Question

The correct order of \(E_{M^{2+} / M}^{0}\) values with negative sign for the four successive elements \(\mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe}\) and \(\mathrm{Co}\) is \([2010]\) (a) \(\mathrm{Mn}>\mathrm{Cr}>\mathrm{Fe}>\mathrm{Co}\) (b) \(\mathrm{Cr}>\mathrm{Fe}>\mathrm{Mn}>\mathrm{Co}\) (c) \(\mathrm{Fe}>\mathrm{Mn}>\mathrm{Cr}>\mathrm{Co}\) (d) \(\mathrm{Cr}>\mathrm{Mn}>\mathrm{Fe}>\mathrm{Co}\)

Short answer

The correct order is (a) \(\mathrm{Mn} > \mathrm{Cr} > \mathrm{Fe} > \mathrm{Co}\).

Step-by-step solution

Understand Standard Electrode Potential

The standard electrode potential, denoted as \(E_{M^{2+} / M}^{0}\), indicates the ease with which an element can be oxidized or reduced. A more negative value means the element is more easily oxidized and prefers to stay in its elemental form rather than in the ionic form.

Recall Standard Electrode Potential Values

Generally, for these elements, the standard electrode potential values are known (or found from tables) as follows: \(E_{Cr^{2+/Cr}}^{0} = -0.91\,\text{V}\), \(E_{Mn^{2+/Mn}}^{0} = -1.18\,\text{V}\), \(E_{Fe^{2+/Fe}}^{0} = -0.44\,\text{V}\), and \(E_{Co^{2+/Co}}^{0} = -0.28\,\text{V}\).

Organize Elements in Order of Increasing Potential

Arrange the elements based on increasing standard reduction potentials (from more negative to less negative): \(Mn > Cr > Fe > Co\). Since we are dealing with negative values, an increasingly negative value indicates a decrease.

Match with Given Options

Compare the arranged order of \(Mn > Cr > Fe > Co\) with the given options to find the correct match. It corresponds to option (a).

Key concepts

Oxidation and Reduction

In chemistry, oxidation and reduction are processes that describe the loss and gain of electrons, respectively. These reactions occur simultaneously in what are called redox reactions. Understanding redox reactions is crucial as they are fundamental to many processes in chemistry, including those in electrochemistry.
In a redox reaction, the substance that loses electrons is said to be oxidized, while the substance that gains electrons is reduced. It's helpful to remember the mnemonic "OIL RIG," which stands for "Oxidation Is Loss" (of electrons) and "Reduction Is Gain" (of electrons).
The standard electrode potential ( E_0 ) helps to predict whether a substance will undergo oxidation or reduction. When the E_0 value is more negative, it indicates a greater tendency to lose electrons and undergo oxidation. Conversely, a less negative or more positive value suggests a tendency toward reduction. This is why manganse ( Mn ) with a high negative potential value tends to remain in its metallic form, while cobalt ( Co ) with a lower negative potential is less reluctant to be reduced to its metallic form.

Transition Metals

Transition metals are elements that have partially filled d orbitals. They are located in the central block of the periodic table and include metals like chromium ( Cr ), manganese ( Mn ), iron ( Fe ), and cobalt ( Co ). These metals exhibit unique properties due to their electron configurations and are known for:

• High conductivity of electricity and heat
• Diverse oxidation states, allowing them to form complex compounds
• Often catalytic properties in reactions, speeding up chemical processes

These metals show varying standard electrode potentials, influencing their behavior in oxidation and reduction reactions. For example, transition metals can easily switch between oxidation states due to their d electrons, a feature leveraged in many industrial and biological applications.
In redox reactions, understanding the behavior of transition metals is essential. In the context of our problem, knowing the standard electrode potentials of these metals is critical for determining which metals are more inclined to lose or gain electrons. This forms the basis for predicting the direction of these redox reactions.

Electrochemistry

Electrochemistry is the branch of chemistry that explores the relationship between electrical energy and chemical changes. It's essential in understanding phenomena such as standard electrode potential and its application in various devices, including batteries and fuel cells.
The core concept of electrochemistry revolves around redox reactions, where electrons move from one element to another. This electron transfer can be harnessed to produce electrical energy in electrochemical cells.

• Galvanic Cells: These convert chemical energy into electrical energy, with electron flow from the anode to the cathode.
• Electrolytic Cells: These use electrical energy to drive a chemical reaction.

Standard electrode potential ( E_0 ) is a crucial factor in electrochemistry, providing insight into an element's propensity to be oxidized or reduced. By comparing potential values, we can determine which metals act as better anodes or cathodes in these reactions. In the given exercise, it's a critical tool for understanding how these transition metals behave electrochemically, helping to design better galvanic cell systems.