Problem 162 - A Complete Resource Book in Chemistry for JEE Main

Question

The electrochemical series is the arrangement of various electrode systems in the increasing order of their standard reduction potentials. It has several important features. On moving from the top to the bottom in the series, tendency to gain electrons, i.e., to get reduced increases. The electrode systems having negative values of standard reduction potentials act as anode when connected to a standard hydrogen electrode, while those having positive values act as cathode. If \(E_{\mathrm{cu}^{2}}^{0}{\underline{\phantom{xx}}}_{\mathrm{Cu}}=0.34 \mathrm{~V}\) and \(E_{\mathrm{Ag}^{+} / \Lambda g}^{0}=0.8 \mathrm{~V}\), predict whether the reaction given below is feasible or not ? $$ \mathrm{Cu}^{2}+(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s}) \longrightarrow \mathrm{Cu}(\mathrm{s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) $$ (a) Not feasible (b) Feasible (c) Feasible on increasing the conc. of \(\mathrm{Ag}^{+}(\mathrm{aq}) .\) (d) easible at high temp.

Step-by-Step Solution

Answer

(a) Not feasible. The standard cell potential is negative, indicating non-spontaneity.

Step 1: Identify the Electrode Reactions

The overall reaction given is : \( \mathrm{Cu}^{2+}(\mathrm{aq}) + 2 \mathrm{Ag}(\mathrm{s}) \rightarrow \mathrm{Cu}(\mathrm{s}) + 2 \mathrm{Ag}^{+}(\mathrm{aq}) \). We first need to break this down into two half-cell reactions. The oxidation half-reaction is: \( 2 \mathrm{Ag}(\mathrm{s}) \rightarrow 2 \mathrm{Ag}^{+}(\mathrm{aq}) + 2e^- \). The reduction half-reaction is: \( \mathrm{Cu}^{2+}(\mathrm{aq}) + 2e^- \rightarrow \mathrm{Cu}(\mathrm{s}) \).

Step 2: Write Standard Reduction Potentials

Identify the standard reduction potentials for each half-reaction: \( E^{0}_{\mathrm{Ag}^{+}/\mathrm{Ag}} = 0.8 \mathrm{~V} \) and \( E^{0}_{\mathrm{Cu}^{2+}/\mathrm{Cu}} = 0.34 \mathrm{~V} \).

Step 3: Determine Reaction Feasibility

Calculate the standard cell potential \( E^{0}_{cell} \) to determine if the reaction is feasible. The balance gives: \( E^{0}_{cell} = E_{ ext{cathode}}^{0} - E_{ ext{anode}}^{0} = E_{\mathrm{Cu}^{2+}/\mathrm{Cu}}^{0} - E_{\mathrm{Ag}^{+}/\mathrm{Ag}}^{0} = 0.34 \mathrm{~V} - 0.8 \mathrm{~V} = -0.46 \mathrm{~V} \). A negative \( E^{0}_{cell} \) indicates the reaction is non-spontaneous.

Step 4: Verify Reaction Conclusion

Since the calculated standard cell potential \( E^{0}_{cell} \) is negative, the reaction is not feasible under standard conditions based on feasibility criteria of electrochemical cells.

Key Concepts

Standard Reduction Potential

The standard reduction potential is a crucial concept in electrochemistry. It refers to the potential difference, measured in volts, of an electrode reaction under standard conditions. These conditions typically include a temperature of 25°C, a 1 mol/L concentration for all aqueous species, and a pressure of 1 atm for gases. This potential is measured relative to the standard hydrogen electrode, which is assigned a potential of 0.00 V.A more positive standard reduction potential means a greater tendency for the species to gain electrons (reduced). Conversely, a more negative value indicates a tendency to lose electrons (oxidized). For instance, silver ions \( \left( E^0_{\mathrm{Ag}^+/\mathrm{Ag}} = 0.80 \ \mathrm{V} \right) \) have a higher standard reduction potential than copper ions \( \left( E^0_{\mathrm{Cu}^{2+}/\mathrm{Cu}} = 0.34 \ \mathrm{V} \right) \), implying that silver is more readily reduced than copper in an electrochemical cell.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, involve the transfer of electrons between chemical species. In these reactions, one substance loses electrons (oxidized) while another gains electrons (reduced). These processes often form the basis for electrochemical reactions, where electron transfer leads to electrical energy production or consumption. In an electrochemical cell, the oxidizing agent receives electrons at the cathode, while the reducing agent donates electrons at the anode. For example, in the reaction \( \mathrm{Cu}^{2+}(\mathrm{aq}) + 2 \mathrm{Ag}(\mathrm{s}) \rightarrow \mathrm{Cu}(\mathrm{s}) + 2 \mathrm{Ag}^+(\mathrm{aq}) \), silver is oxidized to silver ions, losing electrons, while copper ions are reduced to copper metal, gaining electrons. Understanding which species undergoes oxidation and which undergoes reduction is central to predicting the direction and feasibility of reactions in electrochemical series.

Cell Potential Calculation

Cell potential calculation is an essential part of analyzing electrochemical cells. The cell potential, indicated as \( E^0_{\text{cell}} \), is the difference between the standard reduction potentials of the cathode and the anode. The formula generally used is: \[ E^0_{\text{cell}} = E^0_{\text{cathode}} - E^0_{\text{anode}} \] This calculation determines the overall voltage or emf (electromotive force) of the cell under standard conditions. A positive \( E^0_{\text{cell}} \) indicates a spontaneous reaction, meaning the cell can function and produce electricity. Conversely, a negative value suggests a non-spontaneous reaction.In the given exercise, the cell potential was calculated as: \( E^0_{\text{cell}} = 0.34 \ \mathrm{V} - 0.80 \ \mathrm{V} = -0.46 \ \mathrm{V} \). Such a negative result implies that the reaction is not feasible under standard conditions, as the spontaneous direction of the reaction does not match the given sequence of electron flow.