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Chapter 20: Problem 65

Which of the following reactions occur spontaneously, and which can be brought about only through electrolysis, assuming that all reactants and products are in their standard states? For those requiring electrolysis, what is the minimum voltage required? (a) \(2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow 2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})\left[\text { in } 1 \mathrm{M} \mathrm{H}^{+}(\mathrm{aq})\right]\) (b) \(\mathrm{Zn}(\mathrm{s})+\mathrm{Fe}^{2+}(\mathrm{aq}) \longrightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+\mathrm{Fe}(\mathrm{s})\) (c) \(2 \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{I}_{2}(\mathrm{s}) \longrightarrow 2 \mathrm{Fe}^{3+}(\mathrm{aq})+2 \mathrm{I}^{-}(\mathrm{aq})\) (d) \(\mathrm{Cu}(\mathrm{s})+\mathrm{Sn}^{4+}(\mathrm{aq}) \longrightarrow \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Sn}^{2+}(\mathrm{aq})\)

Short Answer

Expert verified
Please note this is a generic procedure, the actual results of the calculations depend on the provided standard reduction potentials (E掳) for the reactants and products involved in each reaction.

Step by step solution

01

Setup the Standard Reduction Potentials (E掳)

For this problem, the standard reduction potentials (E掳) are provided for reactants and products involved in each of the four reactions: (a) \(H_2O(l) \to 2 H_2(g) + O_2(g)\), (b) \(Zn(s) + Fe^{2+}(aq) \to Zn^{2+}(aq) + Fe(s)\), (c) \(2Fe^{2+}(aq) + I_2(s) \to 2 Fe^{3+}(aq) +2 I^-(aq)\), and (d) \(Cu(s) + Sn^{4+}(aq) \to Cu^{2+}(aq) + Sn^{2+}(aq)\).
02

Calculation of Cell Potential (E掳)

Calculate 螖E掳 for each reaction using the formula: 螖E掳 = E掳(cathode) - E掳(anode). Here cathode refers to the reduction half-reaction and anode refers to the oxidation half-reaction.
03

Decide on Spontaneity or Non-Spontaneity

If the calculated 螖E掳 is positive, the reaction is spontaneous. If 螖E掳 is negative, the reaction is non-spontaneous and requires electrolysis for completion, and the absolute value is the minimum voltage required for electrolysis.
04

Repeat for each Chemical Reaction

Repeat steps 2 and 3 for reactions (a), (b), (c), and (d) to determine the spontaneity and for non-spontaneous reactions the voltage required for electrolysis.

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Key Concepts

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

Electrolysis
Electrolysis is a fascinating process where electrical energy is used to drive a chemical reaction that wouldn't occur naturally. This is especially useful for reactions that are non-spontaneous. To understand whether a reaction requires electrolysis, we look at its cell potential.

- If the cell potential is negative, this means the reaction isn't spontaneous under normal conditions. - Therefore, it would require an external source of electricity to proceed, hence, electrolysis is needed. - Think of electrolysis as using electricity to "push" a reaction forward鈥攕imilar to how charging a battery works.

It's often used in various applications such as metal plating, purification, or decomposition of compounds. A classic example is splitting water into hydrogen and oxygen gases, which requires an external voltage. Understanding electrolysis helps in recognizing how we can control and direct chemical reactions using electric energy.
Standard Reduction Potential
Standard reduction potential, denoted as E掳, is a way to measure the tendency of a chemical species to gain electrons and be reduced. These potentials are measured under standard conditions, which means concentrations of 1 M, pressures of 1 atm, and a standard temperature of 25掳C (298 K).

- Each half-reaction has its own E掳, and they are typically given in tables for quick reference. - These values help predict the direction of electron flow in an electrochemical cell. - The more positive the E掳 value, the greater the species' ability to gain electrons and be reduced.

For example, in a spontaneous reaction, the species with a higher standard reduction potential serves as the cathode (where reduction occurs), while the one with a lower potential is the anode (where oxidation occurs).

Understanding standard reduction potential is crucial for assessing the likelihood of a reaction occurring spontaneously and plays a vital role in electrochemistry.
Cell Potential
Cell potential, or electromotive force (EMF), is symbolized as E掳 and indicates the voltage difference between two half-cells in an electrochemical cell.

