Problem 45 - Chemistry Matter and Change

Question

One carbon \((\mathrm{C})\) and one ozone \(\left(\mathrm{O}_{3}\right)\) react to form one carbon monoxide \((\mathrm{CO})\) and one oxygen gas \(\left(\mathrm{O}_{2}\right)\) particle. How many ozone particles are needed to form 24 particles of oxygen gas (O \(_{2} ) ?\)

Step-by-Step Solution

Answer

24 ozone particles are needed to form 24 oxygen gas particles.

Step 1: Understand the Chemical Equation

First, let's write down the chemical equation representing the reaction: \[ \mathrm{C} + \mathrm{O}_3 \rightarrow \mathrm{CO} + \mathrm{O}_2. \] This shows that one molecule of carbon reacts with one molecule of ozone to produce one molecule of carbon monoxide and one molecule of oxygen gas.

Step 2: Identify the Ozone to Oxygen Relationship

Notice from the equation that one molecule of ozone (\(\mathrm{O}_3\)) produces one molecule of oxygen gas (\(\mathrm{O}_2\)). This means a 1:1 relationship exists between the amount of ozone and the oxygen gas produced.

Step 3: Calculate Ozone Needed for Target Oxygen

Since there is a 1:1 ratio of ozone particles to oxygen gas molecules, to produce 24 molecules of oxygen gas (\(\mathrm{O}_2\)), 24 molecules of ozone (\(\mathrm{O}_3\)) are needed.

Key Concepts

Chemical Reactions

Chemical reactions are fundamental processes in chemistry where substances, known as reactants, are transformed into different substances, called products. In the exercise example, the chemical reaction involves carbon and ozone reacting to produce carbon monoxide and oxygen gas. When these reactions occur, there is a breaking and forming of chemical bonds.

In every chemical reaction, the atoms themselves do not change; instead, they rearrange to form new molecules. That's why in our reaction, a carbon atom and an ozone molecule come together and results in a compound of carbon monoxide and a separate oxygen molecule.

• Reactants: The starting substances in a reaction (e.g., carbon and ozone in this case).
• Products: The substances formed from a reaction (e.g., carbon monoxide and oxygen gas).

Understanding the nature of chemical reactions helps us predict the amount of product that can form from a given amount of reactant.

Balancing Chemical Equations

Balancing chemical equations is essential because it ensures that the Law of Conservation of Mass is upheld; this law states that mass cannot be created or destroyed in a chemical reaction. For our reaction, the balanced equation is \[ \mathrm{C} + \mathrm{O}_3 \rightarrow \mathrm{CO} + \mathrm{O}_2. \]This simple equation is already balanced. Each side of the equation has the same number of each type of atom.

Here's a quick breakdown:

• One carbon atom on the reactant side and one carbon atom in carbon monoxide on the product side.
• Three oxygen atoms from ozone react to form one oxygen atom in carbon monoxide and two in oxygen gas, keeping oxygen balanced across the reaction.

Even though it seems straightforward, some reactions can be more complex, requiring multiple steps to ensure that each type of atom has the same count on both sides of the equation.

Mole Concept

The mole concept is a fundamental aspect of stoichiometry, allowing chemists to count particles like atoms and molecules in chemical reactions. A mole is a unit that represents a quantity of particles, specifically Avogadro's number: approximately 6.022 x 10^23 particles. This large number makes it a handy unit for counting atoms and molecules in chemical reactions, which involve significant numbers of these tiny entities.

In our example, though the exercise deals with individual particles, understanding moles can simplify calculations when larger quantities are involved. Knowing that there is a 1:1 ratio between ozone and oxygen in this reaction aligns with the stoichiometric concept that equal moles of each react to produce equivalent moles of product.

If you were asked to scale up from particles to moles:

• 24 molecules of ozone correspond to 24 molecules of oxygen gas.
• But if we think in terms of moles, 1 mole of ozone produces 1 mole of oxygen gas.

Recognizing how stoichiometry links moles and particles helps in performing conversions and understanding the basic principles of chemical reactions on a more manageable scale.