Problem 78 - A Complete Resource Book in Chemistry for JEE Main

Question

The standard reduction potentials of \(\mathrm{Ag}, \mathrm{Cu}, \mathrm{Co}\) and \(\mathrm{Zn}\) are \(0.799,0.337,-0.277\) and \(-0.762 \mathrm{~V}\) respectively. Which of the following cells will have maximum cell emf? (a) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}(\mathrm{IM}) \| \mathrm{Cu}^{2+}(1 \mathrm{M})\right| \mathrm{Cu}\) (b) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}(\mathrm{IM}) \| \mathrm{Ag}^{+}(\mathrm{lM})\right| \mathrm{Ag}\) (c) \(\mathrm{Cu}\left|\mathrm{Cu}^{2+}(\mathrm{IM}) \| \mathrm{Ag}^{+}(\mathrm{IM})\right| \mathrm{Ag}\) (d) \(\mathrm{Zn}\left|\mathrm{Zn}^{2+}(\mathrm{IM}) \| \mathrm{Co}^{2+}(\mathrm{IM})\right| \mathrm{Co}\)

Step-by-Step Solution

Answer

Cell (b) has the maximum EMF of 1.561 V.

Step 1: Understand the Cell EMF Formula

The cell electromotive force (EMF) can be calculated using the formula: \( E_{cell} = E_{cathode} - E_{anode} \). The cathode is the electrode where reduction occurs and the anode is where oxidation occurs.

Step 2: Identify the Standard Reduction Potentials

List the given standard reduction potentials for each metal: \( E(Ag) = 0.799\,V \), \( E(Cu) = 0.337\,V \), \( E(Co) = -0.277\,V \), and \( E(Zn) = -0.762\,V \).

Step 3: Calculate EMF for Each Cell Option

For each cell, identify the anode and cathode and use the reduction potential values to find the EMF:- (a) \( E_{cell} = 0.337 - (-0.762) = 1.099 \) V- (b) \( E_{cell} = 0.799 - (-0.762) = 1.561 \) V- (c) \( E_{cell} = 0.799 - 0.337 = 0.462 \) V- (d) \( E_{cell} = -0.277 - (-0.762) = 0.485 \) V.

Step 4: Identify the Cell with Maximum EMF

Compare the calculated EMF values: 1.099 V, 1.561 V, 0.462 V, and 0.485 V. The cell with the maximum EMF is option (b) with 1.561 V.

Key Concepts

Standard Reduction Potential

The concept of Standard Reduction Potential is fundamental to understanding electrochemical cells. Each electrode in a voltaic cell has a standard reduction potential, which measures the tendency of a species to gain electrons and undergo reduction. This value is typically given in volts (V) and is measured under standard conditions, which include a concentration of 1 M, a pressure of 1 atm, and a temperature of 25°C. To compare different metals, we often use a standard hydrogen electrode (SHE) as a reference, which is arbitrarily assigned a potential of 0.00 V. Any positive potential indicates a greater tendency to gain electrons compared to hydrogen, while a negative potential means a lesser tendency. For example, in our problem, silver (Ag) with a potential of 0.799 V is more likely to be reduced compared to copper (Cu) with 0.337 V. These values help us identify which species can act as a cathode or anode in a cell.

Cell EMF

Cell electromotive force (EMF), often referred to as the cell potential, is a crucial measure that indicates the potential difference between the two electrodes of an electrochemical cell. This potential difference drives the flow of electrons through the external circuit and allows the cell to do work.The formula to calculate cell EMF is simple yet powerful:\[ E_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}} \]Here, the EMF of the cell is determined by subtracting the standard reduction potential of the anode from that of the cathode. The more positive the cell EMF, the greater the tendency for the redox reaction to occur spontaneously.When we solved the exercise, we calculated the EMF for each cell option using their respective standard reduction potentials. The cell with the highest EMF was identified as having the greatest ability to perform work or drive a reaction spontaneously.

Anode and Cathode Identification

In an electrochemical cell, correctly identifying the anode and cathode is vital, as it determines the direction of electron flow and the overall functioning of the cell. The cathode is the electrode where reduction occurs, meaning it gains electrons. Conversely, the anode is where oxidation takes place, thus losing electrons.To distinguish between anodes and cathodes, remember:

• The cathode has a higher standard reduction potential and attracts electrons.
• The anode has a lower standard reduction potential, indicating a stronger tendency to release electrons.

In practical terms, when given a list of standard reduction potentials, the species with the highest potential will typically serve as the cathode, and the one with the lower potential relative to it becomes the anode.For instance, in our exercise, for the cell \( \text{Zn} | \text{Zn}^{2+} || \text{Ag}^{+} | \text{Ag} \), silver (Ag) with the higher reduction potential of 0.799 V is the cathode, and zinc (Zn) with \(-0.762 \text{ V}\) serves as the anode. This distinction is fundamental to correctly calculating the cell's EMF and predicting the direction of the reaction.