Calculating Oxygen Requirements For Acetylene Combustion

Let's dive into the fascinating world of chemical reactions, specifically the combustion of acetylene (C₂H₂). Acetylene, a colorless gas widely used as a fuel in welding torches due to its high heat of combustion, undergoes a fiery reaction with oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O). Understanding the stoichiometry of this reaction is crucial for determining the precise amounts of reactants and products involved. Stoichiometry, in essence, is the language of chemical reactions, allowing us to quantify the relationships between different substances in a chemical equation. This quantitative aspect is vital in various fields, from industrial chemical production to environmental science, where precise measurements and calculations are essential for efficient and safe operations. In the specific context of acetylene combustion, understanding the stoichiometric ratios enables us to calculate the amount of oxygen needed to completely burn a given quantity of acetylene, ensuring optimal energy release and minimizing the formation of unwanted byproducts. The chemical equation for this reaction is:

$2 C_2 H_2 + 5 O_2 \rightarrow 4 CO_2 + 2 H_2O$

This balanced equation tells us that 2 moles of acetylene react with 5 moles of oxygen to produce 4 moles of carbon dioxide and 2 moles of water. The coefficients in front of each chemical formula represent the molar ratios, which are the cornerstone of stoichiometric calculations. These ratios allow us to convert between the amounts of different substances involved in the reaction, using the mole as the central unit of measurement. The balanced equation adheres to the law of conservation of mass, ensuring that the number of atoms of each element is the same on both the reactant and product sides. This fundamental principle underpins all stoichiometric calculations, providing a reliable framework for predicting the outcomes of chemical reactions. In the case of acetylene combustion, the balanced equation provides a roadmap for determining the precise amount of oxygen required for complete combustion, a critical consideration in various applications where acetylene is used as a fuel.

Now, let's tackle the core question: How many grams of oxygen are required to react completely with 859.0 g of acetylene? This is a classic stoichiometry problem that involves several key steps. First, we need to convert the mass of acetylene to moles using its molar mass. The molar mass of a compound is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). To calculate the molar mass of acetylene (C₂H₂), we sum the atomic masses of its constituent elements: 2 carbon atoms and 2 hydrogen atoms. Looking at the periodic table, the atomic mass of carbon is approximately 12.01 g/mol, and the atomic mass of hydrogen is approximately 1.01 g/mol. Therefore, the molar mass of acetylene is (2 * 12.01 g/mol) + (2 * 1.01 g/mol) = 26.04 g/mol. Next, we divide the given mass of acetylene (859.0 g) by its molar mass (26.04 g/mol) to obtain the number of moles of acetylene: 859. 0 g / 26.04 g/mol = 33.00 mol (approximately). This conversion is crucial because stoichiometric calculations are based on molar ratios, not mass ratios. Once we have the number of moles of acetylene, we can use the balanced chemical equation to determine the number of moles of oxygen required. The equation tells us that 2 moles of acetylene react with 5 moles of oxygen. This gives us a mole ratio of 5 moles O₂ / 2 moles C₂H₂. We multiply the moles of acetylene (33.00 mol) by this ratio to find the moles of oxygen needed: 33.00 mol C₂H₂ * (5 mol O₂ / 2 mol C₂H₂) = 82.50 mol O₂. Finally, we convert the moles of oxygen to grams using its molar mass. The molar mass of oxygen (O₂) is 2 * 16.00 g/mol = 32.00 g/mol. Multiplying the moles of oxygen (82.50 mol) by its molar mass (32.00 g/mol) gives us the mass of oxygen required: 82.50 mol O₂ * 32.00 g/mol = 2640 g O₂. Therefore, 2640 grams of oxygen are required to react completely with 859.0 g of acetylene.

Let's break down the calculation into a clear, step-by-step process:

1. Calculate the molar mass of acetylene (C₂H₂):

   • Molar mass of C = 12.01 g/mol
   • Molar mass of H = 1.01 g/mol
   • Molar mass of C₂H₂ = (2 * 12.01 g/mol) + (2 * 1.01 g/mol) = 26.04 g/mol

2. Convert grams of acetylene to moles:

   • Moles of C₂H₂ = 859.0 g / 26.04 g/mol = 33.00 mol

3. Use the stoichiometric ratio from the balanced equation to find moles of oxygen:

   • From the balanced equation, 2 moles C₂H₂ react with 5 moles O₂.
   • Mole ratio: 5 mol O₂ / 2 mol C₂H₂
   • Moles of O₂ = 33.00 mol C₂H₂ * (5 mol O₂ / 2 mol C₂H₂) = 82.50 mol O₂

4. Calculate the molar mass of oxygen (O₂):

   • Molar mass of O = 16.00 g/mol
   • Molar mass of O₂ = 2 * 16.00 g/mol = 32.00 g/mol

5. Convert moles of oxygen to grams:

   • Grams of O₂ = 82.50 mol O₂ * 32.00 g/mol = 2640 g O₂

Therefore, the final answer is 2640 grams of oxygen.

The periodic table is an indispensable tool in chemistry, and it plays a critical role in stoichiometric calculations. As we saw in the calculation above, we used the periodic table to determine the atomic masses of carbon, hydrogen, and oxygen. These atomic masses are the foundation for calculating molar masses, which are essential for converting between mass and moles. The periodic table organizes elements based on their atomic number and electron configuration, and it also provides valuable information about their atomic masses, electronegativity, ionization energies, and other properties. Without the periodic table, we would not be able to accurately determine the molar masses of compounds, making stoichiometric calculations impossible. The periodic table is not just a list of elements; it is a map of the chemical world, providing a framework for understanding the relationships between elements and their behavior in chemical reactions. Its periodic trends allow us to predict the properties of elements and compounds, guiding our understanding of chemical reactions and their outcomes. In the context of stoichiometry, the periodic table is the key to unlocking the quantitative relationships between reactants and products, enabling us to make accurate predictions and design experiments effectively. It serves as a constant reference point, ensuring the accuracy and reliability of our calculations in the ever-evolving field of chemistry.

In summary, we have successfully calculated the amount of oxygen required to react completely with 859.0 g of acetylene using stoichiometric principles and the periodic table. The key steps involved converting the mass of acetylene to moles, using the balanced chemical equation to determine the mole ratio of oxygen to acetylene, and converting the moles of oxygen back to grams. This problem highlights the importance of stoichiometry in chemistry, allowing us to make quantitative predictions about chemical reactions. The periodic table is a fundamental tool in this process, providing the atomic masses necessary for calculating molar masses. Understanding these concepts is crucial for anyone studying chemistry or working in related fields. From industrial processes to environmental monitoring, stoichiometric calculations are essential for ensuring efficiency, safety, and accuracy. The combustion of acetylene, a reaction with significant industrial applications, serves as a practical example of how stoichiometry is applied in real-world scenarios. By mastering these principles, we can gain a deeper understanding of the chemical world around us and make informed decisions in various contexts. The ability to accurately calculate the amounts of reactants and products in a chemical reaction is a cornerstone of chemical knowledge, empowering us to manipulate and control chemical processes for a wide range of applications.