Question

Based on the following reactions, arrange the metals in increasing order of their reduction potentials. $$ \mathbf{Z n}+\mathbf{C u}^{2+} \rightarrow \mathbf{Z n}^{2+}+\mathrm{Cu} ; $$ \(\mathrm{Mg}+\mathrm{Zn}^{2+} \rightarrow \mathrm{Mg}^{2+}+\mathrm{Zn}\) \(\mathrm{Cu}+2 \mathrm{Ag}^{+} \rightarrow \mathrm{Cu}^{2+}+2 \mathrm{Ag}\) (a) \(\quad \mathrm{Mg}>\mathrm{Zn}>\mathrm{Cu}>\mathrm{Ag}\) (b) \(\mathrm{Mg}<\mathrm{Zn}<\mathrm{Cu}<\mathrm{Ag}\) (d) \(\quad \mathrm{Mg}>\mathrm{Cu}>\mathrm{Zn}>\mathrm{Ag}\) (c) \(\quad \mathrm{Zn}<\mathrm{Cu}<\mathrm{Ag}<\mathrm{Mg}\)

Short answer

The correct order of metals in increasing order of their reduction potentials is \(\mathrm{Mg} < \mathrm{Zn} < \mathrm{Cu} < \mathrm{Ag}\), which corresponds to option (b).

Step-by-step solution

Analyze the Chemical Reactions

To order metals by their reduction potentials, we look at the given chemical reactions and determine which way the electron transfer goes. A metal that loses electrons (oxidized) has a lower reduction potential than the metal that gains electrons (reduced).

Deduce the Relative Reduction Potentials

From the first reaction, Zn is oxidized, and Cu is reduced, which means Zn has a lower reduction potential than Cu. From the second reaction, Mg is oxidized, and Zn is reduced, which means Mg has a lower reduction potential than Zn. From the third reaction, Cu is oxidized, and Ag is reduced, which means Cu has a lower reduction potential than Ag.

Arrange Metals in Increasing Order of Reduction Potentials

Based on the reactions, the order of increasing reduction potentials is Mg, Zn, Cu, Ag. A metal with a higher reduction potential gets reduced by a metal with a lower reduction potential.

Key concepts

Electrochemical Series

Understanding the electrochemical series is essential when studying the behavior of different metals in redox reactions. This series is a list that ranks elements according to their standard reduction potentials. The higher an element is on this series, the greater is its ability to gain electrons, and hence, its reactivity as an oxidizing agent increases. In other words, elements at the top of the electrochemical series are the best at gaining electrons, thereby being readily reduced.

In the context of educational textbook exercises, recognizing where metals stand within the electrochemical series is crucial, as it can predict the direction of electron flow in a reaction. For instance, in a provided exercise, if Zinc (Zn) is able to be oxidized by Copper (Cu), this implies that Copper stands higher than Zinc in the electrochemical series.

Redox Reactions

Redox reactions are a type of chemical reaction that involves the transfer of electrons between two species. These reactions are the foundation of many processes in chemistry, biology, and technology, including electrochemistry. In a redox reaction, one substance gets reduced. This means it gains electrons and typically reduces its oxidation state. Conversely, another substance is oxidized—it loses electrons and often has an increased oxidation state.

An everyday example to illustrate redox reactions can be found in battery operation, where redox reactions are harnessed to generate electrical energy. Each metal's tendency to lose or gain electrons in such reactions can be predicted by its standard reduction potential, another critical concept for students to grasp.

Standard Reduction Potential

Every metal has a characteristic value known as the standard reduction potential. This value is measured under standard conditions (1 M concentration, a pressure of 1 atm, and a temperature of 25 degrees Celsius) and it indicates the tendency of a species to gain electrons and thereby get reduced. A positive standard reduction potential signifies a strong ability to be reduced, while a negative value suggests a greater tendency to lose electrons and be oxidized.

When facing the challenge of ranking metals by their reduction potentials, like in the exercise provided, one should analyze the direction in which the redox reactions spontaneously proceed. This is determined by the relative standard reduction potentials of the involved species, resulting in an arrangement from the weakest to the strongest reducing agents. This concept is integral to predicting the spontaneity and directionality of redox reactions in chemistry.

Chemical Reactivity of Metals

Chemical reactivity of metals is influenced by several factors, including their position in the electrochemical series and their standard reduction potentials. Metals that have low reduction potentials are more reactive in terms of losing electrons and are often used as reducing agents. Metals with high reduction potential, on the other hand, are less inclined to give up electrons and are typically seen reacting as oxidizing agents.

Understanding the reactivity is particularly important when predicting reaction outcomes, such as in displacement reactions, where one metal displaces another from a compound. For students, it's vital to recognize that a metal's position in the reactivity series not only influences its behavior in individual reactions but also has broader implications in topics like corrosion, metal extraction, and electroplating.