Calculating Copper Yield: A Chemistry Guide

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Hey there, chemistry enthusiasts! Let's dive into a classic stoichiometry problem. We're going to break down how to calculate the theoretical yield of copper when copper(II) sulfate reacts with zinc. It's a fundamental concept, and understanding this will set you up for success in more complex chemical calculations. So, grab your lab coats (metaphorically, of course), and let's get started!

Understanding the Balanced Equation and Stoichiometry

The Foundation: The Balanced Equation. First things first, we need to understand the chemical reaction. The balanced equation is our roadmap. In this case, we have:

CuSO4+Zn→ZnSO4+CuCuSO_4 + Zn → ZnSO_4 + Cu

This equation tells us that one mole of copper(II) sulfate (CuSO4CuSO_4) reacts with one mole of zinc (ZnZn) to produce one mole of zinc sulfate (ZnSO4ZnSO_4) and one mole of copper (CuCu). The coefficients (the numbers in front of the chemical formulas) are all 1, which simplifies things, but it's crucial to ensure your equation is balanced before proceeding. If the equation isn't balanced, your calculations will be off, leading to incorrect results. Remember, the law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction, only transformed. So, we must have the same number of each type of atom on both sides of the equation.

Key Concepts: Moles and Molar Mass. Stoichiometry is all about the relationships between the amounts of reactants and products in a chemical reaction. The central unit of measurement is the mole, which represents a specific number of particles (6.022 x 10Β²Β³ particles, to be exactβ€”Avogadro's number). We use molar mass (the mass of one mole of a substance) to convert between grams and moles. You can find the molar mass of a compound by adding up the atomic masses of all the atoms in its formula. These atomic masses are found on the periodic table. For example, to find the molar mass of CuSO4CuSO_4, you would add the atomic masses of one copper atom, one sulfur atom, and four oxygen atoms.

Now, Let's break this down. Knowing these two concepts is essential for acing stoichiometry questions. Always start by writing the balanced equation, and then calculate the molar masses of the reactants and products involved in the question. Doing this at the beginning will make the subsequent calculations far easier.

Working with Excess Reactant. In this problem, we're told that zinc metal is present in excess. This means we have more than enough zinc to react with all of the copper(II) sulfate. The copper(II) sulfate is our limiting reactant, because the amount of it determines how much copper can be produced. The excess zinc doesn't play a role in the yield calculation, since there's plenty of it to react with everything.

Step-by-Step Calculation of Theoretical Yield

Alright, let's get down to the nitty-gritty and calculate the theoretical yield of copper. We'll follow these steps:

  1. Calculate the Moles of Copper(II) Sulfate: We're given 200.0 g of CuSO4CuSO_4. First, we need to convert this mass to moles using the molar mass of CuSO4CuSO_4.
  2. Use the Mole Ratio: From the balanced equation, we know that 1 mole of CuSO4CuSO_4 produces 1 mole of CuCu. We'll use this mole ratio to convert the moles of CuSO4CuSO_4 to moles of CuCu.
  3. Calculate the Mass of Copper: Finally, we'll convert the moles of CuCu to grams using the molar mass of CuCu. This will give us the theoretical yield of copper.

Step 1: Calculate Moles of Copper(II) Sulfate. To do this, we need the molar mass of CuSO4CuSO_4. Looking up the atomic masses from the periodic table:

  • Cu: 63.55 g/mol
  • S: 32.07 g/mol
  • O: 16.00 g/mol (x 4 = 64.00 g/mol)

Add those up:

Molar mass of CuSO4CuSO_4 = 63.55 + 32.07 + 64.00 = 159.62 g/mol

Now, convert the grams of CuSO4CuSO_4 to moles:

Moles of CuSO4CuSO_4 = (200.0 g) / (159.62 g/mol) = 1.253 mol

Step 2: Use the Mole Ratio. From the balanced equation, the mole ratio of CuSO4CuSO_4 to CuCu is 1:1. This means that for every 1 mole of CuSO4CuSO_4 that reacts, we get 1 mole of CuCu.

