Calculating The Theoretical Yield Of CopperI Iodide Reaction

In the realm of chemistry, stoichiometry is the cornerstone for understanding the quantitative relationships between reactants and products in chemical reactions. Mastering stoichiometric calculations allows chemists to predict the amount of product formed in a reaction, a concept known as the theoretical yield. This article will delve into a practical example, guiding you through the steps to calculate the theoretical yield of copper(I) iodide ($CuI$) when copper ($Cu$) and iodine ($I_2$) react. By dissecting the reaction, identifying limiting reactants, and applying molar mass conversions, we'll arrive at the correct answer and solidify your understanding of this fundamental chemical principle. To effectively grasp the concepts discussed, it's crucial to understand that stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's like a recipe for a chemical reaction, telling us the exact amounts of ingredients needed to produce a certain amount of the final dish. For our specific case, the reaction involves copper and iodine combining to form copper(I) iodide. The balanced chemical equation, $2Cu + I_2 \rightarrow 2CuI$, is our recipe, showing the precise ratio in which these elements react. This equation tells us that two moles of copper react with one mole of iodine to produce two moles of copper(I) iodide. This balanced equation is crucial because it provides the foundation for all our calculations. It ensures that we account for the conservation of mass, meaning that the number of atoms of each element is the same on both sides of the equation. Without a balanced equation, our calculations would be inaccurate and misleading. This meticulous approach to balancing equations is a hallmark of stoichiometry, and it's what allows us to make accurate predictions about chemical reactions.

The problem at hand presents a scenario where 10 grams of copper ($Cu$) and 10 grams of iodine ($I_2$) are mixed. Our mission is to determine the theoretical yield of copper(I) iodide ($CuI$) produced from this reaction. The balanced chemical equation for the reaction is given as:

$2 Cu + I_2 \rightarrow 2 CuI$

To solve this problem, we will embark on a step-by-step journey, converting masses to moles, identifying the limiting reactant, and finally, calculating the theoretical yield of $CuI$. This process exemplifies how chemists use stoichiometry to predict the outcome of chemical reactions. The first step in our calculation is converting the given masses of copper and iodine into moles. This conversion is essential because chemical reactions occur on a molar basis, meaning that the number of molecules or atoms reacting is proportional to their molar amounts, not their masses. To convert grams to moles, we use the molar mass of each substance. The molar mass of copper is approximately 63.55 g/mol, and the molar mass of iodine ($I_2$) is approximately 253.81 g/mol. Using these molar masses, we can calculate the number of moles of copper and iodine present in the reaction mixture. This conversion is a crucial step in stoichiometry because it allows us to compare the amounts of reactants in terms of their molar ratios, which are directly related to the balanced chemical equation. Once we have the moles of each reactant, we can then determine which reactant is the limiting reactant, the substance that dictates the maximum amount of product that can be formed.

The cornerstone of stoichiometric calculations is the conversion of grams to moles. Moles provide a common unit for quantifying the amount of substance, allowing us to relate the masses of reactants to the number of molecules participating in the reaction. To perform this conversion, we utilize the molar mass of each reactant, which serves as a bridge between mass and moles. For copper ($Cu$), the molar mass is approximately 63.55 g/mol, while for iodine ($I_2$), it is approximately 253.81 g/mol. The molar mass is a fundamental property of each element and compound, representing the mass of one mole of that substance. It's derived from the atomic masses of the elements, which are listed on the periodic table. Understanding molar mass is crucial for any stoichiometry calculation, as it allows us to translate between the macroscopic world of grams, which we can measure in the lab, and the microscopic world of moles, which represent the number of atoms or molecules. In our case, we start with 10 grams of copper and 10 grams of iodine. By dividing the mass of each substance by its molar mass, we can determine the number of moles present. This conversion is a critical first step in determining the theoretical yield, as it sets the stage for identifying the limiting reactant and calculating the maximum amount of product that can be formed. The accurate conversion from grams to moles is paramount to ensuring the validity of all subsequent calculations, highlighting the importance of understanding and applying molar mass correctly.

• Moles of $Cu$ = $\frac{10 \text{ grams}}{63.55 \text{ g/mol}} \approx 0.157 \text{ mol}$
• Moles of $I_2$ = $\frac{10 \text{ grams}}{253.81 \text{ g/mol}} \approx 0.039 \text{ mol}$

