Calculating $ZnCl_2$ Production From Zinc And HCl Stoichiometry Problem

This article explores the stoichiometry involved in the reaction between zinc (Zn) and hydrochloric acid (HCl) to produce zinc chloride ($ZnCl_2$) and hydrogen gas ($H_2$). We will delve into the calculations required to determine the amount of $ZnCl_2$ produced from a given amount of zinc, while also identifying the limiting reagent in the reaction. Understanding stoichiometry is fundamental in chemistry, allowing us to predict the quantities of reactants and products involved in chemical reactions.

The Chemical Reaction

The balanced chemical equation for the reaction between zinc and hydrochloric acid is:

$Zn + 2HCl \rightarrow ZnCl_2 + H_2$

This equation tells us that one mole of zinc (Zn) reacts with two moles of hydrochloric acid (HCl) to produce one mole of zinc chloride ($ZnCl_2$) and one mole of hydrogen gas ($H_2$). The balanced equation is crucial because it provides the mole ratios necessary for stoichiometric calculations. Stoichiometry is the study of the quantitative relationships between reactants and products in chemical reactions. These relationships are governed by the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. Therefore, the number of atoms of each element must be the same on both sides of the balanced chemical equation. In this reaction, one zinc atom reacts with two hydrochloric acid molecules to produce one zinc chloride molecule and one hydrogen molecule. The coefficients in front of each chemical formula in the balanced equation represent the stoichiometric coefficients, which are the ratios in which the reactants and products participate in the reaction. These coefficients are essential for converting between moles of reactants and moles of products. For example, the mole ratio between zinc and zinc chloride is 1:1, meaning that for every mole of zinc that reacts, one mole of zinc chloride is produced. Similarly, the mole ratio between hydrochloric acid and zinc chloride is 2:1, indicating that two moles of hydrochloric acid are required to produce one mole of zinc chloride. These mole ratios are the foundation for calculating the amount of product formed from a given amount of reactant, or vice versa. They allow us to predict the yield of a reaction based on the initial amounts of reactants. In the context of chemical reactions, understanding the balanced equation and the stoichiometric coefficients is paramount for accurate calculations and predictions. The balanced equation serves as a roadmap for the reaction, guiding the quantitative analysis and ensuring that mass is conserved throughout the process. By using the mole ratios derived from the balanced equation, we can precisely determine the amounts of reactants needed and the amounts of products formed, making stoichiometry a cornerstone of chemical calculations.

Problem Statement: Calculating $ZnCl_2$ Production

The question we aim to address is: How many grams of $ZnCl_2$ would be produced from 15 grams of Zn reacting with excess HCl? Additionally, we need to identify the limiting reagent in this reaction. The limiting reagent is the reactant that is completely consumed in a chemical reaction, thereby determining the amount of product formed. In contrast, the excess reagent is the reactant present in a greater quantity than necessary for the reaction. To solve this problem, we will first convert the mass of zinc to moles, then use the stoichiometry of the balanced equation to find the moles of $ZnCl_2$ produced. Finally, we will convert the moles of $ZnCl_2$ back to grams. The concept of limiting reagents is crucial in chemical reactions because it dictates the maximum amount of product that can be formed. The reaction will proceed until the limiting reagent is exhausted, at which point the reaction stops, even if there is excess of the other reactant. Identifying the limiting reagent allows chemists to optimize reactions by ensuring that the reactants are used efficiently and that the desired product yield is maximized. In this particular scenario, we are given 15 grams of zinc and an excess of hydrochloric acid. Since hydrochloric acid is in excess, it means that there is more than enough hydrochloric acid to react completely with the zinc. Therefore, zinc will be the limiting reagent, and the amount of zinc available will determine the amount of zinc chloride produced. The calculation involves several steps, including converting the mass of zinc to moles, using the mole ratio from the balanced equation to find the moles of zinc chloride, and then converting the moles of zinc chloride back to grams. These steps are essential for understanding and predicting the outcome of chemical reactions, ensuring that we can accurately determine the quantities of reactants and products involved.

