Calculating Oxygen Mass In Carbon Dioxide Formation A Stoichiometry Example

Jul 16, 2025 by ADMIN 76 views

Stoichiometry and Mass Conservation in Carbon Dioxide Formation

The fundamental principles of chemistry govern the interactions and transformations of matter. Among these principles, the law of conservation of mass stands as a cornerstone, asserting that matter is neither created nor destroyed in ordinary chemical reactions. This principle is particularly relevant in stoichiometry, the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. In this article, we delve into the reaction between carbon and oxygen to form carbon dioxide, a classic example illustrating stoichiometry and mass conservation. We will analyze a specific scenario where 18 grams of carbon react with oxygen to produce 72 grams of carbon dioxide, and we will determine the mass of oxygen required for this reaction. Understanding these concepts is crucial for predicting and controlling chemical reactions in various scientific and industrial applications.

Understanding the Chemical Reaction: Carbon and Oxygen

The reaction between carbon and oxygen to form carbon dioxide ( ${CO_2}$ ) is a fundamental chemical process with significant implications for both natural phenomena and industrial applications. The balanced chemical equation for this reaction is:

${ C + O_2 \rightarrow CO_2 }$

This equation tells us that one atom of carbon (C) reacts with one molecule of oxygen ( ${O_2}$ ) to produce one molecule of carbon dioxide ( ${CO_2}$ ). This reaction is exothermic, meaning it releases energy in the form of heat and light. It is the same reaction that occurs during combustion, such as burning wood or fossil fuels. To fully grasp the quantitative aspects of this reaction, we must consider the molar masses of the reactants and products. The molar mass of carbon (C) is approximately 12 grams per mole, the molar mass of oxygen ( ${O_2}$ ) is approximately 32 grams per mole, and the molar mass of carbon dioxide ( ${CO_2}$ ) is approximately 44 grams per mole. These molar masses provide the basis for stoichiometric calculations, allowing us to determine the mass relationships between reactants and products in the reaction.

Stoichiometry and the Law of Conservation of Mass

Stoichiometry is the study of the quantitative relationships or ratios between two or more substances undergoing a physical change or chemical reaction. It is rooted in the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. This law implies that the total mass of the reactants must equal the total mass of the products in a balanced chemical equation. In the reaction between carbon and oxygen to form carbon dioxide, the law of conservation of mass dictates that the mass of carbon plus the mass of oxygen consumed must equal the mass of carbon dioxide produced. This principle is crucial for determining the amount of reactants needed or products formed in a chemical reaction. For example, if we know the mass of carbon reacting and the mass of carbon dioxide formed, we can calculate the mass of oxygen required using the conservation of mass principle. This calculation is essential in various fields, including industrial chemistry, environmental science, and chemical research, where precise control over reaction quantities is necessary.

Problem Statement: Determining the Mass of Oxygen

The problem at hand involves a specific scenario: 18 grams of carbon react with oxygen to produce 72 grams of carbon dioxide. Our goal is to determine the mass of oxygen needed in this reaction. This is a classic application of stoichiometric principles and the law of conservation of mass. To solve this, we will use the balanced chemical equation for the reaction:

${ C + O_2 \rightarrow CO_2 }$

and the principle that the total mass of the reactants must equal the total mass of the products. By applying these concepts, we can set up a simple equation to calculate the mass of oxygen consumed in the reaction. This problem not only reinforces the understanding of stoichiometric relationships but also highlights the practical application of the law of conservation of mass in chemical calculations. The ability to solve such problems is fundamental to quantitative chemistry and is essential for various applications, from laboratory experiments to industrial processes. Understanding the mass relationships in chemical reactions allows chemists and engineers to optimize reactions, predict yields, and ensure efficient use of resources.

Applying the Law of Conservation of Mass

The law of conservation of mass is the key to solving this problem. It states that the total mass of the reactants in a chemical reaction must equal the total mass of the products. In our case, the reactants are carbon (C) and oxygen ( ${O_2}$ ), and the product is carbon dioxide ( ${CO_2}$ ). We can express this relationship mathematically as:

${ \text{Mass of Carbon} + \text{Mass of Oxygen} = \text{Mass of Carbon Dioxide} }$

We are given that 18 grams of carbon react to produce 72 grams of carbon dioxide. Let's denote the mass of oxygen as ${m_{O_2}}$ . Plugging in the known values, we get:

${ 18 \text{ g} + m_{O_2} = 72 \text{ g} }$

This equation allows us to solve for the mass of oxygen required in the reaction. By rearranging the equation, we can isolate ${m_{O_2}}$ and calculate its value. This straightforward application of the law of conservation of mass demonstrates its power in solving quantitative problems in chemistry. It underscores the importance of understanding and applying fundamental principles to predict and explain chemical phenomena.

