Question

Given \(\mathrm{A}^{+} / \mathrm{A} \longrightarrow+0.34 \mathrm{~V}\) \(\mathrm{B}^{+} / \mathrm{B} \longrightarrow-1.66 \mathrm{~V}\) \(\mathbf{C}^{+} ; \mathbf{C} \longrightarrow+0.76 \mathrm{~V}\) \(\mathrm{D}^{+} / \mathrm{D} \longrightarrow-0.28 \mathrm{~V}\) The most reactive metal which displaces other metals from their salt solution is (1) \(\mathrm{C}\) (2) D (3) \(\mathrm{B}\) (4) \(\Lambda\)

Short answer

The most reactive metal is B.

Step-by-step solution

Understand Reactivity Series

Reactivity series is determined by the standard electrode potential (E⁰) values. Metals with lower (more negative) E⁰ values are more reactive and can displace metals with higher (more positive) E⁰ values from their salt solutions.

List Electrode Potentials

Given the E⁰ values: \(\text{A}^{+}/\text{A} \rightarrow +0.34 \text{ V}\) \(\text{B}^{+}/\text{B} \rightarrow -1.66 \text{ V}\) \(\text{C}^{+}/\text{C} \rightarrow +0.76 \text{ V}\) \(\text{D}^{+}/\text{D} \rightarrow -0.28 \text{ V}\)

Identify Most Negative Potential

Compare the E⁰ values. The most reactive metal will have the most negative E⁰ value. Reviewing the values: +0.34 V (A), -1.66 V (B), +0.76 V (C), -0.28 V (D), it is clear that \(\text{B}^{+}/\text{B} \rightarrow -1.66 \text{ V}\) is the most negative.

Determine the Most Reactive Metal

Based on the comparison of electrode potentials, the metal with the most negative E⁰ value is B. Therefore, B is the most reactive metal and will displace other metals from their salt solutions.

Key concepts

Reactivity Series

The reactivity series is a critical concept in chemistry that ranks metals based on their ability to displace other metals from their compounds. It is determined by their standard electrode potentials (E⁰). Metals with lower (more negative) E⁰ values are considered more reactive. These metals can displace metals with higher (more positive) E⁰ values from their salt solutions. This means, if you have a metal with a very negative E⁰ value, it will trump a metal with a less negative E⁰ value in reactivity. Understanding the reactivity series helps predict how metals will behave during chemical reactions.

Standard Electrode Potential

Standard electrode potential (E⁰) is a measure of the tendency of a chemical species to be reduced, and it is measured under standard conditions (298 K, 1 M concentration, and 1 atm pressure). It is often represented in volts (V). Each metal has a unique E⁰ value that indicates how easily it can gain electrons compared to the standard hydrogen electrode, which is set at 0 V.
The more negative the E⁰ value, the higher the tendency to lose electrons (oxidize). Conversely, a less negative or more positive E⁰ value indicates a higher tendency to gain electrons (reduce). The given values in the exercise are:

• A: +0.34 V
• B: -1.66 V
• C: +0.76 V
• D: -0.28 V

From these values, you can infer the reactivity of each metal, with B having the most negative value indicating the highest reactivity.

Displacement Reactions

Displacement reactions are reactions where a more reactive metal displaces a less reactive metal from its compound. These reactions are common in aqueous solutions of metal salts. For example, if you add a piece of metal to a solution containing ions of a less reactive metal, the more reactive metal will displace the ions of the less reactive metal, forming a new compound and releasing the less reactive metal.
In the exercise, B (with an E⁰ of -1.66 V) is the most reactive. Thus, B can displace A, C, and D from their salt solutions due to its higher reactivity. This is because B has the highest tendency to lose electrons (most negative E⁰), which drives it to react more readily and take over the spot of less reactive metals.