Problem 28 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

A solution containing one mole per litre of each \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} ; \mathrm{AgNO}_{3}\); \(\mathrm{Hg}_{2}\left(\mathrm{NO}_{3}\right)_{2}\); is being electrolysed by using inert electrodes. The values of standard electrode potentials in volts (reduction potentials) are : [1984-1 Mark] \(\mathrm{Ag} / \mathrm{Ag}^{+}=+0.80,2 \mathrm{Hg} / \mathrm{Hg}_{2}^{++}=+0.79\) \(\mathrm{Cu} / \mathrm{Cu}^{++}=+0.34, \mathrm{Mg} / \mathrm{Mg}^{++}=-2.37\) With increasing voltage, the sequence of deposition of metals on the cathode will be : (a) \(\mathrm{Ag}, \mathrm{Hg}, \mathrm{Cu}, \mathrm{Mg}\) (b) \(\mathrm{Mg}, \mathrm{Cu}, \mathrm{Hg}, \mathrm{Ag}\) (c) \(\mathrm{Ag}, \mathrm{Hg}, \mathrm{Cu}\) (d) \(\mathrm{Cu}, \mathrm{Hg}, \mathrm{Ag}\)

Step-by-Step Solution

Answer

The correct order is Ag, Hg, Cu, Mg (option a).

Step 1: Understand Electrode Potential

The electrode potential of a half-reaction measures the ability of a chemical species to acquire electrons (get reduced), compared to the standard hydrogen electrode. Higher positive values indicate a greater tendency to be reduced.

Step 2: List Construction Based on Electrochemical Series

Using the provided standard reduction potentials: \(\mathrm{Ag} / \mathrm{Ag}^{+}=+0.80V\), \(\mathrm{Hg}_{2}^{++}/2 \mathrm{Hg}=+0.79V\), \(\mathrm{Cu}^{++} / \mathrm{Cu}=+0.34V\), and \(\mathrm{Mg}^{++} / \mathrm{Mg}=-2.37V\), metals with higher positive values will deposit on the cathode first because they have a stronger tendency to gain electrons.

Step 3: Sort Metals by Reduction Potentials

Order the metals from the highest to lowest reduction potential to determine the sequence of deposition. This order is: 1. \(\mathrm{Ag}\), 2. \(\mathrm{Hg}\), 3. \(\mathrm{Cu}\), and 4. \(\mathrm{Mg}\). Thus, the sequence of deposition will be based on these reduction potentials.

Step 4: Match to Answer Choices

Compare the order derived from Step 3 with the given options: (a) \(\mathrm{Ag}, \mathrm{Hg}, \mathrm{Cu}, \mathrm{Mg}\), (b) \(\mathrm{Mg}, \mathrm{Cu}, \mathrm{Hg}, \mathrm{Ag}\), (c) \(\mathrm{Ag}, \mathrm{Hg}, \mathrm{Cu}\), (d) \(\mathrm{Cu}, \mathrm{Hg}, \mathrm{Ag}\). The correct sequence, as determined, matches option (a).

Key Concepts

Electrochemical Series

The electrochemical series is an invaluable tool in understanding how various metals and elements behave in electrochemical reactions. It is essentially a list that arranges elements in order of their electrode potentials when they undergo reduction. This series helps predict which metal ions will gain electrons most readily and consequently, which will deposit on the cathode during an electrolytic process.
Elements listed higher in the electrochemical series have more positive standard reduction potentials. This means they are more likely to undergo reduction and act as cathodes in electrochemical cells. Conversely, those lower on the list have more negative potentials and are less likely to be reduced.
In our case, according to the electrochemical series and provided reduction potentials, silver (Ag) is at the top with +0.80V, indicating it is most eager to gain electrons. This is followed closely by mercury (Hg) and then copper (Cu), with magnesium (Mg) being the least on the list due to its highly negative potential.

Reduction Potentials

Reduction potentials are a measure of the tendency of a chemical species to acquire electrons and be reduced. They are expressed in volts and compare directly to the standard hydrogen electrode, which is set at 0 volts. The more positive the reduction potential, the greater the species' affinity for electrons and its ability to be reduced.
For example, when we consider the reduction potential of silver as +0.80 volts, it signifies that silver ions will easily take up electrons to become elemental silver. In contrast, magnesium's reduction potential of -2.37 volts shows a reluctance to be reduced, as it requires a substantial amount of energy to gain electrons.
Reduction potentials are crucial in predicting how substances will behave in electrochemical processes. When comparing multiple species, you can determine their reduction sequence in a given setup by simply arranging them from the highest to the lowest reduction potential.

Cathode Deposition Sequence

In electrolysis, the cathode deposition sequence follows the order of increasing ease of reduction as dictated by the reduction potentials of the involved ions. Metals with higher positive reduction potentials will deposit on the cathode first, as they readily gain electrons.
When an electrolytic cell is set up with a mixture of metal ions, the sequence in which these metals deposit on the cathode can be determined by listing their reduction potentials from highest to lowest. In the given problem, silver with the highest potential of +0.80V will deposit first, followed by mercury (+0.79V), and then copper (+0.34V), with magnesium being least likely to deposit due to its negative potential.

• Silver ( Ag ) deposits first.
• Mercury ( Hg ) follows due to its slightly lesser potential.
• Copper ( Cu ) deposits thereafter.
• Magnesium ( Mg ) does not deposit under standard conditions due to its very low potential.

This sequence is reflected in option (a) in the provided exercise, illustrating the practical importance of understanding reduction potentials and their role in predicting and controlling electrochemical processes.