Limiting Reactant In Acetylene Combustion Calculating Theoretical Yield

The fiery dance of combustion is a fundamental chemical process, a cornerstone of energy production and a captivating display of molecular transformation. In this comprehensive guide, we will delve into the intricacies of a specific combustion reaction – the burning of acetylene ($C_2H_2$) – to understand the concept of the limiting reactant. Acetylene, a highly flammable hydrocarbon, finds widespread use in welding torches and various industrial applications. Understanding its combustion is crucial for safety and efficiency.

The Acetylene Combustion Reaction: A Stoichiometric Overview

At the heart of our exploration lies the balanced chemical equation that governs the combustion of acetylene:

$2 C_2 H_2(l) + 5 O_2(g) \rightarrow 4 CO_2(g) + 2 H_2 O(g)$

This equation unveils the precise stoichiometry of the reaction, the molar ratios in which reactants combine and products form. It tells us that for every 2 moles of liquid acetylene ($C_2H_2$) that react, 5 moles of gaseous oxygen ($O_2$) are required to completely burn it, producing 4 moles of gaseous carbon dioxide ($CO_2$) and 2 moles of gaseous water ($H_2O$). This stoichiometric relationship is paramount in determining the limiting reactant, which dictates the maximum yield of products in a chemical reaction.

Identifying the Limiting Reactant: A Crucial Step in Reaction Analysis

In any chemical reaction, reactants are rarely present in perfect stoichiometric ratios. One reactant may be in excess, while another may be present in a limited amount. The limiting reactant is the reactant that is completely consumed first, thereby halting the reaction and determining the maximum amount of product that can be formed. The other reactant(s), present in excess, will have some amount remaining after the reaction is complete.

To identify the limiting reactant, we must compare the available moles of each reactant to their stoichiometric requirements. Let's consider a scenario where we have 37.0 moles of acetylene ($C_2H_2$) and 81.0 moles of oxygen ($O_2$). To determine the limiting reactant, we can perform the following calculations:

1. Calculate the moles of $O_2$ required to react completely with 37.0 moles of $C_2H_2$:

   Using the stoichiometric ratio from the balanced equation (5 moles $O_2$ / 2 moles $C_2H_2$), we get:

   Moles of $O_2$ required = (37.0 moles $C_2H_2$) * (5 moles $O_2$ / 2 moles $C_2H_2$) = 92.5 moles $O_2$

2. Calculate the moles of $C_2H_2$ required to react completely with 81.0 moles of $O_2$:

   Using the stoichiometric ratio from the balanced equation (2 moles $C_2H_2$ / 5 moles $O_2$), we get:

   Moles of $C_2H_2$ required = (81.0 moles $O_2$) * (2 moles $C_2H_2$ / 5 moles $O_2$) = 32.4 moles $C_2H_2$

Comparing these results, we see that:

• To react all 37.0 moles of $C_2H_2$, we would need 92.5 moles of $O_2$. However, we only have 81.0 moles of $O_2$ available.
• To react all 81.0 moles of $O_2$, we would need 32.4 moles of $C_2H_2$. We have 37.0 moles of $C_2H_2$ available, which is more than enough.

Therefore, oxygen ($O_2$) is the limiting reactant because we don't have enough of it to react with all the acetylene. Acetylene ($C_2H_2$) is the excess reactant.

Calculating the Theoretical Yield: Maximizing Product Formation

The limiting reactant dictates the theoretical yield, the maximum amount of product that can be formed in a reaction if all of the limiting reactant is consumed. To calculate the theoretical yield, we use the stoichiometry of the balanced equation and the moles of the limiting reactant.

In our acetylene combustion example, oxygen ($O_2$) is the limiting reactant, with 81.0 moles available. Let's calculate the theoretical yield of carbon dioxide ($CO_2$):

1. Determine the mole ratio between the product ($CO_2$) and the limiting reactant ($O_2$) from the balanced equation:

The balanced equation shows that 5 moles of $O_2$ produce 4 moles of $CO_2$. The mole ratio is 4 moles $CO_2$ / 5 moles $O_2$.

