Problem 41 - Chemistry: The Central Science

Question

A \(1 \mathrm{M}\) solution of \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\) is placed in a beaker with a strip of \(\mathrm{Cu}\) metal. A \(1 \mathrm{M}\) solution of \(\mathrm{SnSO}_{4}\) is placed in a second beaker with a strip of \(\mathrm{Sn}\) metal. A salt bridge connects the two beakers, and wires to a voltmeter link the two metal electrodes. (a) Which electrode serves as the anode and which as the cathode? (b) Which electrode gains mass and which loses mass as the cell reaction proceeds? (c) Write the equation for the overall cell reaction. (d) What is the emf generated by the cell under standard conditions?

Step-by-Step Solution

Answer

a) Anode: Sn metal, Cathode: Cu metal b) Sn electrode loses mass, Cu electrode gains mass. c) Overall cell reaction: Sn (s) + Cu²⁺ (aq) --> Sn²⁺ (aq) + Cu (s) d) Emf generated by the cell under standard conditions: 0.48V

Step 1: Identify the standard reduction potentials of Cu²⁺/Cu and Sn²⁺/Sn redox couples

To determine which electrode will serve as the anode and which will serve as the cathode, we must first refer to the standard reduction potentials (sometimes referred to as standard electrode potentials). In this case, we'll be looking at the following redox couples: Cu²⁺ + 2e⁻ ⇌ Cu (E⁰ = +0.34V) Sn²⁺ + 2e⁻ ⇌ Sn (E⁰ = -0.14V)

Step 2: Identify the anode and cathode

In a galvanic cell, the redox couple with the lower standard reduction potential (more negative value) will be oxidized or lose electrons, thereby serving as the anode. The redox couple with the higher (more positive) standard reduction potential will be reduced or gain electrons, thereby serving as the cathode. Comparing the standard reduction potentials: Cu²⁺/Cu: E⁰ = +0.34V Sn²⁺/Sn: E⁰ = -0.14V We can see that Sn²⁺/Sn is the more negative value, so the Sn electrode will serve as the anode, and the Cu²⁺/Cu electrode will serve as the cathode.

Step 3: Determine the mass changes in the electrodes

Since the Sn electrode serves as the anode, it undergoes oxidation, which means the metal loses electrons and goes into the solution as ions. This causes the Sn electrode to lose mass. On the other hand, the Cu²⁺/Cu electrode serves as the cathode. It undergoes reduction, meaning the Cu²⁺ ions gain electrons and are deposited onto the Cu electrode as solid Cu. This causes the Cu electrode to gain mass.

Step 4: Write the equation for the overall cell reaction

Next, we need to find the overall cell reaction. For this, we will use the half-reactions of the anode and cathode. Anode (oxidation): Sn ⇌ Sn²⁺ + 2e⁻ Cathode (reduction): Cu²⁺ + 2e⁻ ⇌ Cu Adding these two half-reactions, we get: Sn (s) + Cu²⁺ (aq) --> Sn²⁺ (aq) + Cu (s)

Step 5: Calculate the cell potential (emf) under standard conditions

Now we need to calculate the emf of the cell under standard conditions. The cell potential is calculated using the Nernst equation, considering that under standard conditions the concentrations are 1M and the temperature is 298K: E_cell = E_cathode - E_anode Using the standard reduction potentials (E⁰) from Step 1, we get: E_cell = (+0.34V) - (-0.14V) = 0.34V + 0.14V = 0.48V The emf generated by the cell under standard conditions is 0.48V. In summary: a) Anode: Sn metal, Cathode: Cu metal b) Sn electrode loses mass, Cu electrode gains mass. c) Overall cell reaction: Sn (s) + Cu²⁺ (aq) --> Sn²⁺ (aq) + Cu (s) d) Emf generated by the cell under standard conditions: 0.48V

Key Concepts

Galvanic Cell

A galvanic cell, also known as a voltaic cell, is a type of electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two electrodes – an anode and a cathode – submerged in electrolyte solutions. These electrodes are connected by a wire that allows electrons to flow, creating an electric current.

In a galvanic cell:

• The anode is where oxidation occurs; electrons are lost by the substance.
• The cathode is where reduction occurs; electrons are gained by the substance.
• A salt bridge connects the two electrolyte solutions to maintain electrical neutrality.

By using different metals and electrolytes, each galvanic cell can generate a unique voltage, allowing for a variety of practical applications, including batteries.

Redox Reactions

Redox reactions, or oxidation-reduction reactions, involve the transfer of electrons between two chemical species. These reactions are central to energy generation in galvanic cells.

In a redox reaction:

• Oxidation is the loss of electrons, leading to an increase in oxidation state.
• Reduction is the gain of electrons, leading to a decrease in oxidation state.
• An oxidizing agent accepts electrons and gets reduced.
• A reducing agent donates electrons and gets oxidized.

Redox reactions are balanced by ensuring that the number of electrons lost and gained are equal, ensuring the conservation of charge.

Standard Reduction Potential

Standard reduction potential ( E^{ ext o} ) is a measure of the tendency of a chemical species to gain electrons in a redox reaction. It is measured in volts (V) and is determined under standard conditions, which include a concentration of 1 M, a pressure of 1 atm, and a temperature of 298 K.

Key points about standard reduction potential:

• A higher (more positive) value indicates a greater tendency to gain electrons and be reduced.
• A lower (more negative) value indicates a propensity to lose electrons and be oxidized.
• The standard hydrogen electrode (SHE) is used as a reference with a value of 0 V.

These potentials help predict the direction of electron flow in electrochemical cells and identify which substances will serve as anodes or cathodes.

Cell Potential

The cell potential, also known as electromotive force (emf), is the voltage developed by an electrochemical cell. It results from the difference in electrode potentials between the cathode and the anode.

The cell potential is calculated as:\[E_{ ext{cell}} = E_{ ext{cathode}} - E_{ ext{anode}}\]Where:

• E_{ ext{cell}} is the overall cell potential.
• E_{ ext{cathode}} is the reduction potential at the cathode.
• E_{ ext{anode}} is the reduction potential at the anode.

The value is positive for a spontaneous reaction, indicating the ability to do work. By understanding and calculating the cell potential, scientists can design batteries with desired voltage characteristics.

Anode and Cathode Identification

Identifying the anode and cathode within an electrochemical cell is crucial for understanding its operation:

• The anode in a galvanic cell is the electrode where oxidation occurs. It is characterized by a lower standard reduction potential, meaning it more readily gives up electrons.
• The cathode is the electrode where reduction occurs. It has a higher standard reduction potential, indicating a stronger desire to gain electrons.

For example, in a galvanic cell with copper ( Cu ) and tin ( Sn ):

• Copper, with a higher reduction potential ( +0.34 V), acts as the cathode.
• Tin, with a lower reduction potential ( -0.14 V), acts as the anode.

Correctly identifying these electrodes is essential for predicting the direction of electron flow and the changes in mass at the electrodes during the cell operation.