Question

Balance this redox reaction by inspection. $$ \mathrm{C}_{18} \mathrm{H}_{38}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} $$

Short answer

2 mol of \(\mathrm{C}_{18}\mathrm{H}_{38}\) reacts with 55 mol of \(\mathrm{O}_{2}\) to form 36 mol of \(\mathrm{CO}_{2}\) and 38 mol of \(\mathrm{H}_{2}\mathrm{O}\).

Step-by-step solution

Identify Reactants and Products

Examine the chemical equation to identify the reactants and products: * Reactants: \ \( \mathrm{C}_{18} \mathrm{H}_{38} \) and \ \( \mathrm{O}_{2} \).* Products: \ \( \mathrm{CO}_{2} \) and \ \( \mathrm{H}_{2} \mathrm{O} \).

Balance Carbon Atoms

There are 18 carbon atoms in * \ \( \mathrm{C}_{18} \mathrm{H}_{38} \).To balance carbon atoms on both sides, equate them with the carbon atoms in \ \( \mathrm{CO}_{2} \):\[ \mathrm{C}_{18} \mathrm{H}_{38} + \mathrm{O}_{2} \rightarrow 18 \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O} \]

Balance Hydrogen Atoms

There are 38 hydrogen atoms in * \ \( \mathrm{C}_{18} \mathrm{H}_{38} \).To balance these, adjust the \ \( \mathrm{H}_{2} \mathrm{O} \) molecules:\[ \mathrm{C}_{18} \mathrm{H}_{38} + \mathrm{O}_{2} \rightarrow 18 \mathrm{CO}_{2} + 19 \mathrm{H}_{2} \mathrm{O} \]

Balance Oxygen Atoms

Calculate the number of oxygen atoms needed on the product side:* Oxygen in \ \( 18 \mathrm{CO}_{2} \) = 18 * 2 = 36 * Oxygen in \ \( 19 \mathrm{H}_{2} \mathrm{O} \) = 19* Total oxygen needed on the product side: 36 + 19 = 55Each \ \( \mathrm{O}_{2} \) molecule has 2 oxygen atoms, so divide by 2 to find the required \ \( \mathrm{O}_{2} \) molecules:\[ \mathrm{C}_{18} \mathrm{H}_{38} + \frac{55}{2} \mathrm{O}_{2} \rightarrow 18 \mathrm{CO}_{2} + 19 \mathrm{H}_{2} \mathrm{O} \]

Clear Fractional Coefficients

To avoid fractions, multiply the entire equation by 2:\[ 2 \mathrm{C}_{18} \mathrm{H}_{38} + 55 \mathrm{O}_{2} \rightarrow 36 \mathrm{CO}_{2} + 38 \mathrm{H}_{2} \mathrm{O} \]This step ensures all coefficients are whole numbers.

Key concepts

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. Understanding this process is crucial in balancing any chemical equation. For the given redox reaction, \[\mathrm{C}_{18} \mathrm{H}_{38} + \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O} \], there are two reactants: octadecane \(\mathrm{C}_{18}\mathrm{H}_{38}\), which is a hydrocarbon, and oxygen \(\mathrm{O}_{2}\). These react to form carbon dioxide \(\mathrm{CO}_{2}\) and water \(\mathrm{H}_{2} \mathrm{O}\), which are the products.

• The reactants and products each have specific atomic compositions.
• Balancing the chemical equation involves ensuring that each side of the equation has an equal number of each type of atom.
• This conservation of atoms reflects the Law of Conservation of Mass, where matter is neither created nor destroyed in a chemical reaction.

The process of balancing requires careful inspection of the equation to ensure the number of carbon, hydrogen, and oxygen atoms are the same on both sides. Learning to recognize the interplay between reactants transforming into products is fundamental to solving these kinds of chemical reactions.

Stoichiometry

Stoichiometry is the quantitative analysis of reactants and products in a chemical reaction. It allows us to understand the proportions necessary for each substance to fully react with no excess. In our example,\[ 2 \mathrm{C}_{18} \mathrm{H}_{38} + 55 \mathrm{O}_{2} \rightarrow 36 \mathrm{CO}_{2} + 38 \mathrm{H}_{2} \mathrm{O} \], we use stoichiometry to ensure that the quantities of octadecane and oxygen align with the quantities of carbon dioxide and water produced.

• Stoichiometric coefficients (like the numbers in front of the molecules in the balanced equation) tell us the mole ratio of reactants to products.
• This allows us to calculate the mass of reactants needed or products formed.
• In this reaction, the ratio between octadecane and oxygen indicates that 55 moles of oxygen react with 2 moles of \(\mathrm{C}_{18} \mathrm{H}_{38}\) to produce 36 moles of carbon dioxide and 38 moles of water.

Understanding stoichiometry provides insights into how much of each substance is consumed or created, guiding both laboratory and industrial chemical processes.

Introductory Chemistry

Introductory Chemistry lays the foundation for understanding the basic principles of chemistry. When first balancing redox reactions like this one, it's important to grasp some key concepts. Here are some fundamental ideas:

• A chemical equation represents the substances at the start (reactants) and end (products) of a chemical reaction.
• The coefficients in a balanced chemical equation show the smallest ratio between molecules needed for each reactant and product.
• Understanding atomic and molecular theory helps predict the outcomes of different reactions.

In simple terms, when balancing equations, we adjust coefficients to have equal numbers of each type of atom on both sides of the equation. For beginners, practicing with simple compounds before advancing to more complex redox reactions is highly beneficial. Mastery of these foundational skills fosters deeper understanding and appreciation of more complex chemical behavior.