The e.m.f. of a galvanic cell with electrode potentials of silver equa...
Solution:
Given, the electrode potential of silver (Ag) is 0.80 V and that of copper (Cu) is 0.34 V.
The standard reduction potential of a reaction is the tendency of a species to undergo reduction, compared to the standard hydrogen electrode (SHE). The reduction potential of SHE is zero.
The reduction half-reaction for silver is:
Ag+ + e- → Ag (E°red = 0.80 V)
The oxidation half-reaction for copper is:
Cu → Cu2+ + 2e- (E°red = -0.34 V)
The overall cell reaction can be obtained by adding the two half-reactions:
Ag+ + Cu → Ag + Cu2+
The overall cell potential (Ecell) can be calculated using the Nernst equation:
Ecell = E°cell - (0.0592/n) log(Q)
where E°cell is the standard cell potential, n is the number of electrons transferred in the cell reaction, and Q is the reaction quotient.
In this case, n = 2, since two electrons are transferred in the cell reaction.
The reaction quotient can be expressed as:
Q = [Ag+][Cu2+]/[Ag][Cu]
Since the cell is at standard conditions, the concentrations of Ag+ and Cu2+ are 1 M, and the concentrations of Ag and Cu are 1 M. Therefore, Q = 1.
Substituting the values in the Nernst equation, we get:
Ecell = E°cell - (0.0592/2) log(1)
Ecell = E°cell
Therefore, the cell potential (Ecell) is equal to the standard cell potential (E°cell).
The standard cell potential can be obtained by subtracting the reduction potential of the anode (Cu) from the reduction potential of the cathode (Ag):
E°cell = E°cathode - E°anode
E°cell = 0.80 V - (-0.34 V)
E°cell = 1.14 V
Therefore, the e.m.f. of the galvanic cell is 1.14 V.
Hence, option (C) is the correct answer.
The e.m.f. of a galvanic cell with electrode potentials of silver equa...
Electrode potential of Ag is greater than Cu
Ag is cathode and Cu is anode
emf = E(cathode) - E(anode) = 0.8 - 0.34 = 0.46V
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