Problem 104 - A Complete Resource Book in Chemistry for JEE Main

Question

Two electrochemical cells \(\mathrm{Zn}\left|\mathrm{Zn}^{2+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) and \(\mathrm{Fe}\left|\mathrm{Fe}^{2+} \| \mathrm{Cu}^{2+}\right| \mathrm{Cu}\) are con- nected in series. What will be the net emf of the cell at \(25^{\circ} \mathrm{C} ?\) Given: \(\mathrm{Zn}^{2+} \mid \mathrm{Zn}=-0.73 \mathrm{~V}\), \(\mathrm{Cu}^{2+} \mid \mathrm{Cu}=+0.34 \mathrm{~V}\) \(\mathrm{Fe}^{2+} \mid \mathrm{Fe}=-0.41 \mathrm{~V}\) (a) \(+1.85\) (b) \(-1.85 \mathrm{~V}\) (c) \(+0.83 \mathrm{~V}\) (d) \(-0.83 \mathrm{~V}\)

Step-by-Step Solution

Answer

The net EMF is 1.82 V; recalibrate options for fit.

Step 1: Calculate the EMF of the Zn-Cu Cell

The Zn-Cu cell can be represented as: \( \text{Zn} \mid \text{Zn}^{2+} \parallel \text{Cu}^{2+} \mid \text{Cu} \). The EMF for this cell is calculated using the standard electrode potentials: \( E_{cell, Zn-Cu} = E^\circ(\text{Cu}^{2+} \mid \text{Cu}) - E^\circ(\text{Zn}^{2+} \mid \text{Zn}) = 0.34 \text{ V} - (-0.73 \text{ V}) = 0.34 \text{ V} + 0.73 \text{ V} = 1.07 \text{ V} \).

Step 2: Calculate the EMF of the Fe-Cu Cell

The Fe-Cu cell can be represented as: \( \text{Fe} \mid \text{Fe}^{2+} \parallel \text{Cu}^{2+} \mid \text{Cu} \). The EMF for this cell is calculated using the standard electrode potentials: \( E_{cell, Fe-Cu} = E^\circ(\text{Cu}^{2+} \mid \text{Cu}) - E^\circ(\text{Fe}^{2+} \mid \text{Fe}) = 0.34 \text{ V} - (-0.41 \text{ V}) = 0.34 \text{ V} + 0.41 \text{ V} = 0.75 \text{ V} \).

Step 3: Calculate the Net EMF of Both Cells in Series

When the two electrochemical cells are connected in series, their EMFs add up algebraically. Thus, the net EMF of the connected series is: \( E_{net} = E_{cell, Zn-Cu} + E_{cell, Fe-Cu} = 1.07 \text{ V} + 0.75 \text{ V} = 1.82 \text{ V} \).

Step 4: Match With Provided Options

The calculated net EMF is \(1.82\text{ V}\), however, none of the options directly match this value. Re-evaluate the EMF calculation or selection, there might need further exploration on the assumption taken, such as considering any misinterpretation in series connection properties or data provided. Check the final assumptions before concluding.

Key Concepts

EMF calculation

Electromotive force (EMF), also known as the cell potential, is a critical concept when studying electrochemical cells. It signifies the voltage generated by a cell when no current flows through it, essentially representing the cell's maximum electric potential output. To calculate EMF, one must refer to the standard electrode potentials of the electrodes involved.
For a galvanic cell, EMF can be determined by using the formula:\[E_{cell} = E^{0}( ext{cathode}) - E^{0}( ext{anode})\]

• The term \(E^{0}( ext{cathode})\) represents the reduction potential at the cathode.
• The term \(E^{0}( ext{anode})\) refers to the reduction potential at the anode, which is often taken as negative because oxidation occurs at the anode.

In the original exercise, the EMF of both the Zn-Cu and Fe-Cu cells is calculated using their standard electrode potentials. This is how we ensure accuracy in determining their respective voltages and subsequently solving for the net EMF in series connection.

standard electrode potentials

Standard electrode potentials are essential in understanding the direction and magnitude of electron flow in electrochemical cells. These potentials are measured under standard conditions (25°C, 1M concentrations, and 1 atm pressure) and denote an electrode's tendency to gain or lose electrons relative to hydrogen, which has an assigned potential of 0.00 V.
In the realm of measuring potentials:

• Reduction potentials indicate an electrode's affinity for electrons — a higher value means a greater ability to gain electrons.
• Oxidation occurs when electrons are lost; therefore, these values are typically negative.

The potentials provided in the exercise (for \( ext{Zn}^{2+}/ ext{Zn}, ext{Cu}^{2+}/ ext{Cu}, ext{Fe}^{2+}/ ext{Fe}\)) are applied to determine the overall cell potential. These values are always used with respect to the more general reduction potential table to ascertain cell voltage and operative conditions.

series connection of cells

When connecting electrochemical cells in series, their individual EMFs contribute linearly to create a cumulative net EMF. This means that the voltages of the respective cells are summed to establish the combined potential of the series.
For the cells in the original exercise:

• The individual cell EMFs for the Zn-Cu and Fe-Cu were calculated as 1.07 V and 0.75 V, respectively.
• The net EMF is simply the arithmetic sum: 1.07 V + 0.75 V = 1.82 V.

Connecting cells in series is comparable to stacking batteries; each cell adds a layer of potential, enhancing the system's overall voltage. This technique is crucial for applications requiring higher voltage outputs. Ensure that the cells are in the correct orientation to avoid unwanted voltage cancellation, which can occur if a reversal in polarity occurs in one of the connections.