Problem 84 - Chemistry The Molecular Nature of Matter

Question

Consider the balanced equation for the combustion of hexane, a component of gasoline: $$ 2 \mathrm{C}_{6} \mathrm{H}_{14}+19 \mathrm{O}_{2} \longrightarrow 12 \mathrm{CO}_{2}+14 \mathrm{H}_{2} \mathrm{O} $$ (a) How many atoms of \(\mathrm{C}\) are on each side of the equation? (b) How many atoms of \(\mathrm{H}\) are on each side of the equation? (c) How many atoms of \(\mathrm{O}\) are on each side of the equation?

Step-by-Step Solution

Answer

There are 12 carbon atoms, 28 hydrogen atoms, and 38 oxygen atoms on each side of the equation.

Step 1: Counting Carbon Atoms

Examine the coefficients and subscripts to determine the number of carbon atoms on each side of the equation. On the left, each molecule of hexane has 6 carbon atoms, and there are 2 molecules, so there are a total of 2 x 6 = 12 carbon atoms. On the right, each molecule of carbon dioxide has 1 carbon atom, and there are 12 molecules, so there are also 12 carbon atoms.

Step 2: Counting Hydrogen Atoms

Similarly, count the hydrogen atoms. On the left, each molecule of hexane has 14 hydrogen atoms, and there are 2 molecules, resulting in 2 x 14 = 28 hydrogen atoms. On the right, each water molecule has 2 hydrogen atoms, and there are 14 molecules of water, so we have 14 x 2 = 28 hydrogen atoms.

Step 3: Counting Oxygen Atoms

Counting oxygen atoms is a bit more complex due to their presence in two compounds on the right side of the equation. On the left, there are 19 oxygen diatomic molecules (O2), which accounts for 19 x 2 = 38 oxygen atoms. On the right, each carbon dioxide molecule contains 2 oxygen atoms, resulting in 12 x 2 = 24 oxygen atoms from CO2, plus the 14 oxygen atoms from the 14 water molecules. Combine these for a total of 24 + 14 = 38 oxygen atoms.

Key Concepts

Stoichiometry

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the substances involved in a chemical reaction. It establishes the proportional relationship between reactants and products using the mole concept, balanced equations, and Avogadro's number. When balancing chemical equations, stoichiometry ensures that the number of atoms for each element is conserved, adhering to the law of conservation of mass.

For instance, in the combustion of hexane (C₆H₁₄), stoichiometry guides us to balance the equation so the number of carbon (C), hydrogen (H), and oxygen (O) atoms are the same on both sides, as seen in the exercise above. This balance is crucial for accurately determining how much product will form from a given amount of reactant, which is essential in fields such as chemical engineering and pharmacology.

In practical terms, stoichiometry is used to calculate the amounts of reactants needed and products formed, making it a foundational concept for both theoretical and applied chemistry. When performing these calculations, moles are used as the standard unit to measure substances, ensuring a common scale for quantifying chemical reactions.

Combustion Reaction

A combustion reaction is a type of chemical reaction where a substance combines with oxygen to release energy, generally in the form of heat and light. Combustion reactions are exothermic, meaning they produce energy, and they are characterized by the presence of oxygen as a reactant. Common examples include the burning of wood, the reaction within automobile engines, and the combustion of fossil fuels like the hexane mentioned in the exercise.

In the combustion of hexane, oxygen (O₂) reacts with hexane (C₆H₁₄) to form carbon dioxide (CO₂) and water (H₂O), releasing energy. The balanced chemical equation, as provided, shows the stoichiometric ratio between reactants and products, ensuring the conservation of mass. In educational settings, analyzing combustion reactions helps students understand energy transformations, reaction enthalpies, and the practical implications for energy production. Moreover, it alerts students to the role of oxygen in combustion and emphasizes the importance of balancing equations to accurately represent the process.

Mole Concept

The mole concept is a fundamental principle in chemistry that acts as a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure and observe. One mole represents Avogadro's number (approximately 6.022 x 10²³) of particles, whether they are atoms, molecules, ions, or electrons. This large number is equivalent to the number of atoms in 12 grams of carbon-12, providing a basis for counting particles by weighing them.

Considering our example, understanding the mole concept allows us to determine how many moiles of carbon atoms (12 moles) and hydrogen atoms (28 moles) are involved in the combustion of hexane. When balancing chemical equations, the mole concept provides a framework for ensuring that the same number of moles of each element is present on both sides of the reaction. This correlation between the mole concept and stoichiometry is vital for predicting the outcomes of chemical reactions and for calculating reactant and product quantities in laboratory settings, industrial processes, and environmental analysis.