Calculating Zinc Mass In Copper Sulfate Reaction

Jul 20, 2025 by qnaftunila 49 views

CuSO₄(aq) + Zn(s) → Cu(s) + ZnSO₄(aq) Reaction Analysis: Zinc Mass Calculation

Hey guys! Today, we're diving deep into a single-replacement reaction, a fascinating corner of chemistry. We're tackling a specific reaction where copper sulfate in solution ( $CuSO_4(aq)$ ) reacts with solid zinc ( $Zn(s)$ ) to produce solid copper ( $Cu(s)$ ) and zinc sulfate in solution ( $ZnSO_4(aq)$ ). The balanced chemical equation for this reaction is:

$CuSO_4(aq) + Zn(s) \longrightarrow Cu(s) + ZnSO_4(aq)$

Understanding the Single-Replacement Reaction

In this single-replacement reaction, zinc (Zn) essentially kicks copper (Cu) out of the copper sulfate ( $CuSO_4$ ) compound. Think of it like a dance-off where zinc has more energy and takes copper's place, leaving copper to stand alone. This type of reaction is characterized by one element replacing another in a compound. To get a solid understanding of this, let's break down the key concepts and steps involved in solving the problem.

Stoichiometry: The Heart of Chemical Calculations

Stoichiometry, which is the calculation of quantitative relationships in chemical reactions, is at the heart of solving this problem. It's like the recipe book for chemistry, telling us exactly how much of each ingredient (reactant) we need and how much of each product we'll get. The balanced chemical equation is our recipe, and the coefficients in front of each chemical formula tell us the molar ratios – the proportions in which substances react and are produced. In our case, the balanced equation tells us that one mole of zinc (Zn) reacts with one mole of copper sulfate ( $CuSO_4$ ) to produce one mole of copper (Cu) and one mole of zinc sulfate ( $ZnSO_4$ ).

Molar Mass: Converting Grams to Moles

Molar mass is a crucial concept in chemistry. It's the mass of one mole of a substance, usually expressed in grams per mole (g/mol). Each element has its unique molar mass, which is numerically equivalent to its atomic weight found on the periodic table. To solve our problem, we need to convert the given mass of copper (160.0 g) into moles using the molar mass of copper. This conversion is essential because the stoichiometry of the reaction is based on molar ratios, not mass ratios. We can use the following formula:

$Moles = \frac{Mass}{Molar \,Mass}$

Applying the Mole Ratio: Zinc to Copper

The balanced chemical equation provides the mole ratio between reactants and products. In our reaction, the mole ratio between zinc (Zn) and copper (Cu) is 1:1. This means that for every one mole of copper produced, one mole of zinc was consumed in the reaction. This mole ratio is the bridge that connects the amount of copper produced to the amount of zinc used. By knowing the moles of copper produced, we can directly determine the moles of zinc that reacted.

Converting Moles Back to Grams: Finding the Mass of Zinc

Once we've calculated the moles of zinc used, we need to convert this back into grams to answer the question, which asks for the mass of zinc. We use the same molar mass concept, but this time we multiply the moles of zinc by the molar mass of zinc. The formula is:

$Mass = Moles \times Molar \,Mass$

This step gives us the mass of zinc in grams, which is the final answer to the problem.

Problem Breakdown: Calculating the Mass of Zinc

Let's get down to brass tacks and calculate the mass of zinc used in the reaction. We know that 160.0 g of copper was produced, and we want to find out how many grams of zinc reacted. Here's how we'll do it:

Convert the mass of copper to moles: First, we need to find the molar mass of copper (Cu). Looking at the periodic table, the molar mass of copper is approximately 63.55 g/mol. Now, we can convert the mass of copper (160.0 g) to moles:

$Moles \, of \, Cu = \frac{160.0 \, g}{63.55 \, g/mol} \approx 2.518 \, mol$

So, about 2.518 moles of copper were produced.
Use the mole ratio to find moles of zinc: From the balanced equation, we know the mole ratio of Zn to Cu is 1:1. This means that the number of moles of zinc used is equal to the number of moles of copper produced:

$Moles \, of \, Zn = Moles \, of \, Cu = 2.518 \, mol$

Therefore, 2.518 moles of zinc were used in the reaction.
Convert moles of zinc to grams: Next, we need to convert moles of zinc to grams using the molar mass of zinc. The molar mass of zinc (Zn) is approximately 65.38 g/mol. Now, we can calculate the mass of zinc:

$Mass \, of \, Zn = 2.518 \, mol \times 65.38 \, g/mol \approx 164.6 \, g$

So, approximately 164.6 grams of zinc were used in the reaction.

