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Chapter 20: Problem 99

Predict whether the following reactions will be spontaneous in acidic solution under standard conditions: (a) oxidation of \(\mathrm{Sn}\) to \(\mathrm{Sn}^{2+} b_{y} \mathrm{I}_{2}\) (to form IT), (b) reduction of \(\mathrm{Ni}^{2+}\) to \(\mathrm{Ni}\) by \(\mathrm{I}\) (to form \(\mathrm{I}_{2}\) ), (c) reduction of \(\mathrm{Ce}^{4+}\) to \(\mathrm{Ce}^{3+}\) by \(\mathrm{H}_{2} \mathrm{O}_{2}\), (d) reduction of \(\mathrm{Cu}^{2+}\) to \(\mathrm{Cuby} \mathrm{Sn}^{2+}\) (to form \(\mathrm{Sn}^{47}\) ).

Short Answer

Expert verified
The reactions under standard conditions for the given cases are as follows: (a) spontaneous, (b) not spontaneous, (c) spontaneous, and (d) likely to be spontaneous.

Step by step solution

01

(Reaction a: Sn to Sn虏鈦 by I鈧)

For this reaction, we have the following half-reactions: Oxidation: Sn -> Sn虏鈦 + 2e鈦 Reduction: I鈧 + 2e鈦 -> 2I鈦 Now we look up the standard reduction potentials (E掳) of these half-reactions: E掳 (Sn -> Sn虏鈦) = -0.14 V E掳 (I鈧 -> 2I鈦) = 0.54 V Add the two half-reactions and sum up the standard reduction potentials: Sn + I鈧 -> Sn虏鈦 + 2I鈦 E掳 (cell) = -0.14 V + 0.54 V = 0.40 V Since E掳 (cell) > 0, the reaction is spontaneous under standard conditions.
02

(Reaction b: Ni虏鈦 reduction to Ni by I鈧)

For this reaction, we have the following half-reactions: Oxidation: 2I鈦 -> I鈧 + 2e鈦 Reduction: Ni虏鈦 + 2e鈦 -> Ni Standard reduction potentials: E掳 (2I鈦 -> I鈧) = -0.54 V E掳 (Ni虏鈦 -> Ni) = -0.25 V Combine the two half-reactions and sum up the standard reduction potentials: 2I鈦 + Ni虏鈦 -> I鈧 + Ni E掳 (cell) = -0.54 V + (-0.25 V) = -0.79 V Since E掳 (cell) < 0, the reaction is not spontaneous under standard conditions.
03

(Reaction c: Ce鈦粹伜 reduction to Ce鲁鈦 by H鈧侽鈧)

Given half-reactions: Oxidation: H鈧侽鈧 -> O鈧 + 2e鈦 Reduction: Ce鈦粹伜 + e鈦 -> Ce鲁鈦 Standard reduction potentials: E掳 (H鈧侽鈧 -> O鈧) = 1.77 V E掳 (Ce鈦粹伜 -> Ce鲁鈦) = -1.72 V Combine the two half-reactions and sum up the standard reduction potentials: H鈧侽鈧 + Ce鈦粹伜 -> O鈧 + Ce鲁鈦 E掳 (cell) = 1.77 V + (-1.72 V) = 0.05 V Since E掳 (cell) > 0, the reaction is spontaneous under standard conditions.
04

(Reaction d: Cu虏鈦 reduction to Cu by Sn虏鈦)

Given half-reactions: Oxidation: Sn虏鈦 -> Sn鈦粹伔 + 2e鈦 Reduction: Cu虏鈦 + 2e鈦 -> Cu Standard reduction potentials: E掳 (Sn虏鈦 -> Sn鈦粹伔) = (?) E掳 (Cu虏鈦 -> Cu) = 0.34 V We don't have the standard reduction potential for Sn虏鈦 -> Sn鈦粹伔. However, we can use the fact that Sn oxidation to Sn虏鈦 is -0.14 V. This means that the oxidation of Sn虏鈦 to Sn鈦粹伔 will have a lower potential than that, making E掳 (Sn虏鈦 -> Sn鈦粹伔) < -0.14 V. Combined and approximate cell potential: Sn虏鈦 + Cu虏鈦 -> Sn鈦粹伔 + Cu E掳 (cell) 鈮 (-0.14 V) + 0.34 V = 0.20 V (approximate) Since E掳 (cell) > 0 (approximate), the reaction is likely to be spontaneous under standard conditions.

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Key Concepts

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

Standard Reduction Potential
In electrochemistry, the standard reduction potential, denoted as \(E^掳\), is a measure of the tendency of a chemical species to gain electrons and be reduced. Defined under standard conditions, \(E^掳\) is usually measured in volts and it provides valuable insights into the likelihood of a reaction occurring.

These potentials are determined by comparing the reduction process of a species with the standard hydrogen electrode (SHE), which has an assigned value of 0.00 V.

