Problem 93 - Chemistry: Principles and Reactions

Question

Copper metal can reduce silver ions to metallic silver. The copper is oxidized to copper ions according to the reaction $$ 2 \mathrm{Ag}^{+}(a q)+\mathrm{Cu}(s) \longrightarrow \mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}(s) $$ A copper strip with a mass of \(2.00 \mathrm{~g}\) is dipped into a solution of \(\mathrm{AgNO}_{3}\). After some time has elapsed, the copper strip is coated with silver. The strip is removed from the solution, dried, and weighed. The coated strip has a mass of \(4.18 \mathrm{~g}\). What are the masses of copper and silver metals in the strip? (Hint: Remember that the copper metal is being used up as silver metal forms.)

Step-by-Step Solution

Answer

Answer: The masses of copper and silver in the strip after the reaction are 1.359 g and 2.18 g, respectively.

Step 1: Calculate the mass gain of silver on the strip

Firstly, we need to find out how much mass the strip has gained after being coated with silver. To do this, subtract the initial mass of the strip (pure copper) from the final mass (copper and silver coated). Mass gain = Final mass - Initial mass Mass gain = 4.18 g - 2.00 g = 2.18 g The strip has gained 2.18 g in mass after being coated with silver.

Step 2: Calculate the amount of silver deposited in moles

Now, find the amount of silver deposited in moles, using the mass gain and molar mass of silver (Ag). Molar mass of Ag = 107.87 g/mol Amount of silver = (Mass gain) / (Molar mass of Ag) Amount of silver = (2.18 g) / (107.87 g/mol) = 0.0202 mol

Step 3: Calculate the moles of copper used

Using the stoichiometry of the reaction, find the amount of copper used in moles. The balanced equation shows that 1 mole of Cu reacts with 2 moles of Ag+. Amount of Cu used = (1/2) × Amount of Ag Amount of Cu used = (1/2) × 0.0202 mol = 0.0101 mol

Step 4: Calculate the mass of copper used in the reaction

Now, calculate the mass of copper used in the reaction using the molar mass of copper (Cu). Molar mass of Cu = 63.55 g/mol Mass of Cu used = Amount of Cu used × Molar mass of Cu Mass of Cu used = 0.0101 mol × 63.55 g/mol = 0.641 g

Step 5: Calculate the remaining mass of copper in the strip

Finally, find the remaining mass of copper in the strip by subtracting the mass of copper used from the initial mass of the strip (pure copper). Mass of remaining Cu = Initial mass of Cu - Mass of Cu used Mass of remaining Cu = 2.00 g - 0.641 g = 1.359 g The remaining mass of copper in the strip is 1.359 g.

Step 6: Determine the masses of copper and silver in the strip

Now, we have found the remaining mass of copper in the strip and the mass of silver that has been coated onto the strip. Mass of Cu in the strip = 1.359 g Mass of Ag in the strip = 2.18 g Thus, the masses of copper and silver in the strip are 1.359 g and 2.18 g, respectively.

Key Concepts

Oxidation-Reduction Reactions

Redox reactions, or oxidation-reduction reactions, are chemical processes where electrons are transferred between substances. In these reactions, one substance gains electrons (is reduced), while another loses electrons (is oxidized).

In the given reaction, copper (\(\text{Cu}\)) is oxidized as it loses electrons and transforms into copper ions (\(\text{Cu}^{2+}\)). Simultaneously, silver ions (\(\text{Ag}^{+}\)) gain electrons, resulting in the formation of metallic silver (\(\text{Ag}\)).

• **Oxidation:** Loss of electrons by copper. \(\text{Cu} \rightarrow \text{Cu}^{2+} + 2e^-\).
• **Reduction:** Gain of electrons by silver ions. \(\text{2Ag}^{+} + 2e^- \rightarrow \text{2Ag}\).

This interaction illustrates the complementary electron transfer characteristic of redox reactions. Understanding both oxidation and reduction processes is crucial for grasping how redox reactions operate.

Stoichiometry in Redox Reactions

Stoichiometry is the calculation of reactants and products in chemical reactions. It helps predict how much of each substance is consumed or produced.

In our reaction, the balanced chemical equation is:
\(\text{2Ag}^{+} + \text{Cu} \rightarrow \text{Cu}^{2+} + 2\text{Ag}\)

This equation tells us the ratios in which reactants combine and products form. For every 2 moles of silver ions, 1 mole of copper is used, and 2 moles of silver are produced.

• **Reactant Ratios:** 2 moles of \(\text{Ag}^+\) react with 1 mole of \(\text{Cu}\).
• **Product Formation:** Produces 2 moles of \(\text{Ag}\) and 1 mole of \(\text{Cu}^{2+}\).

Stoichiometry is essential in determining how much of each reactant is required and the amount of product formed during the reaction.

Molar Mass and Its Importance

Molar mass is a fundamental concept in chemistry, representing the mass of one mole of a substance. It is expressed in grams per mole (g/mol) and is used to convert between mass and moles.

In our exercise, knowing the molar masses of silver and copper is key to solving the problem:

• **Molar Mass of Silver (Ag):** 107.87 g/mol
• **Molar Mass of Copper (Cu):** 63.55 g/mol

By using these values, we were able to find the amount of silver deposited (2.18 g) in moles, and subsequently, the moles and mass of copper used. Calculations involving molar mass are crucial when converting between grams and moles.

Balancing Chemical Equations

Balancing chemical equations is crucial to mirror the conservation of mass and charge. Each element must have the same number of atoms on both sides of the equation.

For the copper and silver reaction, the balanced equation is:
\(\text{2Ag}^{+} + \text{Cu} \rightarrow \text{Cu}^{2+} + 2\text{Ag}\)

Here's how balancing is achieved:

• **Copper:** One copper atom on both sides.
• **Silver:** Two silver ions (\(2\text{Ag}^+\)) become two silver atoms (\(2\text{Ag}\)).
• **Charges:** Reactants carry a total charge of +2, and products also carry a total charge of +2.

Balancing ensures that the equation respects both matter conservation and charge conservation principles. It is foundational for stoichiometry and understanding reaction mechanics.