2. Calculate the moles of $CO_2$ produced using the moles of the limiting reactant and the mole ratio:

Moles of $CO_2$ produced = (81.0 moles $O_2$) * (4 moles $CO_2$ / 5 moles $O_2$) = 64.8 moles $CO_2$

Therefore, the theoretical yield of carbon dioxide ($CO_2$) in this reaction is 64.8 moles. This means that, at most, 64.8 moles of $CO_2$ can be formed when 81.0 moles of $O_2$ react with 37.0 moles of $C_2H_2$.

Similarly, we can calculate the theoretical yield of water ($H_2O$):

1. Determine the mole ratio between the product ($H_2O$) and the limiting reactant ($O_2$) from the balanced equation:

The balanced equation shows that 5 moles of $O_2$ produce 2 moles of $H_2O$. The mole ratio is 2 moles $H_2O$ / 5 moles $O_2$.

2. Calculate the moles of $H_2O$ produced using the moles of the limiting reactant and the mole ratio:

Moles of $H_2O$ produced = (81.0 moles $O_2$) * (2 moles $H_2O$ / 5 moles $O_2$) = 32.4 moles $H_2O$

Therefore, the theoretical yield of water ($H_2O$) in this reaction is 32.4 moles.

Excess Reactant and Its Implications

Since acetylene ($C_2H_2$) is the excess reactant, not all of it will be consumed in the reaction. To determine the amount of acetylene remaining after the reaction, we can perform the following calculation:

1. Calculate the moles of $C_2H_2$ that reacted:

   We know that 81.0 moles of $O_2$ reacted. Using the stoichiometric ratio from the balanced equation (2 moles $C_2H_2$ / 5 moles $O_2$), we get:

Moles of $C_2H_2$ reacted = (81.0 moles $O_2$) * (2 moles $C_2H_2$ / 5 moles $O_2$) = 32.4 moles $C_2H_2$

2. Subtract the moles of $C_2H_2$ reacted from the initial moles of $C_2H_2$:

Moles of $C_2H_2$ remaining = 37.0 moles (initial) - 32.4 moles (reacted) = 4.6 moles $C_2H_2$

Therefore, 4.6 moles of acetylene ($C_2H_2$) will remain unreacted after the combustion is complete. This unreacted acetylene can have implications for the overall efficiency of the reaction and may need to be considered in industrial processes.

Real-World Applications and Considerations

The concept of limiting reactants is not merely a theoretical exercise; it has significant practical implications in various fields:

• Industrial Chemistry: In industrial chemical processes, understanding limiting reactants is crucial for optimizing product yield and minimizing waste. By carefully controlling the amounts of reactants, manufacturers can maximize the production of desired products and reduce the consumption of expensive raw materials.
• Combustion Engineering: In combustion systems, such as engines and power plants, the air-fuel ratio is a critical parameter. The amount of air (oxygen) supplied must be sufficient to completely burn the fuel. If the air supply is limited, incomplete combustion may occur, leading to the formation of harmful pollutants like carbon monoxide.
• Environmental Science: Understanding limiting reactants is also essential in environmental science. For example, in wastewater treatment, the amount of a particular nutrient (e.g., nitrogen or phosphorus) may limit the growth of algae. Identifying and controlling the limiting nutrient can help prevent algal blooms and improve water quality.

Conclusion: Mastering the Limiting Reactant Concept

The limiting reactant concept is a cornerstone of stoichiometry, providing a framework for understanding and predicting the outcomes of chemical reactions. By identifying the limiting reactant, we can calculate the theoretical yield of products, determine the amount of excess reactants remaining, and optimize reaction conditions for maximum efficiency. In the context of acetylene combustion, understanding the limiting reactant is crucial for safe and efficient use of this versatile fuel.

From industrial applications to environmental considerations, the principles of limiting reactants are fundamental to a wide range of scientific and engineering disciplines. Mastering this concept empowers us to control and manipulate chemical reactions, paving the way for innovation and progress.

By exploring the acetylene combustion reaction, we have gained valuable insights into the importance of stoichiometry and the role of the limiting reactant. This knowledge serves as a foundation for further explorations in the fascinating world of chemistry and its applications.