Problem 49 - Chemistry The Science in Context

Question

Using different-colored spheres to represent \(\mathrm{C}\) and \(\mathrm{O}\) sketch the reaction between five C atoms and the necessary number of \(\mathrm{O}_{2}\) molecules to produce a \(50 \%\) mixture of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\).

Step-by-Step Solution

Answer

In a 50% mixture using five C atoms, 2 CO molecules and 3 CO2 molecules are formed.

Step 1: Determine the proportion of CO and CO2 molecules in the mixture

Since we want a 50% mixture of CO and CO2, we shall have equal number of CO and CO2 molecules. We have a total of 5 C atoms, therefore we must have 2 CO molecules and 3 CO2 molecules in the mixture.

Step 2: Determine the number of O2 molecules required for the reaction

For the CO molecules, we require one oxygen atom for each CO molecule. So, we need 2 oxygen atoms for the 2 CO molecules. For the CO2 molecules, we require two oxygen atoms for each CO2 molecule. As we have 3 CO2 molecules, we need a total of 6 oxygen atoms. In summary, we need a total of 8 oxygen atoms. Since 1 O2 molecule contains 2 oxygen atoms, we require \(\frac{8}{2} = 4\) O2 molecules for the reaction.

Step 3: Sketch the reaction using different-colored spheres

Now that we know the number of O2 molecules and the proportion of CO and CO2 molecules formed, we can sketch the reaction. We will represent the C atoms with black spheres and the O atoms with red spheres. Let's use the following representation: - C: Black Sphere - O: Red Sphere The reaction can be written as: 5 C (black spheres) + 4 O2 (8 red spheres) -> 2 CO (2 black spheres + 2 red spheres) + 3 CO2 (3 black spheres + 6 red spheres) In the sketch, we will have: 1. Five black spheres representing the C atoms. 2. Four pairs of red spheres representing the O2 molecules. 3. Two pairs of black and red spheres connected together, representing the 2 CO molecules formed. 4. Three groups of one black sphere connected to two red spheres each, representing the 3 CO2 molecules formed. By following these steps and representing the atoms and molecules using colored spheres, you can visually demonstrate the reaction between five C atoms and the necessary number of O2 molecules to produce a 50% mixture of CO and CO2.

Key Concepts

Molecular Representation

Representing molecules through colored spheres can be a fun and visual way to understand how atoms interact in chemical reactions. Each type of atom is usually represented by a specific color to distinguish them easily. For example:

• Carbon (\( C \)) is often depicted as black spheres.
• Oxygen (\( O \)) might be shown as red spheres.

This kind of molecular representation helps illustrate how molecules are put together. Each sphere represents an atom, and their connections show how these atoms are bonded in a molecule. This visual approach can make complex reactions more tangible by clearly showing how atoms combine and rearrange in a reaction.
In the provided exercise, black spheres represent carbon atoms while red spheres stand for oxygen. The sketching of the reaction through these spheres helps us understand how five carbon atoms combine with oxygen atoms to form a mixture of carbon monoxide (\( CO \)) and carbon dioxide (\( CO_2 \)).

Balancing Chemical Equations

Balancing chemical equations is a crucial part of understanding chemical reactions. It ensures that the same number of atoms of each element are present on both sides of the reaction. This concept is derived from the Law of Conservation of Mass, which states that matter cannot be created or destroyed in an isolated system.To balance an equation, one must adjust the coefficients, which are the numbers placed before molecules in a chemical equation. By doing so, you ensure that the number of atoms for each element is equal on both the reactant and product sides. This guarantees mass conservation and is essential for accurately describing the reaction process.
In our example with carbon and oxygen, we balanced the chemical equation to ensure the reaction produces a 50% mixture of \( CO \) and \( CO_2 \). This involves calculating the proper number of oxygen molecules (\( O_2 \)) needed to completely react with carbon atoms. Through this balancing act, we used 4 \( O_2 \) molecules to react with 5 carbon atoms, leading to the formation of 2 \( CO \) molecules and 3 \( CO_2 \) molecules.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships, or ratios, of substances in chemical reactions. It involves calculations that predict the amounts of reactants needed and products formed in a given reaction. This concept is crucial for practical applications, such as calculating the amount of reactants required to produce a desired quantity of product.The stoichiometric calculations start with writing a balanced chemical equation. From there, you determine the mole ratios between the reactants and products. These ratios help us interpret the quantitative aspect of the reaction.
In the example exercise, stoichiometry was employed to calculate the necessary number of \( O_2 \) molecules needed to react with carbon to produce the desired mixture. By using the stoichiometric ratios, the problem determined that we need 4 \( O_2 \) molecules to provide the 8 oxygen atoms required for producing 2 \( CO \) and 3 \( CO_2 \). It gives us a quantitative look at how much oxygen is involved in the reaction set in the problem, ensuring the reaction is aligned with what is physically possible.