Problem 105 - Introductory Chemistry Atoms First

Question

When propane gas, \(\mathrm{C}_{3} \mathrm{H}_{8}\), reacts with oxygen gas, carbon dioxide gas and water are produced. Write the balanced equation for the reaction.

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction of propane gas with oxygen gas is: \(C_{3}H_{8} + 7O_{2} \rightarrow 3CO_{2} + 4H_{2}O\).

Step 1: Write the unbalanced chemical equation

Write down the unbalanced chemical equation: \(C_{3}H_{8} + O_{2} \rightarrow CO_{2} + H_{2}O\)

Step 2: Balance carbon atoms

There are 3 carbon atoms on the left side of the equation (in the propane molecule) and only 1 on the right side (in the CO2 molecule). Add a coefficient of 3 in front of CO2 to balance the carbon atoms: \(C_{3}H_{8} + O_{2} \rightarrow 3CO_{2} + H_{2}O\)

Step 3: Balance hydrogen atoms

There are 8 hydrogen atoms on the left side of the equation (in the propane molecule) and only 2 on the right side (in the H2O molecule). Add a coefficient of 4 in front of H2O to balance the hydrogen atoms: \(C_{3}H_{8} + O_{2} \rightarrow 3CO_{2} + 4H_{2}O\)

Step 4: Balance oxygen atoms

There are now 6 + 8 = 14 oxygen atoms on the right side of the equation. To balance the oxygen atoms, add a coefficient of 7 in front of O2 on the left side of the equation: \(C_{3}H_{8} + 7O_{2} \rightarrow 3CO_{2} + 4H_{2}O\) Now the chemical equation is balanced with the same number of atoms of each element on both sides of the equation. So, the balanced chemical equation for the reaction of propane gas with oxygen gas is: \(C_{3}H_{8} + 7O_{2} \rightarrow 3CO_{2} + 4H_{2}O\)

Key Concepts

Propane Combustion

Propane combustion is a well-known chemical reaction involving the burning of propane gas. This process requires propane, a hydrocarbon made up of carbon (\( C \)) and hydrogen (\( H \)) atoms, and oxygen gas (\( O_2 \)). When propane combusts, it produces carbon dioxide (\( CO_2 \)) and water (\( H_2O \)) as byproducts. This is a common reaction used in various applications such as heating, cooking, and in engines because it releases a significant amount of energy. To initiate propane combustion, sufficient heat is required, which breaks the bonds in the propane molecules and allows them to react with oxygen.

• Propane is represented by the chemical formula \( C_3H_8 \).
• Combustion requires oxygen, often from the air, to proceed.
• The balanced chemical equation for complete combustion of propane is: \( C_3H_8 + 7O_2 \rightarrow 3CO_2 + 4H_2O \).

Propane combustion, like other combustion reactions, releases energy primarily in the form of heat and light, making it an exothermic process.

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, transform into different substances called products. The fundamental nature of a chemical reaction involves making and breaking of chemical bonds. During a reaction, atoms in the reactants rearrange themselves to form new molecules. In the case of propane combustion, the reactants are propane (\( C_3H_8 \)) and oxygen (\( O_2 \)), and the products are carbon dioxide (\( CO_2 \)) and water (\( H_2O \)).

• The reactants and products must balance; meaning, the same number of each type of atom is found on both sides of the chemical equation.
• Balancing a chemical equation involves adjusting coefficients (the numbers in front of molecules) until there’s an equal amount of each atom on each side.
• Chemical reactions often involve energy changes, such as the release or absorption of heat.

These reactions form the basis of many processes both in the natural world and in industrial settings, contributing to everything from energy production to the synthesis of new materials.

Stoichiometry

Stoichiometry is a branch of chemistry involving quantitative relationships in chemical reactions. It is a vital tool for understanding how reactants turn into products in a chemical equation. Stoichiometry allows chemists to calculate how much of a substance is required or produced in a given reaction. In our propane combustion example, stoichiometry helps to determine the specific amounts of oxygen needed to fully combust one mole of propane gas. Using stoichiometry, we can figure out:

• For each mole of \( C_3H_8 \), 7 moles of \( O_2 \) are required to produce 3 moles of \( CO_2 \) and 4 moles of \( H_2O \).
• This balanced equation reveals the proportional relationships between reactants and products.
• These calculations can also be extended to measure quantities in grams, liters, or even molecules, depending on the units needed.

Thus, stoichiometry is essential for accurately predicting the outcomes of chemical reactions and for practical applications in laboratory and industrial environments.