Question

Write a balanced chemical equation for the complete combustion of pentene, \(\mathrm{C}_{7} \mathrm{H}_{14} .\) In combustion, pentene reacts with oxygen to produce carbon dioxide and water.

Short answer

The balanced equation for the complete combustion of pentene is: \(2C_7H_{14} + 21O_2 \rightarrow 14CO_2 + 14H_2O\)

Step-by-step solution

Write the unbalanced equation

Write the unbalanced equation representing the complete combustion of pentene with oxygen gas as the reactant and carbon dioxide and water as the products: C7H14 + O2 -> CO2 + H2O

Balance the carbon atoms

There are 7 carbon atoms on the reactant side (in C7H14) and only 1 carbon atom in CO2 on the product side, so we need to multiply CO2 by 7 to balance the carbon atoms: C7H14 + O2 -> 7CO2 + H2O Now we have 7 carbon atoms on both sides.

Balance the hydrogen atoms

There are 14 hydrogen atoms on the reactant side (in C7H14) and 2 hydrogen atoms in H2O on the product side, so we need to multiply H2O by 7 to balance the hydrogen atoms: C7H14 + O2 -> 7CO2 + 7H2O Now we have 14 hydrogen atoms on both sides.

Balance the oxygen atoms

Finally, we need to balance the oxygen atoms. On the product side, we have 14 oxygen atoms in CO2 and another 7 oxygen atoms in H2O, making a total of 21 oxygen atoms. On the reactant side, we have 2 oxygen atoms in O2, so we need to multiply O2 by 10.5 to balance the oxygen atoms: C7H14 + 10.5O2 -> 7CO2 + 7H2O However, it is not common to see fractions in balanced chemical equations. To get rid of the fraction, we will multiply the entire equation by 2: 2C7H14 + 21O2 -> 14CO2 + 14H2O

Write the final balanced equation

The balanced equation for the complete combustion of pentene is: 2C7H14 + 21O2 -> 14CO2 + 14H2O

Key concepts

Combustion Reactions

Combustion reactions are a type of chemical process where a substance reacts with oxygen to produce heat and new chemical products. In our case with pentene, the combustion is classified as a complete combustion. This occurs when a hydrocarbon burns in the presence of ample oxygen. The primary products of complete combustion reactions are carbon dioxide \(\text{(CO}_2)\) and water \(\text{(H}_2\text{O)}\).
Complete combustion reactions are highly exothermic, meaning they release a significant amount of energy, usually in the form of heat and light.
In practical terms, this is what happens when fuels like gasoline burn in car engines or natural gas is used in heaters.
Key features of combustion reactions include:

• Involvement of oxygen as a reactant.
• Hydrocarbons, like pentene, serving as common fuel sources.
• Production of water and carbon dioxide as common by-products.
• Release of energy, often making flames appear.

Understanding combustion reactions is essential in both environmental and energy-related disciplines since they play a vital role in processes that involve energy production and consumption.

Hydrocarbons

Hydrocarbons are organic compounds composed entirely of hydrogen and carbon atoms. They serve as the base structure for many important substances like fuels, plastics, and even some pharmaceuticals. Pentene, the hydrocarbon involved in our exercise, is an unsaturated hydrocarbon classified as an alkene.
An alkene is characterized by having at least one double bond between carbon atoms.
This double bond gives alkenes unique properties like reactivity, which makes them suitable for combustion reactions.
There are different classes of hydrocarbons:

• Alkanes: Only single bonds between carbon atoms, making them less reactive.
• Alkenes: One or more double bonds, like pentene, with increased reactivity.
• Alkynes: One or more triple bonds, making them even more reactive.

Hydrocarbons can therefore vary in their chemical behavior, but they consistently serve as a significant energy source due to the energy released when their bonds are broken and reformed in reactions like combustion.
In environmental terms, combustion of hydrocarbons is a major source of energy but also contributes to greenhouse gas emissions. Hence, understanding hydrocarbons is crucial in discussions around sustainable energy and environmental impact.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with measuring the amounts of reactants and products in chemical reactions. It essentially ensures that chemical equations adhere to the law of conservation of mass, which dictates that matter cannot be created or destroyed in chemical processes.
A balanced chemical equation is a fundamental application of stoichiometry.In the balanced equation for the combustion of pentene:\[2\text{C}_7\text{H}_{14} + 21\text{O}_2 \rightarrow 14\text{CO}_2 + 14\text{H}_2\text{O}\]Every atom present in the reactants must be accounted for in the products.
This means the number of atoms for each element is the same on both sides of the equation:

• 14 carbon atoms on both sides.
• 28 hydrogen atoms on each side.
• 42 oxygen atoms on both sides (21 O2 molecules consumed).

Balancing equations like this is crucial not just for theoretical chemistry but also for practical applications like industrial production, where misuse of stoichiometry could lead to reactions that are inefficient or even hazardous.
Overall, stoichiometry is key in ensuring that all reactions conducted, whether in a lab or by natural processes, observe the inherent law of conservation of mass.