Problem 77 - Chemistry Matter and Change

Question

Carbon reacts with oxygen to form two different compounds. Compound I contains 4.82 g of carbon for every 6.44 g of oxygen. Compound II contains 20.13 \(\mathrm{g}\) of carbon for every 53.7 \(\mathrm{g}\) of oxygen. What is the ratio of carbon to a fixed mass of oxygen for the two compounds?

Step-by-Step Solution

Answer

The ratio of carbon to a fixed mass of oxygen for Compound I to Compound II is 2:1.

Step 1: Understand the Problem

We need to find the ratio of carbon for a fixed mass of oxygen in two different compounds, using the given masses of carbon and oxygen.

Step 2: Calculate the Ratio for Compound I

For Compound I, the ratio of carbon to oxygen is calculated as follows:\[\text{Ratio for Compound I} = \frac{4.82\,\text{g of carbon}}{6.44\,\text{g of oxygen}}\]This simplifies to:\[\text{Ratio for Compound I} = 0.748\,\frac{\text{g of carbon}}{\text{g of oxygen}}\]

Step 3: Calculate the Ratio for Compound II

For Compound II, the ratio of carbon to oxygen is calculated as follows:\[\text{Ratio for Compound II} = \frac{20.13\,\text{g of carbon}}{53.7\,\text{g of oxygen}}\]This simplifies to:\[\text{Ratio for Compound II} = 0.375\,\frac{\text{g of carbon}}{\text{g of oxygen}}\]

Step 4: Compare the Ratios

Now that we have both ratios, we can compare them by calculating the ratio of the two ratios (carbon to oxygen across the two compounds).\[\text{Compound Ratio} = \frac{0.748}{0.375} \approx 2\]This indicates that for a fixed mass of oxygen, Compound I contains twice as much carbon as Compound II.

Key Concepts

Law of Multiple Proportions

The Law of Multiple Proportions is a fundamental principle in chemistry that explains the composition of different compounds formed from the same elements. It states that when two elements form more than one compound, the ratios of the masses of one element that combine with a fixed mass of the other are simple whole numbers. This means, for our case, when carbon and oxygen form two distinct compounds, the amount of carbon that combines with a specific mass of oxygen will form a simple ratio between these compounds.

In our example, you can observe this through the given compounds where both involve carbon and oxygen. By comparing their mass ratios, the law is exemplified by finding a whole-number relationship. Hence, through calculation, we find that the ratio of carbon in the two compounds relative to the fixed mass of oxygen is approximately 2:1. This practical illustration echoes the principle of the law of multiple proportions.

Chemical Reactions

Chemical reactions are processes where substances (reactants) change to produce new substances (products). They are governed by various principles, including the Law of Multiple Proportions, which provides insight on how elements combine in fixed ratios. In our example, carbon reacts with oxygen to form different compounds under different conditions.

Each chemical reaction follows a balanced chemical equation, ensuring the conservation of mass. This means that in our cases of Compound I and II, while the proportions in which carbon and oxygen react are different, the total amount of carbon and oxygen atoms remains consistent before and after the reaction. Understanding how these reactions work provides crucial insights into the stoichiometry of the compounds formed, offering a deeper view into the molecular composition and the conditions required for different outcomes.

Mass Ratios

Mass ratios are a critical concept in stoichiometry, allowing us to quantify the relationship between different elements within a compound or between compounds. In simple terms, a mass ratio tells us how much of one element is present relative to another in a compound.

In the exercise, by calculating the mass ratios of carbon to oxygen for both compounds, we derive meaningful data about the structure and composition of these compounds. Compound I shows a ratio of 0.748, while Compound II has a ratio of 0.375, indicating that different amounts of carbon combine with the same mass of oxygen.

• This difference highlights how different amounts of an element are required to form different compounds with the same element.
• It showcases the diversity of chemical combinations possible from just a few elements, underscoring the essence of stoichiometry in predicting the makeup of substances.

Understanding mass ratios can therefore provide a window into the building blocks of substances, demonstrating how the same elements can create entirely different compounds when combined in various proportions.