Oxygen Required For Combustion Of 859.0 G Acetylene

In the realm of chemistry, stoichiometry serves as a fundamental pillar, enabling us to quantitatively analyze chemical reactions. This analysis hinges on the balanced chemical equation, which unveils the precise molar ratios between reactants and products. Stoichiometric calculations empower us to predict the amounts of reactants needed or products formed in a given reaction, making them indispensable in diverse fields, from industrial chemistry to environmental science. In this article, we will delve into a classic stoichiometry problem involving the combustion of acetylene, a highly versatile fuel widely employed in welding and cutting applications. We will embark on a step-by-step journey to determine the mass of oxygen required for the complete combustion of a specified amount of acetylene. This exploration will not only solidify our understanding of stoichiometric principles but also underscore the practical significance of these concepts in real-world scenarios. Stoichiometric calculations are essential for optimizing chemical processes, minimizing waste, and ensuring safety in industrial settings. Furthermore, they play a vital role in environmental monitoring and pollution control, allowing us to accurately assess the impact of chemical reactions on the environment. By mastering stoichiometry, we gain the ability to make informed decisions about chemical reactions, fostering efficiency, sustainability, and safety in various endeavors.

In this section, we will explore the stoichiometry of the combustion reaction of acetylene ($C_2H_2$) with oxygen ($O_2$) to produce carbon dioxide ($CO_2$) and water ($H_2O$). Stoichiometry is the study of the quantitative relationships between reactants and products in chemical reactions. It allows us to determine the amounts of substances that are involved in a chemical reaction, whether it's the mass, moles, or volume of the reactants and products. The balanced chemical equation for this reaction is:

$2 C_2H_2 + 5 O_2 \rightarrow 4 CO_2 + 2 H_2O$

This equation tells us that two moles of acetylene react with five moles of oxygen to produce four moles of carbon dioxide and two moles of water. The coefficients in front of each chemical formula represent the stoichiometric coefficients, which indicate the molar ratios between the reactants and products. For instance, the ratio between acetylene and oxygen is 2:5, meaning that for every two moles of acetylene, five moles of oxygen are required for complete combustion. Understanding these ratios is crucial for stoichiometric calculations.

The balanced chemical equation is the cornerstone of stoichiometry. It provides the essential information needed to perform calculations related to the amounts of reactants and products involved in a chemical reaction. Without a balanced equation, it is impossible to accurately determine the stoichiometric relationships between the substances. The coefficients in the balanced equation represent the molar ratios, which are the key to converting between the amounts of different substances. To balance a chemical equation, we must ensure that the number of atoms of each element is the same on both sides of the equation. This is achieved by adjusting the coefficients in front of the chemical formulas. The balanced equation not only tells us the molar ratios but also reflects the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. The total mass of the reactants must equal the total mass of the products.

The combustion of acetylene is an exothermic reaction, meaning it releases heat. This is why acetylene is commonly used as a fuel in welding and cutting torches, where the high heat produced is essential for melting and cutting metals. The reaction also produces carbon dioxide and water as byproducts, which are greenhouse gases that contribute to climate change. Therefore, understanding the stoichiometry of acetylene combustion is not only important for chemical calculations but also for environmental considerations. By accurately determining the amounts of reactants and products, we can optimize the combustion process to minimize the production of greenhouse gases. This can be achieved by ensuring that the reaction is complete and that there is sufficient oxygen for combustion. Incomplete combustion can lead to the formation of carbon monoxide, a toxic gas, and soot, which is harmful to the environment. Stoichiometric calculations can help us avoid these issues and ensure that the combustion process is both efficient and environmentally friendly.

The problem at hand asks us to determine the mass of oxygen required to react completely with 859.0 grams of acetylene ($C_2H_2$). To solve this problem, we will employ a step-by-step approach that utilizes the principles of stoichiometry. This approach involves converting the given mass of acetylene to moles, using the stoichiometric ratio from the balanced chemical equation to find the moles of oxygen required, and finally, converting the moles of oxygen to grams. This methodical approach is essential for solving stoichiometric problems accurately and efficiently.