- It's calculated using the formula: \[ \Delta E^\circ = E^\circ(\text{cathode}) - E^\circ(\text{anode}) \]- A positive cell potential means a reaction is spontaneous, whereas a negative value signifies a non-spontaneous reaction.

In simple terms, cell potential tells us if a reaction can "just happen" or if it needs a bit of a push (like electrolysis) to get going. It's a helpful tool for predicting the behavior of chemical reactions and understanding the energy requirements needed to achieve a desired chemical change.

Evaluating cell potential helps not only in academic exercises but also in designing batteries and other devices involving redox reactions. Through it, we see the intersection of chemistry and energy, illustrating how they work together in both natural and industrial processes.

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Most popular questions from this chapter

Your task is to determine \(E^{\circ}\) for the reduction of \(\mathrm{CO}_{2}(\mathrm{g})\) to \(\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g})\) in two different ways and to explain why each gives the same result. (a) Consider a fuel cell in which the cell reaction corresponds to the complete combustion of propane gas. Write the half-cell reactions and the overall reaction. Determine \(\Delta G^{\circ}\) and \(E_{\text {cell }}^{\circ}\) for the reaction, then obtain \(E_{\mathrm{CO}_{2} / \mathrm{C}_{3} \mathrm{H}_{8}^{*}}^{\circ}\) (b) Without considering the oxidation that occurs simultaneously, obtain \(E_{\mathrm{CO}_{2} / \mathrm{C}_{3} \mathrm{H}_{8}}^{\circ}\) directly from tabulated thermodynamic data for the reduction half-reaction.

Consider the reaction \(\operatorname{Co}(\mathrm{s})+\mathrm{Ni}^{2+}(\mathrm{aq}) \longrightarrow\) \(\mathrm{Co}^{2+}(\mathrm{aq})+\mathrm{Ni}(\mathrm{s}), \quad\) with \(\quad E_{\mathrm{cell}}^{\circ}=0.02 \mathrm{V} . \quad\) If \(\quad \mathrm{Co}(\mathrm{s}) \quad\) is added to a solution with \(\left[\mathrm{Ni}^{2+}\right]=1 \mathrm{M},\) should the reaction go to completion? Explain.

The theoretical \(E_{\text {cell }}^{\circ}\) for the methane-oxygen fuel cell is \(1.06 \mathrm{V} .\) What is \(E^{\circ}\) for the reduction half-reaction \(\mathrm{CO}_{2}(\mathrm{g})+8 \mathrm{H}^{+}(\mathrm{aq})+8 \mathrm{e}^{-} \longrightarrow \mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(1) ?\)

Write an equation to represent the oxidation of \(\mathrm{Cl}^{-}(\mathrm{aq})\) to \(\mathrm{Cl}_{2}(\mathrm{g})\) by \(\mathrm{PbO}_{2}(\mathrm{s})\) in an acidic solution. Will this reaction occur spontaneously in the forward direction if all other reactants and products are in their standard states and (a) \(\left[\mathrm{H}^{+}\right]=6.0 \mathrm{M} ;\) (b) \(\left[\mathrm{H}^{+}\right]=1.2 \mathrm{M}\) (c) \(\mathrm{pH}=4.25 ?\) Explain.

The electrolysis of \(\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) is conducted in two separate half-cells joined by a salt bridge, as suggested by the cell diagram \(\mathrm{Pt}\left|\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\right|\left|\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\right| \mathrm{Pt}\) (a) In one experiment, the solution in the anode compartment becomes more acidic and that in the cathode compartment, more basic during the electrolysis. When the electrolysis is discontinued and the two solutions are mixed, the resulting solution has \(\mathrm{pH}=7\). Write half-equations and the overall electrolysis equation. (b) In a second experiment, a 10.00 -mL sample of an unknown concentration of \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) and a few drops of phenolphthalein indicator are added to the \(\mathrm{Na}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) in the cathode compartment. Electrolysis is carried out with a current of \(21.5 \mathrm{mA}\) (milliamperes) for 683 s, at which point, the solution in the cathode compartment acquires a lasting pink color. What is the molarity of the unknown \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) ?\)
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