Determining Limiting Reactant And Theoretical Yield In Acetylene Combustion

Jul 12, 2025 by ADMIN 76 views

Understanding the Combustion Reaction of Acetylene The combustion of acetylene is a fascinating chemical process that plays a significant role in various industrial applications, most notably in welding and cutting. This article delves into the intricacies of the combustion reaction of acetylene ($C_2H_2$) with oxygen ($O_2$), providing a comprehensive analysis of the stoichiometry, limiting reactants, and theoretical yield. We will explore a specific scenario where 37.0 moles of acetylene react with 81.0 moles of oxygen, ultimately determining the **limiting reactant** and the **theoretical yield** of water ($H_2O$). This exploration will help you understand the concepts of chemical reactions, stoichiometry, and yield calculations.

The Balanced Chemical Equation

The cornerstone of any stoichiometric calculation is a balanced chemical equation. It provides the molar ratios of reactants and products involved in the reaction. For the combustion of acetylene, the balanced equation is:

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

This equation reveals that 2 moles of acetylene react with 5 moles of oxygen to produce 4 moles of carbon dioxide and 2 moles of water. These coefficients are crucial for determining the stoichiometric relationships between the reactants and products.

Stoichiometric Ratios

The coefficients in the balanced equation define the stoichiometric ratios, which are the mole ratios of reactants and products. For example, the ratio between acetylene and oxygen is 2:5, meaning that for every 2 moles of acetylene, 5 moles of oxygen are required for complete combustion. Similarly, the ratio between acetylene and water is 2:2 or 1:1, indicating that 2 moles of acetylene produce 2 moles of water.

These ratios are essential for identifying the limiting reactant. The limiting reactant is the reactant that is completely consumed in a chemical reaction, thereby determining the maximum amount of product that can be formed. To determine the limiting reactant, we must compare the mole ratios of the reactants available with the stoichiometric ratios from the balanced equation.

Identifying the Limiting Reactant

In our scenario, we have 37.0 moles of acetylene and 81.0 moles of oxygen. To identify the limiting reactant, we can calculate how many moles of one reactant are required to react completely with the given amount of the other reactant. Let's start by determining the amount of oxygen required to react with 37.0 moles of acetylene. Based on the stoichiometric ratio, we can set up the following proportion:

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

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

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

This calculation shows that 92.5 moles of oxygen are needed to react completely with 37.0 moles of acetylene. However, we only have 81.0 moles of oxygen available. This means that oxygen will be consumed before all the acetylene can react. Therefore, oxygen is the limiting reactant in this scenario. Acetylene is the excess reactant.

Calculating the Theoretical Yield of Water

The limiting reactant determines the theoretical yield of the products. The theoretical yield is the maximum amount of product that can be formed from a given amount of limiting reactant, assuming complete conversion and no losses. In our case, we want to calculate the theoretical yield of water ( $H_2O$ ).

Using the balanced equation, we know that 5 moles of oxygen produce 2 moles of water. We can use this stoichiometric ratio to calculate the amount of water produced from 81.0 moles of oxygen:

(Moles of $H_2O$ produced) / (Moles of $O_2$ ) = 2/5

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

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

Therefore, the theoretical yield of water is 32.4 moles. This is the maximum amount of water that can be produced from the given amounts of acetylene and oxygen, considering that oxygen is the limiting reactant.

Converting Moles to Grams

Sometimes, it's necessary to express the theoretical yield in grams rather than moles. To do this, we multiply the number of moles by the molar mass of the substance. The molar mass of water ( $H_2O$ ) is approximately 18.015 g/mol. Therefore, the theoretical yield of water in grams is:

Theoretical yield (grams) = 32.4 moles * 18.015 g/mol = 583.7 grams

This means that the maximum amount of water that can be produced in this reaction is approximately 583.7 grams.

Discussion on Combustion Reactions and Stoichiometry

Combustion reactions are exothermic chemical processes that involve the rapid reaction between a substance with an oxidant, usually oxygen, to produce heat and light. The combustion of acetylene is a highly exothermic reaction, making it suitable for applications like welding and cutting. Understanding the stoichiometry of combustion reactions is crucial for optimizing these processes, ensuring efficient fuel consumption, and minimizing the formation of unwanted byproducts.

Factors Affecting Reaction Yield

The theoretical yield represents the ideal scenario where the reaction proceeds to completion with no losses. However, in reality, the actual yield of a reaction is often less than the theoretical yield. Several factors can contribute to this discrepancy, including:

Incomplete reaction: The reaction may not proceed to completion, leaving some reactants unreacted.
Side reactions: Other reactions may occur simultaneously, consuming reactants and producing unwanted byproducts.
Losses during product isolation: Some product may be lost during separation, purification, or transfer processes.
Experimental errors: Inaccurate measurements or handling techniques can affect the yield.

To maximize the actual yield of a reaction, it's important to carefully control reaction conditions, use high-purity reactants, and minimize losses during product isolation.

Applications of Stoichiometry

Stoichiometry is a fundamental concept in chemistry with numerous applications in various fields, including:

Industrial chemistry: Stoichiometry is used to optimize chemical processes, calculate reactant requirements, and predict product yields in industrial settings.
Analytical chemistry: Stoichiometric calculations are essential for quantitative analysis, such as determining the concentration of a substance in a sample.
Environmental chemistry: Stoichiometry helps in understanding and controlling chemical reactions related to pollution and environmental remediation.
Pharmaceutical chemistry: Stoichiometric principles are crucial for drug synthesis, formulation, and analysis.

Conclusion

The combustion reaction of acetylene provides a clear illustration of stoichiometric principles and their importance in chemical calculations. By understanding the balanced chemical equation, stoichiometric ratios, and the concept of the limiting reactant, we can accurately predict the theoretical yield of products. In the given scenario, with 37.0 moles of acetylene and 81.0 moles of oxygen, oxygen was identified as the limiting reactant, and the theoretical yield of water was calculated to be 32.4 moles or 583.7 grams. This exercise highlights the practical application of stoichiometry in understanding and predicting the outcomes of chemical reactions. Furthermore, understanding the factors affecting reaction yield and the broad applications of stoichiometry reinforces its central role in the field of chemistry and related disciplines. By mastering these concepts, students and professionals can effectively analyze and optimize chemical processes across various industries and research areas.