The first step in our solution strategy is to convert the mass of acetylene to moles. To do this, we will use the molar mass of acetylene, which is the mass of one mole of the substance. The molar mass of acetylene can be calculated by adding the atomic masses of its constituent atoms, which are carbon and hydrogen. Carbon has an atomic mass of approximately 12.01 grams per mole, and hydrogen has an atomic mass of approximately 1.01 grams per mole. Acetylene ($C_2H_2$) has two carbon atoms and two hydrogen atoms, so its molar mass is calculated as follows:

Molar mass of $C_2H_2 = (2 imes 12.01 ext{ g/mol}) + (2 imes 1.01 ext{ g/mol}) = 26.04 ext{ g/mol}$

Once we have the molar mass of acetylene, we can convert the given mass of 859.0 grams to moles using the formula:

Moles = Mass / Molar mass

By dividing the given mass by the molar mass, we obtain the number of moles of acetylene. This conversion is a crucial step because stoichiometric calculations are based on molar ratios, not mass ratios. Moles provide a consistent unit for comparing the amounts of different substances in a chemical reaction. Converting to moles allows us to use the stoichiometric coefficients from the balanced chemical equation to determine the amount of other reactants or products involved in the reaction.

The second step in our solution strategy is to use the stoichiometric ratio from the balanced chemical equation to find the moles of oxygen required. The balanced equation for the combustion of acetylene is:

$2 C_2H_2 + 5 O_2 \rightarrow 4 CO_2 + 2 H_2O$

From this equation, we can see that 2 moles of acetylene react with 5 moles of oxygen. This gives us the stoichiometric ratio of 2:5 between acetylene and oxygen. We can use this ratio to set up a proportion and calculate the moles of oxygen required to react with the moles of acetylene we calculated in the previous step. The proportion is set up as follows:

(Moles of $O_2$) / (Moles of $C_2H_2$) = 5 / 2

By multiplying the moles of acetylene by the stoichiometric ratio (5/2), we obtain the moles of oxygen required for complete combustion. This step is essential because it directly relates the amount of one substance to the amount of another substance in the reaction. The stoichiometric ratio acts as a conversion factor, allowing us to move from the moles of one substance to the moles of another. Without the balanced chemical equation and the stoichiometric ratio, it would be impossible to accurately determine the amount of oxygen required.

The final step in our solution strategy is to convert the moles of oxygen to grams. To do this, we will use the molar mass of oxygen, which is the mass of one mole of oxygen molecules ($O_2$). Oxygen has an atomic mass of approximately 16.00 grams per mole, so the molar mass of $O_2$ is:

Molar mass of $O_2 = 2 imes 16.00 ext{ g/mol} = 32.00 ext{ g/mol}$

Once we have the molar mass of oxygen, we can convert the moles of oxygen to grams using the formula:

Mass = Moles × Molar mass

By multiplying the moles of oxygen by the molar mass, we obtain the mass of oxygen required for the reaction. This conversion provides the final answer to the problem, expressed in the desired unit of grams. The conversion from moles to grams is essential because mass is a common unit for measuring and handling substances in the laboratory and in industrial processes. By expressing the answer in grams, we provide a practical and easily understandable result.

By following this step-by-step approach, we can systematically solve stoichiometric problems and gain a deeper understanding of the quantitative relationships in chemical reactions. This strategy not only provides the correct answer but also reinforces the fundamental principles of stoichiometry, making it a valuable tool for problem-solving in chemistry.

Now, let's apply the strategy outlined above to solve the problem. We are given 859.0 grams of acetylene ($C_2H_2$) and we need to find the mass of oxygen ($O_2$) required for complete reaction.

Step 1: Convert grams of acetylene to moles

We calculated the molar mass of acetylene to be 26.04 g/mol. Using the formula:

Moles = Mass / Molar mass

Moles of $C_2H_2$ = 859.0 g / 26.04 g/mol = 32.99 mol

Therefore, we have 32.99 moles of acetylene.

