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Chapter 18: Problem 9

You are told that metal \(\mathrm{A}\) is a better reducing agent than metal B. What, if anything, can be said about \(\mathrm{A}^{+}\) and \(\mathrm{B}^{+}\) ? Explain.

Short Answer

Expert verified
In conclusion, since metal A is a better reducing agent than metal B, this implies that A has a more negative standard reduction potential than B. Therefore, A⁺ will have a less positive (or more negative) standard reduction potential than B⁺. Consequently, B⁺ is a stronger oxidizing agent than A⁺, meaning it will tend to gain electrons more readily than A⁺.

Step by step solution

01

Understanding reducing agents

A reducing agent is a substance that donates electrons in a redox reaction, thereby causing the other substance to be reduced. In our case, metal A and metal B act as reducing agents.
02

Relating reducing agents to reduction potentials

The standard reduction potential is a measure of the tendency of a chemical species to be reduced. A more negative standard reduction potential indicates that a species is more likely to donate electrons (thus, it is a better reducing agent). Conversely, a more positive standard reduction potential indicates that a species is less likely to donate electrons (thus, it is a less effective reducing agent).
03

Comparing the reduction potentials of A⁺ and B⁺

Since metal A is a better reducing agent than metal B, we can deduce that A has a more negative standard reduction potential than B. This means that A is more likely to donate electrons than B. Now, we need to analyze the relationship between the standard reduction potentials of the metal ions A⁺ and B⁺.
04

Relationship between metal ions and their standard reduction potentials

When a metal is oxidized to its ionic form (A → A⁺ + e⁻ or B → B⁺ + e⁻), its standard reduction potential becomes more positive. Therefore, in this case, the standard reduction potentials of A⁺ and B⁺ are the reverse of their metallic forms (A and B).
05

Comparing A⁺ and B⁺ based on their reducing nature

Since metal A is a better reducing agent and has a more negative standard reduction potential than metal B, it means that A⁺ will have a less positive (or more negative) standard reduction potential than B⁺. Therefore, we can conclude that B⁺ is a stronger oxidizing agent compared to A⁺. A stronger oxidizing agent will have a greater tendency to be reduced, i.e., it will tend to gain electrons more readily than a weaker oxidizing agent. In conclusion, since metal A is a better reducing agent than metal B, B⁺ is a stronger oxidizing agent than A⁺.

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Most popular questions from this chapter

The equation \(\Delta G^{\circ}=-\mathrm{nF} \mathscr{E}^{\circ}\) also can be applied to half-reactions. Use standard reduction potentials to estimate \(\Delta G_{\mathrm{f}}^{\circ}\) for \(\mathrm{Fe}^{2+}(a q)\) and $\mathrm{Fe}^{3+}(a q) .\left(\Delta G_{\mathrm{f}}^{\circ} \text { for } \mathrm{e}^{-}=0 .\right)$

A factory wants to produce \(1.00 \times 10^{3}\) kg barium from the electrolysis of molten barium chloride. What current must be applied for 4.00 \(\mathrm{h}\) to accomplish this?

An aqueous solution of an unknown salt of ruthenium is electrolyzed by a current of 2.50 A passing for 50.0 min. If 2.618 g Ru is produced at the cathode, what is the charge on the ruthenium ions in solution?

A standard galvanic cell is constructed so that the overall cell reaction is $$2 \mathrm{Al}^{3+}(a q)+3 \mathrm{M}(s) \longrightarrow 3 \mathrm{M}^{2+}(a q)+2 \mathrm{Al}(s)$$ where \(\mathrm{M}\) is an unknown metal. If \(\Delta G^{\circ}=-411 \mathrm{kJ}\) for the overall cell reaction, identify the metal used to construct the standard cell.

The black silver sulfide discoloration of silverware can be removed by heating the silver article in a sodium carbonate solution in an aluminum pan. The reaction is $$3 \mathrm{Ag}_{2} \mathrm{S}(s)+2 \mathrm{Al}(s) \rightleftharpoons 6 \mathrm{Ag}(s)+3 \mathrm{S}^{2-}(a q)+2 \mathrm{Al}^{3+}(a q)$$ a. Using data in Appendix \(4,\) calculate \(\Delta G^{\circ}, K,\) and \(\mathscr{E}^{\circ}\) for the above reaction at $25^{\circ} \mathrm{C} .\left[\text { For } \mathrm{Al}^{3+}(a q), \Delta G_{\mathrm{f}}^{\circ}=-480 . \mathrm{kJ} / \mathrm{mol.}\right]$ b. Calculate the value of the standard reduction potential for the following half-reaction: $$2 \mathrm{e}^{-}+\mathrm{Ag}_{2} \mathrm{S}(s) \longrightarrow 2 \mathrm{Ag}(s)+\mathrm{S}^{2-}(a q)$$
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