Question

Challenge When copper wire is placed into a silver nitrate solution \(\left(\mathrm{AgNO}_{3}\right)\), silver crystals and copper(II) nitrate \(\left(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\right)\) solution form. a. Write the balanced chemical equation for the reaction. b. If a 20.0-g sample of copper is used, determine the theoretical yield of silver. c. If 60.0 g of silver is recovered from the reaction, determine the percent yield of the reaction.

Short answer

The balanced chemical equation for the reaction is \(2\mathrm{Cu} + 4\mathrm{AgNO}_{3} \rightarrow 4\mathrm{Ag} + 2\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\). When using a 20.0 g sample of copper, the theoretical yield of silver is calculated to be 67.91 grams. With an actual yield of 60.0 g of silver, the percent yield of the reaction is approximately 88.35%.

Step-by-step solution

Write the balanced chemical equation

First, let's write the unbalanced chemical equation based on the given information. Copper reacts with silver nitrate to produce silver and copper(II) nitrate: Cu + AgNO3 -> Ag + Cu(NO3)2 Now we can balance the chemical equation: 2Cu + 4AgNO3 -> 4Ag + 2Cu(NO3)2 The balanced equation is: \(2\mathrm{Cu} + 4\mathrm{AgNO}_{3} \rightarrow 4\mathrm{Ag} + 2\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\)

Calculate the theoretical yield of silver

To calculate the theoretical yield of silver, we'll use stoichiometry. We're given a mass of copper, which we can use to determine the moles of copper, and then use the stoichiometric coefficients from the balanced equation to find the moles of silver produced. 1. Convert the mass of copper to moles: 20.0 g Cu * (1 mol Cu / 63.55 g Cu) = 0.3148 mol Cu 2. Use the stoichiometry of the balanced equation to find the moles of silver produced: (0.3148 mol Cu) * (4 mol Ag / 2 mol Cu) = 0.6296 mol Ag 3. Convert the moles of silver to grams: (0.6296 mol Ag) * (107.87 g Ag / 1 mol Ag) = 67.91 g Ag The theoretical yield of silver is 67.91 grams.

Calculate the percent yield

We are given that 60.0 g of silver is recovered from the reaction, which represents the actual yield. Now, we can calculate the percent yield using the theoretical yield calculated in Step 2 and the given actual yield: Percent yield = (Actual yield / Theoretical yield) * 100 Percent yield = (60.0 g Ag / 67.91 g Ag) * 100 = 88.35% The percent yield of the reaction is approximately 88.35%.

Key concepts

Stoichiometry

Stoichiometry is like a recipe for chemistry. It helps you figure out the right amounts of substances needed for a reaction and what you'll get at the end. Imagine cooking. You need a set amount of ingredients to make a dish. In chemistry, stoichiometry uses ratios from the balanced equation to relate amounts of reactants and products.
In our copper and silver nitrate reaction, the balanced equation tells us that:

• 2 moles of Cu react with 4 moles of AgNO either pushing the nose3 to produce 4 moles of Ag and 2 moles of Cu(NO either pushing the nose3

This relationship guides us to convert between moles of different substances during the reaction.
When you start with 20.0 grams of copper, stoichiometry lets you calculate the moles of copper and then, using the balanced equation, find the moles and mass of silver expected from the reaction. This process of conversion keeps everything proportionate according to the chemical equation.

Balanced Chemical Equation

A balanced chemical equation is crucial in stoichiometry as it ensures that the number of atoms for each element is equal on both sides of the reaction. It's like saying the ingredients at the start equal the final product quantities.
The initial step in balancing equations involves listing reactants and products. For copper reacting with silver nitrate:

• Copper (Cu) reacts with silver nitrate (AgNO either pushing the nose3) to form silver (Ag) and copper(II) nitrate (Cu(NO either pushing the nose3

Unbalanced, it appears as: Cu + AgNO₃ → Ag + Cu(NO₃)₂.
Balancing this, you adjust coefficients to match atoms on both sides:

• The balanced equation then is: 2Cu + 4AgNO₃ → 4Ag + 2Cu(NO₃)₂.

This balance is essential for accurate stoichiometric calculations, ensuring conservation of mass and correct measurement of reactants and products.

Percent Yield

Percent yield compares what you actually get from a reaction to what you theoretically expect. It's useful for understanding efficiency and loss in chemical processes.
In the reaction between copper and silver nitrate, after calculating that the theoretical yield of silver is 67.91 grams using stoichiometry, we were told the actual recovery was 60.0 grams.
The formula for percent yield is:

• Percent Yield = (Actual Yield / Theoretical Yield) × 100

Plugging the numbers in:

• (60.0 g / 67.91 g) × 100 ≈ 88.35%

This result tells you how well the reaction performed compared to its theoretical efficiency. Percent yield helps identify sources of inefficiency, whether through incomplete reactions, side reactions, or product losses, thus aiding in improving chemical processes.