Final Answer: Mass of Zinc Used

Therefore, the mass of zinc used in the reaction is approximately 164.6 grams. Remember, guys, it’s essential to pay attention to significant figures and round your final answer appropriately. In this case, the initial mass of copper (160.0 g) has four significant figures, so our final answer should also have four significant figures. However, since the question asks for the answer to the tenths place, we round our answer to 164.6 g.

This step-by-step approach should help you tackle similar stoichiometry problems with confidence. By understanding the core concepts and practicing regularly, you'll become a pro at balancing equations and calculating masses in no time!

Additional Insights and Tips

To further enhance your understanding and problem-solving skills, let's explore some additional insights and tips related to stoichiometry and single-replacement reactions. These will not only help you tackle similar problems but also deepen your overall grasp of chemical principles.

Balancing Chemical Equations: The Foundation of Stoichiometry

Balancing chemical equations is a fundamental skill in chemistry, and it's the bedrock upon which stoichiometry calculations are built. A balanced equation ensures that the number of atoms of each element is the same on both sides of the equation, adhering to the law of conservation of mass. When tackling a stoichiometry problem, always double-check that the equation is balanced before proceeding with any calculations. This will prevent errors and ensure your results are accurate. There are various methods for balancing equations, including the trial-and-error method and the algebraic method. Practice different techniques to find the one that works best for you.

Identifying Single-Replacement Reactions

Single-replacement reactions, also known as single-displacement reactions, are a specific type of chemical reaction where one element replaces another in a compound. These reactions generally follow the form:

$A + BC \longrightarrow AC + B$

where A is an element, and BC is a compound. In our problem, zinc (Zn) replaces copper (Cu) in copper sulfate ( $CuSO_4$ ). To identify single-replacement reactions, look for an element reacting with a compound. Understanding the activity series of metals can help predict whether a single-replacement reaction will occur. A more reactive metal will replace a less reactive metal in a compound.

Limiting Reactant: When One Runs Out First

In real-world scenarios, reactions often involve multiple reactants, and one of these reactants may be the limiting reactant. The limiting reactant is the reactant that is completely consumed in a reaction, determining the amount of product that can be formed. If we had information about the amounts of both zinc and copper sulfate, we would need to identify the limiting reactant before calculating the amount of copper produced. This involves calculating the moles of each reactant and comparing them based on the stoichiometry of the balanced equation. The reactant that produces the least amount of product is the limiting reactant.

Percent Yield: Real-World Reaction Efficiency

In practical experiments, the actual yield of a reaction is often less than the theoretical yield, which is the amount calculated using stoichiometry. The percent yield is a measure of the efficiency of a reaction and is calculated using the formula:

$Percent \, Yield = (\frac{Actual \, Yield}{Theoretical \, Yield}) \times 100\%$

Knowing the percent yield gives you a realistic understanding of how much product you can expect from a reaction, considering factors like incomplete reactions and loss of product during purification.

Common Mistakes to Avoid

To ensure accurate calculations, it's essential to avoid common mistakes in stoichiometry. Here are a few pitfalls to watch out for:

Forgetting to balance the chemical equation: Always balance the equation before doing any calculations.
Using incorrect molar masses: Double-check the molar masses of elements and compounds using the periodic table.
Incorrectly applying mole ratios: Make sure to use the correct mole ratios from the balanced equation.
Mixing up units: Ensure that all masses are in grams and molar masses are in grams per mole.
Rounding errors: Avoid rounding intermediate values, and only round the final answer to the appropriate number of significant figures.

By keeping these tips in mind and practicing consistently, you'll be well-equipped to tackle a wide range of stoichiometry problems. Keep up the great work, and happy calculating!

By understanding these additional insights and tips, you’ll be better prepared to tackle a wider range of stoichiometry problems and deepen your understanding of chemical reactions. Remember, guys, practice makes perfect, so keep working at it, and you’ll master these concepts in no time!