Problem 5 - Introductory Chemistry Atoms First

Question

Balance the chemical equation for the combustion of hexane, \(\mathrm{C}_{6} \mathrm{H}_{14}(l)\). The unbalanced equation is: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) Answer: Balance C: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) Balance H: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+7 \mathrm{H}_{2} \mathrm{O}(g)\) Balance O: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\frac{19}{2} \mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+7 \mathrm{H}_{2} \mathrm{O}(g)\) Multiply through by 2 to get rid of the fractional coefficient: \(2 \mathrm{C}_{6} \mathrm{H}_{14}(l)+19 \mathrm{O}_{2}(g) \rightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

The balanced equation for the combustion of hexane is: \(2 \mathrm{C}_{6} \mathrm{H}_{14}(l)+19 \mathrm{O}_{2}(g) \rightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(g)\)

Step 1: Balance C atoms

To balance the C atoms, we will count the number of C atoms on both sides of the equation and adjust the coefficients accordingly. There are 6 C atoms in hexane, so we will need 6 CO₂ molecules to balance the C atoms: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)

Step 2: Balance H atoms

Next, we will balance the H atoms. There are 14 H atoms in hexane, so we need 7 H₂O molecules to balance the H atoms: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+7 \mathrm{H}_{2} \mathrm{O}(g)\)

Step 3: Balance O atoms

Finally, we will balance the O atoms. There are 12 O atoms in 6 CO₂ molecules and 7 O atoms in 7 H₂O molecules, giving us a total of 19 O atoms on the products' side. We need 19/2 O₂ molecules to balance the O atoms: \(\mathrm{C}_{6} \mathrm{H}_{14}(l)+\frac{19}{2} \mathrm{O}_{2}(g) \rightarrow 6 \mathrm{CO}_{2}(g)+7 \mathrm{H}_{2} \mathrm{O}(g)\)

Step 4: Convert fractional coefficients to whole numbers

Since fractional coefficients are not proper, we must convert them into whole numbers. To do this, we will multiply the entire equation by 2: \(2 \mathrm{C}_{6} \mathrm{H}_{14}(l)+19 \mathrm{O}_{2}(g) \rightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(g)\) The balanced equation for the combustion of hexane is: \(2 \mathrm{C}_{6} \mathrm{H}_{14}(l)+19 \mathrm{O}_{2}(g) \rightarrow 12 \mathrm{CO}_{2}(g)+14 \mathrm{H}_{2} \mathrm{O}(g)\)

Key Concepts

Combustion Reaction

A combustion reaction is a chemical process in which a fuel, usually a hydrocarbon, reacts with oxygen to release energy in the form of heat and light. This type of reaction is key to many everyday processes, such as burning fuels in car engines or home heating systems. A hallmark of combustion reactions is that they produce oxides, typically carbon dioxide and water when hydrocarbons are involved. These reactions are typically exothermic, meaning they release energy. This energy results from the breaking and forming of chemical bonds during the reaction.

Hexane Combustion

Hexane is a type of hydrocarbon with the chemical formula \( \mathrm{C}_6\mathrm{H}_{14} \). It is used as a fuel due to its high energy output when burned. In the combustion of hexane, it reacts with oxygen gas \( \mathrm{O}_2 \) to form carbon dioxide \( \mathrm{CO}_2 \) and water \( \mathrm{H}_2\mathrm{O} \). The balanced equation for this reaction is: \[ 2\mathrm{C}_6\mathrm{H}_{14(l)} + 19\mathrm{O}_{2(g)} \rightarrow 12\mathrm{CO}_{2(g)} + 14\mathrm{H}_{2} \mathrm{O}_{(g)} \] This means that two molecules of hexane react with nineteen molecules of oxygen to produce twelve molecules of carbon dioxide and fourteen molecules of water. Balancing this equation involves ensuring that the number of each type of atom is the same on both sides of the chemical equation.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is crucial to understanding and balancing chemical equations. When balancing a chemical equation, coefficients are used to ensure that the law of conservation of mass is followed. This means the mass of the reactants equals the mass of the products, and atoms are neither created nor destroyed in a chemical reaction.

Key Points:

• Determine the number of atoms for each element on both sides of the equation.


• Adjust the coefficients to balance each type of atom.


• Use the smallest possible coefficients that maintain balance.


• In the combustion of hexane, stoichiometry helps ensure that the quantities of hexane, oxygen, carbon dioxide, and water are balanced according to their proportions in the balanced equation.

Chemical Reactions

Chemical reactions involve the transformation of substances into new materials with different properties. They are described by chemical equations that show the reactants transforming into products. These reactions are fundamental to everything around us, from the food we digest to the air we breathe. In the context of the combustion of hexane, the initial substances (hexane and oxygen) undergo a chemical change to become carbon dioxide and water.

Features of Chemical Reactions:

• Reactants and products are involved in every chemical reaction.


• The reaction can be exothermic or endothermic.


• Chemical reactions always obey the law of conservation of mass.


• Balancing these equations is a fundamental skill in chemistry because it ensures that the chemical process behaves according to natural laws.