygen atoms on each side.

To balance the equation,

• Identify all reactants and products.
• Count atoms of each element in reactants and products.
• Adjust coefficients to get equal numbers of atoms on both sides.
• Verify that elements and charges are balanced.

While balancing equations, it's crucial to adjust only the coefficients, not the subscripts of the chemical formulas, as this would change the substances involved.

Complete Combustion

Complete combustion occurs when a substance reacts fully with oxygen, producing the maximum energy output, and the products typically include carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)). In the complete combustion of benzene:

\[2\mathrm{C}_6 \mathrm{H}_6 + 15\mathrm{O}_2 \rightarrow 12\mathrm{CO}_2 + 6\mathrm{H}_2 \mathrm{O}.\]Here, each \(\mathrm{C}_6\mathrm{H}_6\) molecule reacts with oxygen, resulting in carbon atoms forming carbon dioxide and hydrogen atoms forming water.
The ratio of oxygen is important. If insufficient oxygen is present, combustion cannot remain complete. Complete combustion is preferred for maximum energy efficiency and minimal pollution.

Incomplete Combustion

Incomplete combustion occurs when a substance reacts with insufficient oxygen, leading to different and often harmful products, like carbon monoxide (\(\mathrm{CO}\)). For benzene, the reaction is:

\[2\mathrm{C}_6 \mathrm{H}_6 + 9\mathrm{O}_2 \rightarrow 12\mathrm{CO} + 6\mathrm{H}_2 \mathrm{O}.\]In this scenario, not all carbon atoms form carbon dioxide (leading to carbon monoxide instead), which is a dangerous gas due to its toxicity. Incomplete combustion usually occurs in limited oxygen environments and is less efficient in terms of energy because more molecular bonds are left under-utilized.

Chemical Reaction Balancing

Balancing chemical reactions involves making sure the number of each type of atom on the reactant side equals the number on the product side. This fundamental process follows the law of conservation of mass.
Here’s a structured approach to balance equations:

• Write down the unbalanced equation.
• List the number of atoms for each element available.
• Adjust coefficients of reactants/products to match atom counts on both sides.
• Check each element once more to confirm the balance.

For instance, in balancing benzene combustion, we needed to ensure the same number of carbon, hydrogen, and oxygen on each side are accounted for. This guarantees the reaction is mathematically consistent and physically feasible.