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Chapter 19: Problem 61

Use tabulated electrode potentials to calculate Grxn for each reaction at 25 C. a. Pb2+(aq) + Mg(s)-Pb(s) + Mg2+(aq) b. Br2(l) + 2 Cl-(aq)-2 Br-(aq) + Cl2(g) c. MnO2(s) + 4 H+(aq) + Cu(s)-Mn2+(aq) + 2 H2O(l) + Cu2+(aq)

Short Answer

Expert verified
For each reaction, identify the reduction and oxidation half-reactions, look up their standard electrode potentials, calculate the cell potential, and then use the Gibbs free energy formula to determine ΔG° for the reaction at 25°C.

Step by step solution

01

Identify the Half-Reactions

For each reaction, we first split them into oxidation and reduction half-reactions. For reaction (a) the half-reactions are: Oxidation, Mg(s) → Mg2+(aq) + 2e−, and Reduction, Pb2+(aq) + 2e− → Pb(s). For reaction (b): Oxidation, 2Cl−(aq) → Cl2(g) + 2e−, and Reduction, Br2(l) + 2e− → 2Br−(aq). For reaction (c): Oxidation, Cu(s) → Cu2+(aq) + 2e−, and Reduction, MnO2(s) + 4H+(aq) + 2e− → Mn2+(aq) + 2H2O(l).
02

Look up Standard Electrode Potentials

Using standard electrode potential tables, find the standard potentials for all half-reactions at 25°C. For example, for Mg2+/Mg, and Pb2+/Pb, locate the corresponding standard reduction potentials.
03

Write the Standard Electrode Potentials

Record the standard reduction potential for each half-reaction. Ensure the potentials align correctly with oxidation or reduction (reduction potentials may need to be reversed for oxidation reactions).
04

Calculate Cell Potential

The standard electromotive force (EMF) of the cell, E°cell, is calculated by: E°cell = E°cathode - E°anode, where E°cathode is the reduction potential of the cathode and E°anode is the oxidation potential (reversed reduction potential) of the anode.
05

Calculate the Gibbs Free Energy Change

Use the formula ΔG° = -nFE°cell to calculate the Gibbs free energy change, where ΔG° is the change in Gibbs free energy, n is the number of moles of electrons transferred in the balanced equation, F is Faraday's constant (96,485 C/mol e−), and E°cell is the standard cell potential.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electrochemistry
Electrochemistry is the branch of chemistry that studies the relationship between electricity and chemical reactions. Specifically, it focuses on reactions where the transfer of electrons occurs, known as redox reactions. These reactions are essential in various applications, including batteries, electroplating, and electrolysis. An electrochemical cell is a device that can either generate electrical energy from chemical reactions or use electrical energy to cause chemical changes.
Gibbs Free Energy
Gibbs free energy, represented by the symbol \( \Delta G \), is a thermodynamic quantity that predicts the direction of chemical reactions and determines if a process is spontaneous at constant pressure and temperature. A negative \( \Delta G \) value indicates a spontaneous reaction, while a positive value suggests non-spontaneity. In the context of electrochemistry, the Gibbs free energy is related to the cell potential through the equation \( \Delta G = -nFE \), which helps us to understand the feasibility of electrochemical reactions.
Cell Potential
Cell potential, denoted as \( E^{\circ}_{\text{cell}} \), is the measure of the electrical difference between the two electrodes of a galvanic (voltaic) cell. It determines the electromotive force (EMF) generated by the total reaction in the cell. The greater the cell potential, the greater the cell's ability to do electrical work. Cell potential is vital for calculating the amount of electrical energy that can be obtained from a chemical reaction.
Redox Reactions
Redox reactions, or oxidation-reduction reactions, involve the transfer of electrons between two substances. Oxidation refers to the loss of electrons, while reduction describes the gain of electrons. In a balanced redox reaction, the total number of electrons lost is equal to the total number of electrons gained. Being able to identify and split a reaction into its respective half-reactions is crucial in understanding how electrochemical cells, such as batteries, operate.
Standard Reduction Potential
The standard reduction potential is an intrinsic chemical property that measures the tendency of a chemical species to acquire electrons and be reduced. It is measured under standard conditions (25°C, 1 M concentration, and 1 atm pressure) and is represented by \( E^{\circ} \). The standard electrode potential helps us determine the direction of electron flow in an electrochemical cell and is used to calculate \( E^{\circ}_{\text{cell}} \) by the difference between the cathode and anode potentials. When using these potentials, it's essential to reverse the sign for the anode (oxidation half-reaction) before performing the subtraction to obtain the correct cell potential.

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Most popular questions from this chapter

Make a sketch of a concentration cell employing two Zn>Zn2+ halfcells. The concentration of Zn2+ in one of the half-cells is 2.0 M, and the concentration in the other half-cell is 1.0 * 10-3 M. Label the anode and the cathode and indicate the half-reaction occurring at each electrode. Also indicate the direction of electron flow.

What voltage can theoretically be achieved in a battery in which lithium metal is oxidized and fluorine gas is reduced? Why might such a battery be difficult to produce?

Use tabulated electrode potentials to calculate Grxn for each reaction at 25 C. a. 2 Fe3+(aq) + 3 Sn(s)-2 Fe(s) + 3 Sn2+(aq) b. O2(g) + 2 H2O(l) + 2 Cu(s)-4 OH-(aq) + 2 Cu2+(aq) c. Br2(l) + 2 I-(aq)-2 Br-(aq) + I2(s)

Balance each redox reaction occurring in basic aqueous solution. a. H2O2(aq) + ClO2(aq)-ClO2-(aq) + O2(g) b. Al(s) + MnO4-(aq)-MnO2(s) + Al(OH)4-(aq) c. Cl2(g)-Cl-(aq) + ClO-(aq)

Explain the difference between a voltaic (or galvanic) electro-chemical cell and an electrolytic one.
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