Problem 125 - Chemistry Matter and Change

Question

A single-replacement reaction occurs between copper and silver nitrate. When 63.5 \(\mathrm{g}\) of copper reacts with 339.8 \(\mathrm{g}\) of silver nitrate, 215.8 \(\mathrm{g}\) of silver is produced. Write a balanced chemical equation for this reaction. What other product formed? What is the mass of the second product?

Step-by-Step Solution

Answer

The balanced equation is \( \text{Cu} + 2\text{AgNO}_3 \rightarrow 2\text{Ag} + \text{Cu(NO}_3)_2 \). The other product is 187.55 g of copper(II) nitrate.

Step 1: Identify the Reactants and Products

In a single-replacement reaction, copper replaces silver in silver nitrate. The reactants are copper ( Cu ) and silver nitrate ( AgNO_3 ). The products are silver ( Ag ) and copper(II) nitrate ( Cu(NO_3)_2 ).

Step 2: Write the Unbalanced Equation

Write the unbalanced chemical equation using the identified reactants and products:\[ \text{Cu} + \text{AgNO}_3 \rightarrow \text{Ag} + \text{Cu(NO}_3)_2 \]

Step 3: Balance the Chemical Equation

Balance the chemical equation by ensuring the same number of each type of atom appears on both sides. The balanced equation is:\[ \text{Cu} + 2\text{AgNO}_3 \rightarrow 2\text{Ag} + \text{Cu(NO}_3)_2 \]

Step 4: Calculate Molar Masses

Find molar masses: - Cu = 63.5 g/mol - AgNO_3 = 169.87 g/mol - Ag = 107.87 g/mol - Cu(NO_3)_2 = 187.55 g/mol

Step 5: Determine Moles of Reactants and Silver Produced

- Moles of Cu: \( \frac{63.5 \text{ g}}{63.5 \text{ g/mol}} = 1 \text{ mol} \)- Moles of AgNO_3: \( \frac{339.8 \text{ g}}{169.87 \text{ g/mol}} \approx 2 \text{ moles} \)- Moles of Ag produced: \( \frac{215.8 \text{ g}}{107.87 \text{ g/mol}} \approx 2 \text{ moles} \)

Step 6: Determine Moles of Copper(II) Nitrate Produced

According to the balanced equation, 1 mole of Cu produces 1 mole of Cu(NO_3)_2. Thus, 1 mole of Cu would produce 1 mole of Cu(NO_3)_2.

Step 7: Calculate the Mass of Copper(II) Nitrate

Multiply the number of moles of Cu(NO_3)_2 produced by its molar mass:\[ 1 \text{ mol} \times 187.55 \text{ g/mol} = 187.55 \text{ g} \]Thus, 187.55 g of copper(II) nitrate is formed.

Key Concepts

Chemical Equation Balancing

Balancing a chemical equation is crucial for representing a chemical reaction accurately. The goal is to have the same number of each type of atom on both sides of the equation.

In the copper and silver nitrate reaction, copper (Cu) replaces silver (Ag) to form copper(II) nitrate (Cu(NO₃)₂) and silver (Ag).

Here's how the balancing process works:

• Write the unbalanced equation: Cu + AgNO₃ → Ag + Cu(NO₃)₂.
• Notice that to balance the nitrates, you need 2 AgNO₃ on the reactant side since each Cu(NO₃)₂ contains two nitrate groups.
• This adjustment gives you 2 silver atoms on the product side, so add 2 Ag in the reactant side: Cu + 2 AgNO₃ → 2 Ag + Cu(NO₃)₂.

This balanced equation visually confirms that for every atom used in the equation, an equal atom is produced.

Balancing equations is not just a paper exercise. It reflects the conservation of mass—a cornerstone of chemistry—ensuring everything aligns with real-world reactions.

Molar Mass Calculation

Molar mass is essential to convert grams to moles, which helps us understand the quantities needed or produced in a reaction.

To find the molar mass of a compound, add up the atomic masses of each element. For instance, calculating the molar mass for copper nitrate involves:

• Copper (Cu): 63.5 g/mol.
• Nitrate (NO₃): For silver nitrate (AgNO₃), this includes Ag: 107.87 g/mol + N: 14.01 g/mol + O₃: 16.00 g/mol x 3 = 48.00 g/mol;
• Adding these gives AgNO₃ total: 107.87 + 14.01 + 48 = 169.87 g/mol.

Understanding molar mass allows us to move from the macroscopic world of grams to the microscopic world of moles, leading to accurate chemical calculations.

Using molar masses:

• Moles of Cu: 63.5 g / 63.5 g/mol = 1 mol.
• Moles of AgNO₃: 339.8 g / 169.87 g/mol ≈ 2 mol.
• Similarly, convert mass to moles for the products to analyze the reaction's efficiency and completeness.

Ultimately, this makes it easier to scale reactions for practical chemical use.

Copper and Silver Nitrate Reaction

This reaction illustrates a **single-replacement reaction**, where one element displaces another in a compound.

Here, copper (Cu) replaces silver (Ag) in silver nitrate (AgNO₃). As a result, the products are silver (Ag) and copper(II) nitrate (Cu(NO₃)₂).

Key points of this reaction include:

• It's a redox reaction where copper is oxidized and silver is reduced.
• This type of reaction showcases activity series, where more reactive copper replaces less reactive silver.
• Practical indication: the physical change as copper's blue color signifies copper(II) nitrate, and silver precipitates out.

This experiment provides insight into the reactivity and practical applications of metals, laying a foundation for more complex chemical synthesis and industrial applications. Understanding this reaction will sharpen your skills in recognizing patterns and predicting outcomes in chemical processes.