Moles of CuCu = 1.253 mol CuSO4CuSO_4 * (1 mol CuCu / 1 mol CuSO4CuSO_4) = 1.253 mol CuCu

Step 3: Calculate the Mass of Copper. Now, we need the molar mass of copper (CuCu), which is 63.55 g/mol (from the periodic table). Convert moles of CuCu to grams:

Mass of CuCu = 1.253 mol * 63.55 g/mol = 79.63 g

Therefore, the theoretical yield of copper is 79.63 g. The answer is C. 79.63 g.

Detailed Explanation of Each Step

Let's go through each step in a bit more detail, to make sure you've got it. First, remember our goal: to determine the mass of copper (CuCu) that can be produced from the reaction. Here's a deeper look:

  • Step 1: Convert Grams of Reactant to Moles. We started with 200.0 g of copper(II) sulfate (CuSO4CuSO_4). We had to convert this to moles, because chemical reactions happen on a mole-to-mole basis. The balanced chemical equation gives us the relationship between moles of reactants and products. To do this conversion, we used the molar mass of CuSO4CuSO_4, which we calculated by adding up the atomic masses of each element in the compound.

  • Step 2: Use the Mole Ratio from the Balanced Equation. The balanced equation is critical. It tells us the ratio in which the reactants combine and the products are formed. In this case, 1 mole of CuSO4CuSO_4 reacts to produce 1 mole of CuCu. This is our mole ratio, and it's essential for converting between moles of reactants and moles of products. It's the heart of the stoichiometric calculation. Without the balanced equation and the correct mole ratio, all calculations from here on would be incorrect.

  • Step 3: Convert Moles of Product to Grams. Once we knew the number of moles of copper (CuCu) produced, we converted this value back to grams. Why grams? Because the question asked for the theoretical yield in grams. The theoretical yield is the maximum amount of product that can be formed from a given amount of reactant, assuming the reaction goes to completion and there are no losses. The molar mass of CuCu was then used to convert from moles to grams.

Tips and Tricks for Stoichiometry Problems

Here are some tips to help you master stoichiometry problems, including the theoretical yield calculations:

  • Always Balance the Equation: This is the first and most critical step. If your equation isn't balanced, everything else will be wrong. Check and double-check.
  • Know Your Units: Make sure you're consistent with your units. Always convert to moles when working with chemical reactions. Ensure all units cancel properly in your calculations. If the units don't cancel correctly, you know you've made a mistake.
  • Identify the Limiting Reactant: If you're given the amounts of multiple reactants, you need to identify the limiting reactant. The limiting reactant determines the amount of product that can be formed. The other reactants are present in excess.
  • Use the Mole Ratio Correctly: The mole ratio from the balanced equation is the key to converting between reactants and products. Make sure you set up the ratio correctly, so your units cancel properly.
  • Check Your Work: Does your answer make sense? Is it reasonable, considering the amounts of reactants you started with? Double-check all calculations and make sure you haven't made any errors.

Common Mistakes to Avoid. When working on stoichiometry problems, watch out for these common errors:

  • Incorrectly balancing the chemical equation. Always double-check.
  • Forgetting to convert grams to moles using molar mass.
  • Using the wrong mole ratio. Always make sure you're using the mole ratio from your balanced chemical equation.
  • Making careless calculation errors. Take your time, use a calculator, and double-check your work.

Conclusion: Mastering Stoichiometry

And there you have it, guys! We've successfully calculated the theoretical yield of copper in this chemical reaction. Remember, practice is key. Work through several stoichiometry problems to solidify your understanding. The more you practice, the easier it becomes. Understanding stoichiometry is a fundamental skill in chemistry, and it's essential for solving a wide variety of chemical problems.

Keep practicing, and you'll be acing those chemistry exams in no time! If you have any questions, don't hesitate to ask. Happy calculating, and keep exploring the fascinating world of chemistry! Remember to always prioritize safety when conducting any experiments in a lab setting.