Silver Yield From Copper Reaction: A Chemistry Calculation

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Silver Yield from Copper Reaction: A Chemistry Calculation

Hey guys! Today, we're diving into a classic chemistry problem: figuring out how much silver you get from reacting copper with silver nitrate. It sounds like fun, right? Let’s break it down step by step so it's super easy to follow. We will go through each stage in detail so that nothing is missed.

Understanding the Chemical Reaction

Our starting point is the balanced chemical equation:

Cu + 2AgNO3 -> Cu(NO3)2 + 2Ag

This equation tells us that one atom of copper (Cu) reacts with two molecules of silver nitrate (2AgNO3) to produce one molecule of copper(II) nitrate (Cu(NO3)2) and two atoms of silver (2Ag). Basically, copper kicks silver out of the nitrate party, and we end up with solid silver.

To solve this problem, we'll use stoichiometry, which is just a fancy way of saying we'll use the relationships between the amounts of reactants and products in a chemical reaction. The key here is to use molar masses to convert between grams and moles, and then use the balanced equation to relate the moles of copper to the moles of silver.

Step 1: Calculate Moles of Copper

We know we have 10 grams of copper. To find out how many moles that is, we need the molar mass of copper. The molar mass of copper (Cu) is approximately 63.55 g/mol. This means that one mole of copper weighs 63.55 grams. So, to find the number of moles in 10 grams, we use the formula:

Moles = Mass / Molar Mass

Moles of Cu = 10 g / 63.55 g/mol ≈ 0.157 moles

So, we have about 0.157 moles of copper reacting.

Step 2: Use Stoichiometry to Find Moles of Silver

Now, let’s use the balanced equation to find out how many moles of silver (Ag) will be produced. According to the equation:

Cu + 2AgNO3 -> Cu(NO3)2 + 2Ag

One mole of copper (Cu) produces two moles of silver (2Ag). This is a 1:2 relationship. So, if we have 0.157 moles of copper, we’ll produce twice that amount of silver.

Moles of Ag = 2 * Moles of Cu = 2 * 0.157 moles ≈ 0.314 moles

Therefore, approximately 0.314 moles of silver will be produced.

Step 3: Calculate Grams of Silver

We now know how many moles of silver will be produced. To find out how many grams that is, we need the molar mass of silver. The molar mass of silver (Ag) is approximately 107.87 g/mol. This means one mole of silver weighs 107.87 grams. To find the mass of 0.314 moles of silver, we use the formula:

Mass = Moles * Molar Mass

Mass of Ag = 0.314 moles * 107.87 g/mol ≈ 33.86 grams

So, about 33.86 grams of silver will be produced in the reaction.

Detailed Explanation of Each Step

Diving Deeper into Molar Mass

The molar mass is a critical concept in chemistry. It's the mass of one mole of a substance, expressed in grams per mole (g/mol). You can find the molar mass of an element on the periodic table. For compounds, you add up the molar masses of all the atoms in the formula. For example, if we wanted to find the molar mass of silver nitrate (AgNO3), we would add the molar masses of silver (Ag), nitrogen (N), and three oxygen atoms (O).

Understanding Mole Ratios

The balanced chemical equation provides the mole ratios between reactants and products. In our equation:

Cu + 2AgNO3 -> Cu(NO3)2 + 2Ag

The mole ratio between copper and silver is 1:2. This means for every 1 mole of copper that reacts, 2 moles of silver are produced. Mole ratios are essential for stoichiometric calculations because they allow us to predict how much of a product will be formed from a given amount of reactant.

Why Stoichiometry Matters

Stoichiometry is the foundation of quantitative chemistry. It allows us to make predictions about chemical reactions and design experiments effectively. Whether you're in the lab synthesizing a new compound or scaling up a chemical process for industrial production, understanding stoichiometry is crucial for success.

Common Mistakes to Avoid

When tackling stoichiometry problems, it’s easy to make mistakes if you’re not careful. Here are a few common pitfalls to watch out for:

  1. Forgetting to Balance the Equation: Always make sure your chemical equation is balanced before doing any calculations. An unbalanced equation will lead to incorrect mole ratios and wrong answers.
  2. Using the Wrong Molar Masses: Double-check that you’re using the correct molar masses for each substance. A small mistake here can throw off your entire calculation.
  3. Mixing Up Mole Ratios: Make sure you correctly interpret the mole ratios from the balanced equation. It’s easy to flip the numbers if you’re not paying attention.
  4. Incorrect Units: Always include units in your calculations and make sure they cancel out correctly. This will help you catch errors and ensure your final answer has the correct units.

Real-World Applications

Stoichiometry isn't just an academic exercise; it has numerous real-world applications. Here are a few examples:

  • Pharmaceutical Industry: In drug manufacturing, stoichiometry is used to ensure that the correct amounts of reactants are combined to produce the desired amount of a drug. This is critical for ensuring the safety and efficacy of medications.
  • Environmental Science: Stoichiometry is used to analyze and mitigate environmental pollution. For example, it can be used to calculate the amount of a chemical needed to neutralize an acid spill or to determine the amount of greenhouse gases produced by a particular activity.
  • Materials Science: In materials science, stoichiometry is used to design and synthesize new materials with specific properties. By carefully controlling the amounts of reactants, scientists can create materials with desired characteristics such as strength, conductivity, and optical properties.
  • Cooking: Yes, even cooking involves stoichiometry! When you follow a recipe, you're essentially using stoichiometry to ensure that you have the right proportions of ingredients to create the desired dish.

Practice Problem

Let's try another practice problem to solidify your understanding. Suppose you want to produce copper(II) chloride (CuCl2) by reacting copper with chlorine gas (Cl2). The balanced equation is:

Cu + Cl2 -> CuCl2

If you start with 5 grams of copper, how many grams of chlorine gas are needed to react completely with the copper?

Solution

  1. Calculate Moles of Copper:

Moles of Cu = 5 g / 63.55 g/mol ≈ 0.0787 moles

  1. Use Stoichiometry to Find Moles of Chlorine Gas:

From the balanced equation, 1 mole of Cu reacts with 1 mole of Cl2. So:

Moles of Cl2 = Moles of Cu = 0.0787 moles

  1. Calculate Grams of Chlorine Gas:

The molar mass of Cl2 is approximately 70.90 g/mol.

Mass of Cl2 = 0.0787 moles * 70.90 g/mol ≈ 5.58 grams

So, you need approximately 5.58 grams of chlorine gas to react completely with 5 grams of copper.

Conclusion

So, to wrap things up, if 10 grams of copper react with silver nitrate, you'll get about 33.86 grams of silver. Stoichiometry can be tricky, but with practice, you’ll get the hang of it. Remember to always balance your equations, use the correct molar masses, and pay attention to mole ratios. You've got this! Keep practicing, and you'll become a stoichiometry master in no time!

Hope this helps you guys out! Happy calculating!