Question

Consider the unbalanced equation for the combustion of hexane: $$ \mathrm{C}_{6} \mathrm{H}_{14}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ Balance the equation and determine how many moles of \(\mathrm{O}_{2}\) are required to react completely with 7.2 moles of \(\mathrm{C}_{6} \mathrm{H}_{14}\).

Short answer

68.4 moles of \(\mathrm{O}_{2}\) are required to react completely with 7.2 moles of \(\mathrm{C}_{6} \mathrm{H}_{14}\).

Step-by-step solution

Write the Unbalanced Equation

Start with the unbalanced chemical equation for the combustion of hexane: \[ \mathrm{C}_{6} \mathrm{H}_{14}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) + \mathrm{H}_{2} \mathrm{O}(g) \]

Balance the Carbon Atoms

Hexane has 6 carbon atoms, so you need 6 molecules of carbon dioxide to balance the carbon atoms: \[ \mathrm{C}_{6} \mathrm{H}_{14}(g) + \mathrm{O}_{2}(g) \longrightarrow 6\mathrm{CO}_{2}(g) + \mathrm{H}_{2} \mathrm{O}(g) \]

Balance the Hydrogen Atoms

Hexane has 14 hydrogen atoms, which means you need 7 water molecules to balance the hydrogen atoms: \[ \mathrm{C}_{6} \mathrm{H}_{14}(g) + \mathrm{O}_{2}(g) \longrightarrow 6\mathrm{CO}_{2}(g) + 7\mathrm{H}_{2} \mathrm{O}(g) \]

Balance the Oxygen Atoms

Count the oxygen atoms on the product side: 6 molecules of CO2 contribute 12 oxygen atoms and 7 molecules of H2O contribute 7 oxygen atoms, making a total of 19 oxygen atoms. Therefore, you need 19/2 molecules of O2 to balance the oxygen atoms: \[ \mathrm{C}_{6} \mathrm{H}_{14}(g) + \frac{19}{2}\mathrm{O}_{2}(g) \longrightarrow 6\mathrm{CO}_{2}(g) + 7\mathrm{H}_{2} \mathrm{O}(g) \]

Calculate the Moles of Oxygen Needed

Using the balanced equation, it can be seen that 1 mole of hexane requires 19/2 moles of oxygen. To find out how many moles of oxygen are needed for 7.2 moles of hexane, set up a proportion: \[ \frac{19/2 \text{ moles of } \mathrm{O}_{2}}{1 \text{ mole of } C_{6}H_{14}} = \frac{x \text{ moles of } \mathrm{O}_{2}}{7.2 \text{ moles of } C_{6}H_{14}} \]Solve for x by cross-multiplication: \[ x = \frac{19}{2} \times 7.2 \]

Perform the Calculation

Now calculate the moles of oxygen required for 7.2 moles of hexane: \[ x = \frac{19}{2} \times 7.2 = 68.4 \text{ moles of } \mathrm{O}_{2} \]

Key concepts

Chemical Equation Balancing

Chemical equation balancing is the process of ensuring that the number of each type of atom on the reactant side is equal to the number on the product side of a chemical reaction. This is a fundamental concept in chemistry because it reflects the conservation of matter—no atoms are lost or gained in a chemical reaction.

To balance a chemical equation, follow these general steps:

• Write down the unbalanced equation.
• Count the number of atoms of each element in the reactants and products.
• Adjust coefficients (the numbers before the chemical formulas) in front of compounds to balance the atoms, starting with the most complex molecule.
• Iterate the process until all elements are balanced.
• Check your work by confirming that all elements have the same number of atoms on both sides of the equation.

In our hexane combustion example, we first adjusted the coefficient of CO₂ to balance the carbons, then the H₂O for hydrogens, and finally adjusted the O₂ to account for the oxygens. It's crucial to tackle the elements that appear in the least number of compounds first, typically leaving hydrogen and oxygen for last.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is a quantitative relationship based on the balanced equations and the mole concept.

To perform stoichiometric calculations, one must follow these steps:

• Ensure that the chemical equation is balanced.
• Convert all given information into moles (if they're not already).
• Use the balanced equation to set up mole ratios.
• Apply these ratios to find the answer to the problem in question.

In the combustion of hexane, after balancing the equation, we established a mole ratio of O₂ to C₆H₁₄ from the balanced equation (19/2 moles of O₂ for every mole of hexane). We then calculated the moles of oxygen needed for combustion when 7.2 moles of hexane are burned using this mole ratio. This type of calculation is a classic example of stoichiometry in action.

Mole Concept

The mole concept is a method of quantifying the amount of substance. One mole is the amount of substance that contains as many entities (atoms, molecules, ions, etc.) as there are in 12 grams of carbon-12—the Avogadro number, approximately 6.022 x 10²³ entities.

To use the mole concept in chemical reactions:

• Understand that the coefficients in a balanced equation represent the ratio of moles of reactants and products involved in the reaction.
• Use the mole ratio to convert between moles of different substances in the reaction.
• Calculate quantities of reactants or products (in moles, mass, volume, particles, etc.) based on these ratios.

In the hexane example, we used the mole concept to determine that if 1 mole of hexane requires 19/2 moles of O₂ for complete combustion, then 7.2 moles would require 7.2 times that amount of oxygen, leading to a calculation that shows 68.4 moles of oxygen are necessary.