The limiting reactant plays a pivotal role in determining the theoretical yield of a reaction. It is the reactant that is completely consumed during the reaction, thereby dictating the maximum amount of product that can be formed. Identifying the limiting reactant is akin to finding the shortest link in a chain – it's the constraint that limits the overall process. To pinpoint the limiting reactant, we must compare the mole ratio of the reactants to the stoichiometric ratio from the balanced chemical equation. In our case, the balanced equation ($2 Cu + I_2 \rightarrow 2 CuI$) reveals that 2 moles of copper ($Cu$) react with 1 mole of iodine ($I_2$). This stoichiometric ratio is our yardstick for comparison. We have calculated the moles of $Cu$ to be approximately 0.157 mol and the moles of $I_2$ to be approximately 0.039 mol. To determine which reactant is limiting, we can divide the moles of each reactant by its coefficient in the balanced equation. For copper, we divide 0.157 mol by 2, and for iodine, we divide 0.039 mol by 1. The reactant with the smaller result is the limiting reactant. This comparison allows us to determine which reactant will run out first, effectively stopping the reaction and limiting the amount of product that can be formed. The concept of the limiting reactant is fundamental to understanding reaction yields and is a critical component of stoichiometric calculations. Correctly identifying the limiting reactant ensures that we calculate the theoretical yield based on the reactant that truly limits the reaction's progress, leading to accurate predictions about product formation.

• For $Cu$: $\frac{0.157 \text{ mol}}{2} \approx 0.0785$
• For $I_2$: $\frac{0.039 \text{ mol}}{1} = 0.039$

Since 0.039 is less than 0.0785, $I_2$ is the limiting reactant.

With the limiting reactant identified as iodine ($I_2$), we can now proceed to calculate the theoretical yield of copper(I) iodide ($CuI$). The theoretical yield represents the maximum amount of product that can be formed, assuming the reaction proceeds to completion and no product is lost in the process. This is an idealized value, and the actual yield obtained in a laboratory setting may be lower due to various factors such as incomplete reactions or loss of product during purification. To calculate the theoretical yield, we use the stoichiometric ratio from the balanced chemical equation to relate the moles of the limiting reactant to the moles of product formed. In our case, the balanced equation ($2 Cu + I_2 \rightarrow 2 CuI$) shows that 1 mole of $I_2$ produces 2 moles of $CuI$. This stoichiometric relationship is crucial for converting the moles of the limiting reactant to the moles of product. Once we have the moles of $CuI$, we can convert this value back to grams using the molar mass of $CuI$. The molar mass of $CuI$ is approximately 190.45 g/mol. Multiplying the moles of $CuI$ by its molar mass will give us the theoretical yield in grams. This final calculation completes the stoichiometric problem, providing us with the maximum amount of product that can be expected from the reaction. Understanding how to calculate the theoretical yield is essential for chemists, as it allows them to plan experiments, predict product outcomes, and assess the efficiency of a reaction.

From the balanced equation, 1 mole of $I_2$ produces 2 moles of $CuI$. Therefore, 0.039 moles of $I_2$ will produce:

• Moles of $CuI = 0.039 \text{ mol } I_2 \times \frac{2 \text{ mol } CuI}{1 \text{ mol } I_2} = 0.078 \text{ mol } CuI$

Now, convert moles of $CuI$ to grams using its molar mass (190.45 g/mol):

• Theoretical yield of $CuI = 0.078 \text{ mol } CuI \times 190.45 \text{ g/mol} \approx 14.85 \text{ grams}$

The closest answer to our calculated theoretical yield of 14.85 grams is:

• B. 15 grams

In this comprehensive exploration of stoichiometry, we successfully calculated the theoretical yield of copper(I) iodide ($CuI$) when 10 grams of copper ($Cu$) and 10 grams of iodine ($I_2$) are mixed. Our journey involved several key steps: converting grams to moles, identifying the limiting reactant, and finally, calculating the theoretical yield using molar mass conversions. Each step is a cornerstone of stoichiometric calculations, and mastering these techniques is crucial for any aspiring chemist. We began by converting the given masses of reactants to moles, a fundamental step that allows us to work with the stoichiometric ratios dictated by the balanced chemical equation. This conversion is essential because chemical reactions occur on a molar basis, and it's the foundation for all subsequent calculations. Next, we identified the limiting reactant, iodine ($I_2$), which dictates the maximum amount of product that can be formed. The limiting reactant is like the weakest link in a chain, limiting the overall progress of the reaction. Identifying it allows us to accurately predict the maximum yield of product. Finally, we calculated the theoretical yield of $CuI$ using the moles of the limiting reactant and the stoichiometric ratio from the balanced equation. This calculation gave us an theoretical yield of approximately 14.85 grams, which we rounded to 15 grams, matching answer option B. This exercise underscores the power of stoichiometry in predicting the outcomes of chemical reactions. By applying these principles, chemists can accurately determine the amount of product formed, optimize reaction conditions, and gain a deeper understanding of chemical processes. The ability to perform these calculations is not only essential for academic success but also for practical applications in various fields, including pharmaceuticals, materials science, and environmental chemistry. Therefore, a firm grasp of stoichiometry is a valuable asset for anyone pursuing a career in chemistry or related disciplines.