Question

What is the mass of silver that can be prepared from \(1.00 \mathrm{~g}\) of copper metal? $$\mathrm{Cu}(s)+2 \mathrm{AgNO}_{3}(a q) \longrightarrow \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(aq)+2 \mathrm{Ag}(s)$$

Short answer

3.393 grams of silver can be prepared from 1.00 gram of copper.

Step-by-step solution

Understand the Reaction Equation

The given chemical reaction is \( \mathrm{Cu}(s) + 2 \mathrm{AgNO}_{3}(aq) \rightarrow \mathrm{Cu}(\mathrm{NO}_{3})_{2}(aq) + 2 \mathrm{Ag}(s) \). In this reaction, one mole of copper reacts with two moles of silver nitrate to produce one mole of copper(II) nitrate and two moles of silver.

Calculate the Moles of Copper

First, determine the moles of copper using its molar mass. The molar mass of copper is about \( 63.55 \text{ g/mol} \). Calculate the moles of copper from \( 1.00 \text{ g} \) of copper as follows: \[ \text{moles of Cu} = \frac{1.00 \text{ g}}{63.55 \text{ g/mol}} \approx 0.01574 \text{ mol} \]

Determine the Moles of Silver Produced

According to the reaction stoichiometry, one mole of copper produces two moles of silver. Therefore, \( 0.01574 \text{ mol} \) of copper will produce \( 2 \times 0.01574 \text{ mol} = 0.03148 \text{ mol of Ag} \).

Calculate the Mass of Silver

Finally, convert the moles of silver to grams. The molar mass of silver is approximately \( 107.87 \text{ g/mol} \). Thus, the mass of silver is: \[ \text{mass of Ag} = 0.03148 \text{ mol} \times 107.87 \text{ g/mol} \approx 3.393 \text{ g} \]

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry and an essential tool for stoichiometry calculations. It refers to the mass of one mole of a substance, typically expressed in grams per mole (g/mol).
To find the molar mass of an element, you simply use the atomic mass from the periodic table. For example, copper (Cu) has an atomic mass of about 63.55 g/mol. This means that one mole of copper atoms weighs 63.55 grams.
In practical scenarios, knowing the molar mass enables you to convert between the mass of a substance and the number of moles. This conversion is crucial in chemical reactions where the amount of reactants and products needs to be quantified.

• To calculate moles from grams: \( ext{moles} = \frac{\text{grams}}{\text{molar mass}} \)
• To calculate grams from moles: \( ext{grams} = \text{moles} \times \text{molar mass} \)

Chemical Reaction Equation

A chemical reaction equation is a symbolic representation of a chemical reaction. It shows the reactants (the starting substances) and the products (the substances formed) in a reaction.
The essential feature of a chemical equation is that it obeys the law of conservation of mass; matter is neither created nor destroyed. This means that the number of atoms for each element must be the same on both sides of the equation.
In the equation \( \mathrm{Cu}(s) + 2 \mathrm{AgNO}_{3}(aq) \longrightarrow \mathrm{Cu}(\mathrm{NO}_{3})_{2}(aq) + 2 \mathrm{Ag}(s) \), we see that:

• One mole of solid copper (Cu) reacts with two moles of aqueous silver nitrate (AgNO₃).
• This reaction produces one mole of aqueous copper(II) nitrate \( \mathrm{Cu}(\mathrm{NO}_{3})_{2} \) and two moles of solid silver (Ag).

This equation also provides the stoichiometric coefficients which describe the ratios of reactants and products. These ratios are crucial for calculating the quantities of substances consumed and produced in the reaction.

Copper and Silver Reaction

The reaction between copper and silver nitrate is an example of a single replacement reaction, where an element replaces another in a compound.
Here, copper displaces silver from silver nitrate solution to produce silver metal and copper(II) nitrate.
This reaction can be broken down into several clear steps:

• Copper (Cu), being more reactive than silver (Ag), can replace silver ions in solution.
• The chemical equation shows that one mole of copper produces two moles of silver by replacing silver ions in the nitrate solution.
• The nitrate ions (NO₃⁻) remain unchanged in the solution; they are spectator ions.
• This scalability allows you to predict how much silver can form from any given mass of copper.

Understanding the copper and silver reaction is not just about the reaction itself but also about honing skills in stoichiometry. By determining how much product forms for a given amount of reactant, you deepen your understanding of chemical processes.