A positive \(E^掳\) indicates a strong tendency to be reduced, while a negative \(E^掳\) suggests a weaker tendency.
  • For example, a half-reaction with an \(E^掳\) of 0.54 V (e.g., \(I_2\) reducing to \(2I^-\)) is more likely to occur spontaneously compared to one with an \(E^掳\) of -0.14 V (e.g., Sn reducing to \(\text{Sn}^{2+}\)).
  • By summing the standard reduction potentials of the oxidation and reduction half-reactions in a redox reaction, we can determine the cell potential \(E^掳_{\text{cell}}\) and predict if the entire reaction is spontaneous.
Half-Reactions
Half-reactions are a crucial part of understanding the full flow of electrons in redox reactions. In such reactions, one species is oxidized and loses electrons, while another is reduced and gains electrons.

These half-reactions help to break down the complex redox processes into manageable parts, making them easier to analyze and understand.
  • The oxidation half-reaction describes the loss of electrons, such as \(\text{Sn} \rightarrow \text{Sn}^{2+} + 2e^-\).
  • The reduction half-reaction refers to the gain of electrons, for example, \(\text{I}_2 + 2e^- \rightarrow 2\text{I}^-\).
To determine if the overall redox reaction is spontaneous, we combine the standard reduction potentials of these half-reactions.

Summing them helps to compute the cell potential, thus giving hints on the spontaneity of the reaction.
Spontaneous Reaction
In the context of redox reactions, a spontaneous reaction is one that tends to occur on its own without any external influence. To determine the spontaneity, we rely on the calculated cell potential \(E^掳_{\text{cell}}\).

When examining reactions under standard conditions:
  • If \(E^掳_{\text{cell}} > 0\), the reaction is spontaneous; it naturally progresses from reactants to products.
  • In contrast, if \(E^掳_{\text{cell}} < 0\), the reaction is non-spontaneous and requires an external source of energy to proceed.
Consider the case of \(\text{Sn} + \text{I}_2 \rightarrow \text{Sn}^{2+} + 2\text{I}^-\), which has an \(E^掳_{\text{cell}}\) of 0.40 V, confirming that it can proceed spontaneously under standard conditions.

Understanding the conditions and calculations that lead to spontaneity is pivotal in electrochemistry, allowing predictions about reaction feasibility.

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Most popular questions from this chapter

The cell in Figure \(20.9\) could be used to provide a measure of the \(\mathrm{pH}\) in the cathode half-cell. Calculate the \(\mathrm{pH}\) of the cathode half-cell solution if the cell emf at \(298 \mathrm{~K}\) is measured to be \(+0.684 \mathrm{~V}\) when \(\left[\mathrm{Zn}^{2+}\right]=0.30 \mathrm{M}\) and \(P_{\mathrm{H}_{2}}=0.90 \mathrm{~atm}\).

A voltaic cell is constructed that is based on the following reaction: $$ \mathrm{Sn}^{2+}(a q)+\mathrm{Pb}(s) \longrightarrow \mathrm{Sn}(s)+\mathrm{Pb}^{2+}(a q) $$ (a) If the concentration of \(\mathrm{Sn}^{2+}\) in the cathode half-cell is \(1.00 \mathrm{M}\) and the cell generates an emf of \(+0.22 \mathrm{~V}\), what is the concentration of \(\mathrm{Pb}^{2+}\) in the anode half-cell? (b) If the anode half-cell contains \(\left[\mathrm{SO}_{4}{ }^{2-}\right]=1.00 \mathrm{M}\) in equilibrium with \(\mathrm{PbSO}_{4}(s)\), what is the \(K_{4 p}\) of \(\mathrm{PbSO}_{4}\) ? Batteries and Fuel Cells (Section 20.7)

Complete and balance the following equations, and identify the oxidizing and reducing agents. (Recall that the \(\mathrm{O}\) atoms in hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\), have an atypical oxidation state.) (a) \(\mathrm{NO}_{2}^{-}(a q)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{NO}_{3}^{-}(a q)\) (acidic solution) (b) \(\mathrm{S}(s)+\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{N}_{2} \mathrm{O}(g)\) (acidic solution) Exercises 901 (c) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{CH}_{3} \mathrm{OH}(a q) \longrightarrow \mathrm{HCO}_{2} \mathrm{H}(a q)+\) \(\mathrm{Cr}^{3+}(a q)\) (acidic solution) (d) \(\mathrm{BrO}_{3}{ }^{-}(a q)+\mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{Br}^{-}(a q)+\mathrm{N}_{2}(g)\) (acidic solution) (e) \(\mathrm{NO}_{2}{ }^{-}(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{AlO}_{2}{ }^{-}(a q)\) (basic solution) (f) \(\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{ClO}_{2}(a q) \longrightarrow \mathrm{ClO}_{2}^{-}(a q)+\mathrm{O}_{2}(g)\) (basic solution) Voltaic Cells (Section 20.3)

Consider a redox reaction for which \(E^{b}\) is a negative number. (a) What is the sign of \(\Delta G^{\text {e }}\) for the reaction? (b) Will the equilibrium constant for the reaction be larger or smaller than 1? (c) Can an electrochemical cell based on this reaction accomplish work on its surroundings? [Section 20.5]

(a) What does the term electromotive force mean? (b) What is the definition of the wolt? (c) What does the term cell potential mean?
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