Step-by-Step Solution

1. Convert Grams of Zn to Moles of Zn

To convert the mass of zinc to moles, we use the molar mass of zinc, which is given as 65.38 g/mol. The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). We use this value as a conversion factor to transform the given mass of zinc into moles. To perform the conversion, we divide the mass of zinc by its molar mass: Moles of Zn = (Mass of Zn) / (Molar mass of Zn) = 15 g / 65.38 g/mol ≈ 0.229 moles. This calculation is a fundamental step in stoichiometry, as it allows us to move from the macroscopic world of grams to the microscopic world of moles. Moles are a crucial unit in chemistry because they provide a direct link to the number of particles (atoms, molecules, ions) involved in a reaction. By converting grams to moles, we can use the balanced chemical equation to determine the stoichiometric relationships between reactants and products. In this case, we have found that 15 grams of zinc corresponds to approximately 0.229 moles of zinc. This value will be used in the next step to calculate the moles of zinc chloride produced. Understanding the concept of molar mass and its application in converting grams to moles is essential for stoichiometric calculations and for accurately predicting the outcome of chemical reactions. The molar mass serves as a bridge between mass and moles, enabling us to quantify the amount of substance in chemical reactions and processes.

2. Use the Stoichiometry of the Reaction to Find Moles of $ZnCl_2$

From the balanced chemical equation ($Zn + 2HCl \rightarrow ZnCl_2 + H_2$), we see that the mole ratio between Zn and $ZnCl_2$ is 1:1. This means that for every one mole of zinc that reacts, one mole of zinc chloride is produced. This stoichiometric relationship is derived directly from the coefficients in the balanced equation, which represent the relative number of moles of each substance involved in the reaction. The mole ratio serves as a conversion factor to translate the moles of one substance into the moles of another. In this case, we use the 1:1 mole ratio to convert the moles of zinc to moles of zinc chloride. Since we calculated that we have 0.229 moles of zinc, and the mole ratio is 1:1, we can directly say that the moles of zinc chloride produced will also be 0.229 moles. Moles of $ZnCl_2$ = Moles of Zn × (1 mole $ZnCl_2$ / 1 mole Zn) = 0.229 moles. This step highlights the importance of the balanced chemical equation in stoichiometry. The balanced equation provides the crucial mole ratios that allow us to quantitatively relate the reactants and products in a chemical reaction. Without a balanced equation, it would be impossible to accurately determine the amounts of substances involved in a reaction. By understanding the stoichiometric relationships, we can predict the yield of a reaction and optimize reaction conditions to maximize product formation. In this instance, the 1:1 mole ratio between zinc and zinc chloride simplifies the calculation, but in other reactions, more complex mole ratios may be involved, requiring careful attention to the coefficients in the balanced equation.

3. Convert Moles of $ZnCl_2$ to Grams of $ZnCl_2$

To convert moles of $ZnCl_2$ to grams, we need to use the molar mass of $ZnCl_2$. First, we calculate the molar mass of $ZnCl_2$ by adding the atomic masses of one zinc atom and two chlorine atoms. The atomic mass of zinc (Zn) is 65.38 g/mol, and the atomic mass of chlorine (Cl) is 35.45 g/mol. Therefore, the molar mass of $ZnCl_2$ is: Molar mass of $ZnCl_2$ = (1 × Molar mass of Zn) + (2 × Molar mass of Cl) = (1 × 65.38 g/mol) + (2 × 35.45 g/mol) = 65.38 g/mol + 70.90 g/mol = 136.28 g/mol. The molar mass of a compound is the sum of the atomic masses of all the atoms in its chemical formula. It represents the mass of one mole of the compound and is a crucial conversion factor for converting between moles and grams. Once we have the molar mass of $ZnCl_2$, we can convert the moles of $ZnCl_2$ we calculated in the previous step (0.229 moles) to grams. To do this, we multiply the moles of $ZnCl_2$ by its molar mass: Grams of $ZnCl_2$ = Moles of $ZnCl_2$ × Molar mass of $ZnCl_2$ = 0.229 moles × 136.28 g/mol ≈ 31.21 grams. This calculation allows us to determine the mass of zinc chloride that would be produced from 15 grams of zinc reacting with excess hydrochloric acid. The molar mass acts as a bridge between the microscopic world of moles and the macroscopic world of grams, allowing us to measure and quantify the amount of substances in chemical reactions. Understanding how to calculate molar mass and use it for conversions is essential for stoichiometry and quantitative chemical analysis.

