Problem 115 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard oxidation potential \(E^{\circ}\) for the half reactions are as \(\mathrm{Zn} \longrightarrow \mathrm{Zn}^{2+}+2 \mathrm{e}^{-} ; E^{\circ}=+0.76 \mathrm{~V}\) \(\mathrm{Fe} \longrightarrow \mathrm{Fe}^{2+}+2 \mathrm{e} ; E^{\circ}=+0.41 \mathrm{~V}\) The emf for the cell reaction \(\mathrm{Fe}^{2+}+\mathrm{Zn} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Fe}\) is (a) \(+1.17 \mathrm{~V}\) (b) \(-0.35 \mathrm{~V}\) (c) \(+0.35 \mathrm{~V}\) (d) \(0.117 \mathrm{~V}\)

Step-by-Step Solution

Answer

The emf for the cell reaction is \(-0.35 \mathrm{~V}\).

Step 1: Identify the Oxidation and Reduction Half Reactions

For the given cell reaction, determine which species is oxidized and which is reduced. In the reaction \( \text{Fe}^{2+} + \text{Zn} \rightarrow \text{Zn}^{2+} + \text{Fe} \), \( \text{Zn} \) is oxidized to \( \text{Zn}^{2+} \), and \( \text{Fe}^{2+} \) is reduced to \( \text{Fe} \).

Step 2: Use Standard Reduction Potentials

The standard oxidation potential of \( \text{Zn} \rightarrow \text{Zn}^{2+} + 2e^- \) is given as \( +0.76 \text{ V} \). To obtain this reaction as a reduction, we need the negative of its oxidation potential: \( -0.76 \text{ V} \).The standard reduction potential for \( \text{Fe}^{2+} + 2e^- \rightarrow \text{Fe} \) is \( -0.41 \text{ V} \) since the given \( \text{Fe} \rightarrow \text{Fe}^{2+} + 2e^- \) has \( +0.41 \text{ V} \).

Step 3: Calculate the Electromotive Force (EMF)

The electromotive force (EMF) of the cell is given by the difference between the reduction potential of the cathode and the anode (\( E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}} \)). Here, \( E_{\text{cathode}} = -0.76 \text{ V} \) (Zn reduction) and \( E_{\text{anode}} = -0.41 \text{ V} \) (Fe reduction). The EMF becomes \( -0.76 \text{ V} - (-0.41 \text{ V}) = -0.76 \text{ V} + 0.41 \text{ V} = -0.35 \text{ V} \).

Key Concepts

Oxidation-Reduction Reactions

Oxidation-reduction, commonly known as redox reactions, are processes where electrons are transferred between chemical species. This transfer can often result in the change of oxidation states among the components of the reaction. Understanding these reactions is crucial in electrochemistry because they are the foundation of how energy is transferred in chemical cells.
In a redox reaction:

• One species, which loses electrons, undergoes oxidation. Consider the loss of electrons as the oxidation process – it's all about letting go!
• Another species gains these electrons in a process known as reduction. You can think of reduction as gaining something valuable, i.e., electrons.

In the example provided, zinc (Zn) undergoes oxidation as it releases electrons to form Zn²⁺. Meanwhile, iron (Fe²⁺) gains these electrons to form elemental Fe, demonstrating reduction.
These reactions occur simultaneously, with one species undergoing oxidation and the other reduction, like in a careful dance of energy transfer. This coordination is what underlies electrochemical cell function, driving the current flow.

Standard Electrode Potential

The standard electrode potential is a vital measurement in electrochemistry. It refers to the potential difference between the electrode and a standard hydrogen electrode under standard conditions (1 M concentration, 1 atmospheric pressure, and a temperature of 25°C).
An electrode potential can tell us:

• Whether a species is likely to be oxidized or reduced in a redox reaction, depending on its standard potential value compared to others.
• The tendency of a chemical species to gain or lose electrons – essentially, its eagerness for electrons.

When electrodes have a positive standard potential, they are more inclined to gain electrons, favoring reduction. Conversely, a negative standard potential suggests a propensity to lose electrons, favoring oxidation.
In the cell reaction example, zinc’s oxidation potential is +0.76 V. It is given in its oxidized form, signifying it is likely to release electrons. The standard reduction potentials are essential for figuring out the cell's behavior and calculating EMF.

Electromotive Force (EMF) Calculation

Electromotive Force (EMF), often called cell potential, is the measure of energy provided by a battery or cell to move electrons through an external circuit. The EMF can be calculated using standard electrode potentials. This calculation helps determine how effectively a cell can do work.
To calculate EMF:

• Identify the cathode (where reduction occurs) and anode (where oxidation occurs) in the cell's reaction.
• Use the standard reduction potentials to find the difference. EMF is calculated using the formula:
  \[ E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}} \]

In our example, the reduction occurs at Zn with a potential of -0.76 V (as it is reversed from its oxidation potential), and oxidation at Fe with our given reduction potential of -0.41 V. The formula gives:
\[ E_{\text{cell}} = -0.76\, \text{V} - (-0.41\, \text{V}) = -0.35\, \text{V} \]
This negative EMF value suggests that under standard conditions, this cell would not spontaneously produce an electric current. Understanding EMF calculations is integral to designing efficient electrochemical cells.