Step 2: Use the stoichiometric ratio to find moles of oxygen

From the balanced chemical equation:

$2 C_2H_2 + 5 O_2 \rightarrow 4 CO_2 + 2 H_2O$

The stoichiometric ratio between $C_2H_2$ and $O_2$ is 2:5. Therefore:

(Moles of $O_2$) / (Moles of $C_2H_2$) = 5 / 2

Moles of $O_2$ = (5 / 2) × Moles of $C_2H_2$

Moles of $O_2$ = (5 / 2) × 32.99 mol = 82.48 mol

So, we need 82.48 moles of oxygen.

Step 3: Convert moles of oxygen to grams

We calculated the molar mass of oxygen ($O_2$) to be 32.00 g/mol. Using the formula:

Mass = Moles × Molar mass

Mass of $O_2$ = 82.48 mol × 32.00 g/mol = 2639.36 g

Therefore, 2639.36 grams of oxygen are required to react completely with 859.0 grams of acetylene.

The mass of oxygen required to react completely with 859.0 g of acetylene is approximately 2639.36 grams. This calculation demonstrates the practical application of stoichiometry in determining the quantities of reactants needed for a chemical reaction. By following the step-by-step approach, we have successfully converted the mass of acetylene to moles, used the stoichiometric ratio to find the moles of oxygen required, and finally converted the moles of oxygen to grams. This methodical approach is essential for solving stoichiometric problems accurately and efficiently. The answer highlights the importance of stoichiometry in various fields, including industrial chemistry, where precise calculations are necessary for optimizing chemical processes and minimizing waste. In the case of acetylene combustion, understanding the stoichiometry allows us to determine the exact amount of oxygen needed for complete combustion, which is crucial for safety and efficiency in welding and cutting applications. Furthermore, this knowledge can be applied to environmental considerations, as it helps us assess the impact of combustion processes on air quality and greenhouse gas emissions. By mastering stoichiometric principles, we can make informed decisions and contribute to sustainable chemical practices.

In summary, we have successfully determined the mass of oxygen required for the complete combustion of 859.0 grams of acetylene. Through the application of stoichiometric principles and a step-by-step approach, we converted the mass of acetylene to moles, utilized the balanced chemical equation to find the stoichiometric ratio between acetylene and oxygen, and finally converted the moles of oxygen to grams. This exercise underscores the importance of stoichiometry as a fundamental tool in chemistry, enabling us to make quantitative predictions about chemical reactions. Stoichiometry is not merely a theoretical concept; it has practical implications in various fields, including industrial chemistry, environmental science, and materials science. In industrial chemistry, stoichiometric calculations are essential for optimizing chemical processes, minimizing waste, and ensuring the safety of chemical operations. For example, in the production of pharmaceuticals, the accurate calculation of reactant quantities is crucial for maximizing product yield and minimizing the formation of unwanted byproducts. In environmental science, stoichiometry plays a vital role in understanding and mitigating pollution. By quantifying the amounts of pollutants released from various sources, scientists can develop strategies to reduce emissions and protect air and water quality. In materials science, stoichiometry is used to design and synthesize new materials with specific properties. The precise control of the elemental composition of a material is essential for achieving desired characteristics, such as strength, conductivity, and reactivity. Stoichiometry is also fundamental to other areas of chemistry, such as analytical chemistry, where it is used to determine the composition of unknown substances, and physical chemistry, where it is used to study the thermodynamics and kinetics of chemical reactions. The principles of stoichiometry are applicable to a wide range of chemical phenomena, making it an indispensable tool for chemists and scientists in various disciplines. By mastering stoichiometry, we gain the ability to make accurate predictions about chemical reactions, design efficient chemical processes, and address environmental challenges. As we continue to advance in chemistry and related fields, the importance of stoichiometry will only continue to grow.

By understanding and applying stoichiometric principles, we can accurately predict and control the outcomes of chemical reactions, leading to safer, more efficient, and more sustainable chemical practices.