4. Identify the Limiting Reagent

In this reaction, zinc (Zn) is the limiting reagent. This is because the problem states that hydrochloric acid (HCl) is in excess. The limiting reagent is the reactant that is completely consumed in the reaction, and its amount determines the maximum amount of product that can be formed. Since HCl is in excess, there is more than enough HCl to react completely with the 15 grams of Zn. Therefore, the reaction will proceed until all the Zn is used up. The concept of a limiting reagent is critical in understanding and optimizing chemical reactions. In many chemical reactions, reactants are not present in stoichiometric amounts, meaning they are not in the exact mole ratios as specified by the balanced chemical equation. In such cases, one reactant will be completely consumed before the other, thereby limiting the amount of product that can be formed. Identifying the limiting reagent is essential for predicting the yield of a reaction and for ensuring that reactants are used efficiently. In industrial processes, it is particularly important to determine the limiting reagent to minimize waste and maximize product output. In this specific reaction, because HCl is in excess, Zn is the limiting reagent, and the amount of $ZnCl_2$ produced is directly determined by the amount of Zn available. If we had instead been given a specific amount of HCl, we would need to calculate the moles of HCl and compare it to the moles of Zn to determine which reactant is limiting. This would involve using the mole ratio from the balanced equation to find out how much of each reactant is required to react completely with the other. By understanding the concept of limiting reagents, we can effectively control and predict the outcome of chemical reactions.

Final Answer

From 15 grams of Zn reacting with excess HCl, approximately 31.21 grams of $ZnCl_2$ would be produced. Zinc (Zn) is the limiting reagent in this reaction. These calculations are based on the principles of stoichiometry, which provide a quantitative framework for understanding chemical reactions. Stoichiometry allows us to predict the amounts of reactants and products involved in a reaction, ensuring that we can accurately plan and execute chemical processes. In this specific example, we have demonstrated how to convert mass to moles, use mole ratios from a balanced equation, and calculate the mass of a product formed. These skills are fundamental in chemistry and are applicable to a wide range of chemical reactions and scenarios. The identification of the limiting reagent is also a crucial aspect of stoichiometric calculations. The limiting reagent determines the maximum amount of product that can be formed, and understanding its role allows us to optimize reaction conditions for maximum yield. In the case of the reaction between zinc and hydrochloric acid, the excess of HCl ensures that zinc is the limiting reagent, and the amount of zinc present directly dictates the amount of zinc chloride produced. By mastering the concepts and techniques of stoichiometry, we can confidently tackle quantitative problems in chemistry and gain a deeper understanding of the behavior of chemical substances and their interactions. This knowledge is essential not only for chemists but also for anyone working in fields that involve chemical processes, such as materials science, environmental science, and medicine.

Conclusion

This exercise illustrates the importance of stoichiometry in predicting the outcome of chemical reactions. By understanding mole ratios and limiting reagents, we can accurately calculate the amounts of products formed in a reaction. These principles are fundamental to various fields, including chemistry, chemical engineering, and materials science. Mastering stoichiometry is essential for anyone seeking a deeper understanding of chemical processes and their applications. The ability to perform stoichiometric calculations allows us to design and optimize chemical reactions, predict product yields, and ensure efficient use of resources. In the context of industrial chemistry, stoichiometry plays a critical role in scaling up chemical processes from laboratory scale to industrial production. By carefully controlling the amounts of reactants and understanding the limiting reagent, chemists and engineers can maximize product output and minimize waste. Stoichiometry is also crucial in analytical chemistry, where it is used to determine the concentration of substances in a sample. Techniques such as titrations rely on stoichiometric principles to accurately quantify the amount of a specific compound in a solution. Furthermore, stoichiometry is essential in environmental chemistry for understanding and mitigating pollution. By analyzing chemical reactions that occur in the environment, we can predict the fate of pollutants and develop strategies for remediation. The applications of stoichiometry extend beyond traditional chemistry into interdisciplinary fields such as biochemistry and materials science. In biochemistry, stoichiometry is used to understand metabolic pathways and enzyme kinetics, while in materials science, it is used to design new materials with specific properties. In summary, stoichiometry is a cornerstone of chemistry, providing a quantitative framework for understanding and predicting chemical phenomena. Its principles are widely applicable and essential for anyone working in the chemical sciences or related fields. By mastering stoichiometry, we gain the ability to control and manipulate chemical reactions, leading to advancements in various scientific and technological domains.