Calculation: Determining the Mass of Oxygen

To determine the mass of oxygen ( ${m_{O_2}}$ ) needed in the reaction, we rearrange the equation derived from the law of conservation of mass:

${ 18 \text{ g} + m_{O_2} = 72 \text{ g} }$

Subtracting 18 grams from both sides of the equation, we get:

${ m_{O_2} = 72 \text{ g} - 18 \text{ g} }$

${ m_{O_2} = 54 \text{ g} }$

Therefore, the mass of oxygen needed in the reaction is 54 grams. This calculation demonstrates a direct application of the law of conservation of mass, a fundamental principle in chemistry. The result provides a quantitative understanding of the reaction between carbon and oxygen to form carbon dioxide. It highlights how stoichiometric relationships can be used to predict the amount of reactants required or products formed in a chemical reaction. This type of calculation is essential in various scientific and industrial contexts, where precise control over chemical reactions is necessary.

Step-by-Step Solution

To summarize the solution process, here's a step-by-step breakdown:

State the law of conservation of mass: The total mass of reactants equals the total mass of products.
Write the equation: Mass of Carbon + Mass of Oxygen = Mass of Carbon Dioxide.
Plug in the known values: 18 g + ${m_{O_2}}$ = 72 g.
Solve for the mass of oxygen ( ${m_{O_2}}$ ): ${m_{O_2}}$ = 72 g - 18 g.
Calculate the mass of oxygen: ${m_{O_2}}$ = 54 g.

This step-by-step approach provides a clear and organized method for solving stoichiometric problems. It emphasizes the importance of understanding the underlying principles and applying them systematically. By following these steps, students and practitioners can confidently tackle a wide range of quantitative chemistry problems. This structured approach not only aids in problem-solving but also reinforces the understanding of the fundamental concepts involved.

Answer and Discussion

The mass of oxygen needed in the reaction is 54 grams. This corresponds to option B in the given choices. The correct answer is:

B. 54 g

This result is a direct consequence of the law of conservation of mass, which is a cornerstone of chemistry. The law ensures that the total mass remains constant throughout a chemical reaction. In this specific reaction, the 18 grams of carbon react with 54 grams of oxygen to form 72 grams of carbon dioxide. This quantitative relationship is crucial for understanding and predicting the outcomes of chemical reactions. It allows chemists and engineers to precisely control the amounts of reactants and products in various applications, from laboratory experiments to large-scale industrial processes. The conservation of mass is not just a theoretical concept but a practical tool that underpins much of modern chemistry.

Significance of the Result

The result, 54 grams of oxygen, highlights the quantitative nature of chemical reactions. It demonstrates that reactions occur in specific proportions, and these proportions are governed by the laws of chemistry. In this case, the 18 grams of carbon react with exactly 54 grams of oxygen to produce 72 grams of carbon dioxide. If the amount of oxygen were less than 54 grams, the reaction would not proceed completely, and some carbon would remain unreacted. If the amount of oxygen were more than 54 grams, the excess oxygen would not participate in the reaction. This precise stoichiometry is essential for optimizing chemical processes and ensuring efficient use of resources. Understanding these quantitative relationships allows for the design of reactions that maximize product yield and minimize waste. It is a fundamental aspect of green chemistry and sustainable practices in the chemical industry. Furthermore, it underscores the importance of accurate measurements and calculations in chemical experiments and industrial applications.

Conclusion

In conclusion, the reaction between 18 grams of carbon and oxygen to produce 72 grams of carbon dioxide requires 54 grams of oxygen. This result is a direct application of the law of conservation of mass, a fundamental principle in chemistry. The law states that the total mass of reactants equals the total mass of products in a chemical reaction. By understanding and applying this principle, we can solve a wide range of stoichiometric problems and quantitatively analyze chemical reactions. The ability to perform such calculations is crucial for various applications in science and industry, including chemical synthesis, environmental monitoring, and materials science. Mastering these concepts is essential for anyone pursuing a career in chemistry or related fields. The conservation of mass is not just a theoretical concept but a practical tool that enables us to predict, control, and optimize chemical processes, ensuring efficient and sustainable use of resources.

This problem illustrates the importance of stoichiometry in predicting the outcome of chemical reactions. By applying the law of conservation of mass, we can accurately determine the mass of reactants needed or products formed in a chemical reaction. This understanding is crucial for various scientific and industrial applications, where precise control over reaction quantities is necessary.