Moles Of Oxygen Produced From Aluminum Reaction

In chemistry, understanding stoichiometry is crucial for calculating the amounts of reactants and products involved in a chemical reaction. Stoichiometry is the study of the quantitative relationships or ratios between two or more substances when they undergo a physical change or chemical reaction. This article will guide you through the process of determining the moles of oxygen produced from a given amount of aluminum in the reaction: $2 Al_2 O_3 ightarrow 4 Al + 3 O_2$. We'll break down the steps, making it easy to understand and apply to similar problems. Let's dive in and unravel the relationship between aluminum and oxygen in this chemical equation.

Understanding the Chemical Equation

The first step in solving any stoichiometry problem is to understand the balanced chemical equation. The balanced equation provides the mole ratios between reactants and products. In this case, the reaction is:

$2 Al_2 O_3 ightarrow 4 Al + 3 O_2$

This equation tells us that 2 moles of aluminum oxide ($Al_2 O_3$) decompose to produce 4 moles of aluminum (Al) and 3 moles of oxygen ($O_2$). The coefficients in front of each chemical formula represent the number of moles of that substance involved in the reaction. These coefficients are the key to unlocking the mole ratios we need to solve the problem. Understanding these ratios is fundamental to calculating the amounts of products formed from a given amount of reactant. It's like having a recipe; the balanced equation tells you how much of each ingredient you need. For instance, if you were baking a cake, the recipe would specify the amount of flour, sugar, and eggs you need. Similarly, in chemistry, the balanced equation specifies the moles of each substance required for the reaction to occur. We can use this information to predict the amount of product formed or the amount of reactant needed for a specific reaction outcome. Without a balanced equation, we wouldn't be able to accurately determine these amounts, and our calculations would be off. So, before we proceed with any stoichiometric calculation, we must ensure that the chemical equation is correctly balanced. This ensures that the law of conservation of mass is obeyed, which states that matter cannot be created or destroyed in a chemical reaction. By correctly interpreting the balanced equation, we can confidently move forward in calculating the moles of oxygen produced from the given amount of aluminum.

Determining the Mole Ratio

The mole ratio is a crucial concept in stoichiometry. It is derived from the coefficients in the balanced chemical equation and represents the proportion of moles of one substance to another. In the given reaction:

$2 Al_2 O_3 ightarrow 4 Al + 3 O_2$

We are interested in the relationship between aluminum (Al) and oxygen ($O_2$). According to the balanced equation, 4 moles of Al are produced for every 3 moles of $O_2$ formed. This gives us the mole ratio:

rac{3 ext{ mol } O_2}{4 ext{ mol } Al}

This ratio is the key to converting moles of Al to moles of $O_2$. It tells us that for every 4 moles of aluminum produced, 3 moles of oxygen are also produced. We can use this ratio as a conversion factor in our calculations. Think of the mole ratio as a bridge that allows you to cross from the world of one substance (aluminum) to the world of another substance (oxygen). Without this bridge, you wouldn't be able to relate the amounts of the two substances. The mole ratio is derived directly from the balanced chemical equation, which is why understanding the equation is so important. It provides the fundamental relationship between the reactants and products in the reaction. In this case, the mole ratio of 3 moles of $O_2$ to 4 moles of Al allows us to calculate how many moles of oxygen are produced when a specific number of moles of aluminum are formed. This ratio holds true regardless of the actual amounts of reactants and products involved, as long as the reaction proceeds according to the balanced equation. The ability to determine and use mole ratios is a fundamental skill in chemistry, enabling us to make accurate predictions and calculations about chemical reactions. So, by identifying the correct mole ratio, we are one step closer to solving the problem and determining the moles of oxygen produced.

Calculating Moles of Oxygen

Now that we have the mole ratio, we can calculate the moles of oxygen produced when 11.0 moles of aluminum are formed. We start with the given amount of aluminum and use the mole ratio as a conversion factor:

11. 0 ext{ mol } Al imes rac{3 ext{ mol } O_2}{4 ext{ mol } Al}

To solve this, we multiply 11.0 mol Al by the fraction rac{3}{4}:

11. 0 ext{ mol } Al imes rac{3 ext{ mol } O_2}{4 ext{ mol } Al} = rac{11.0 imes 3}{4} ext{ mol } O_2

Calculating the result:

rac{11.0 imes 3}{4} = rac{33}{4} = 8.25 ext{ mol } O_2

Therefore, 8.25 moles of oxygen are produced when 11.0 moles of aluminum are formed. This calculation demonstrates the power of stoichiometry in predicting the outcomes of chemical reactions. It's like having a recipe where you know exactly how much of each ingredient you need to get the desired result. In this case, we knew how many moles of aluminum were produced, and using the mole ratio from the balanced equation, we could precisely calculate the moles of oxygen formed. This process is not limited to just aluminum and oxygen; it can be applied to any chemical reaction as long as you have a balanced equation. The key is to identify the correct mole ratio between the substances of interest and use it as a conversion factor. By setting up the calculation correctly, with the units canceling out appropriately (in this case, moles of Al canceling out), you can confidently arrive at the correct answer. Stoichiometric calculations are fundamental in many areas of chemistry, from industrial processes to research labs, allowing chemists to control and optimize chemical reactions. So, understanding how to calculate moles of products from moles of reactants is an essential skill for anyone studying or working in chemistry.

The Correct Answer

Based on our calculations, the correct answer is:

A. 8.25 mol

This result confirms that when 11.0 moles of aluminum are produced in the reaction $2 Al_2 O_3 ightarrow 4 Al + 3 O_2$, 8.25 moles of oxygen are produced. This answer is not just a number; it represents a tangible quantity of oxygen that is formed as a result of the chemical reaction. It's like knowing that if you bake a cake using a specific recipe, you'll end up with a certain number of slices. Similarly, in chemistry, stoichiometric calculations allow us to predict the amount of product we'll obtain from a given amount of reactant. The fact that we arrived at 8.25 moles of oxygen underscores the importance of stoichiometry in making accurate predictions about chemical reactions. It allows chemists and scientists to plan experiments, optimize industrial processes, and understand the fundamental relationships between substances at the molecular level. Furthermore, this answer highlights the direct relationship between aluminum and oxygen in this particular reaction, as dictated by the balanced chemical equation. Each mole of aluminum produced is linked to a specific amount of oxygen, and we were able to precisely quantify this relationship through our calculations. So, the answer of 8.25 mol is not just a solution to the problem; it's a testament to the power and precision of stoichiometric calculations in chemistry.

Conclusion

In conclusion, we have successfully calculated the moles of oxygen produced from the decomposition of aluminum oxide, given the moles of aluminum produced. The key steps involved understanding the balanced chemical equation, determining the mole ratio between the substances of interest, and using this ratio to convert moles of one substance to moles of another. Stoichiometry is a fundamental concept in chemistry that allows us to make quantitative predictions about chemical reactions. By mastering these principles, you can confidently tackle a wide range of stoichiometry problems. Remember to always start with a balanced equation and pay close attention to the mole ratios. This will ensure accurate and reliable results in your calculations. Understanding these calculations not only helps in academic settings but also has practical applications in various fields, such as chemical engineering, materials science, and environmental science. For further learning on stoichiometry and related topics, consider exploring resources like Khan Academy's chemistry section.