Q.11 The EMF of the following cell at 298.15 K is
Ag(s)|Ag+(0.01 M)||Ag+(0.1 M)|Ag(s)
(Standard reduction potential for Ag+ + e– → Ag = -0.80 V)
(A) 0.12 V
(B) 0.08 V
(C) 0.80 V
(D) 0.92 V
EMF of Ag(s)|Ag+(0.01 M)||Ag+(0.1 M)|Ag(s) Cell at 298.15 K
Concentration Cell Setup
This is a concentration cell where both half-cells involve the Ag+/Ag electrode but with different Ag+ concentrations:
- Anode (left): [Ag+] = 0.01 M
- Cathode (right): [Ag+] = 0.1 M
The standard cell potential, E°cell, is 0 V since both electrodes are identical.
Cell Reaction
The spontaneous reaction transfers Ag+ from higher to lower concentration:
Ag+(0.1 M) → Ag+(0.01 M)
Formally: Ag(s, anode) + Ag+(0.1 M) → Ag+(0.01 M) + Ag(s, cathode)
Number of electrons transferred, n = 1.
Nernst Equation Calculation
At 298.15 K, the Nernst equation simplifies to:
Ecell = E°cell − 0.059/n × log([Ag+]anode / [Ag+]cathode)
Substituting values:
Ecell = 0 − 0.059 × log(0.01 / 0.1)
= −0.059 × log(0.1)
= −0.059 × (−1)
= 0.059 V
Note: The given E° = -0.80 V for Ag+/Ag is the reduction potential but irrelevant for E°cell in this symmetric concentration cell.
Option Analysis
| Option | Value (V) | Explanation |
|---|---|---|
| A | 0.12 | Too high; would require log term ~2 (ratio 100:1), not matching 10:1 ratio here. |
| B | 0.08 | Closest to calculated 0.059 V; likely intended answer if approximating 0.06 V or minor rounding. |
| C | 0.80 | Equals |E°| but ignores concentration difference; applies only to standard conditions. |
| D | 0.92 | Unrelated; possibly confuses with other cells like Cu/Ag (E°cell ~0.46 V adjusted). |
Summary for CSIR NET
Key takeaways for exams:
- The EMF of Ag(s)|Ag+(0.01 M)||Ag+(0.1 M)|Ag(s) cell at 298.15 K is approximately 0.059 V.
- Use the Nernst equation for concentration cells: Ecell = 0.059/n × log([Ag+]cathode / [Ag+]anode).
- Do not confuse with standard reduction potentials; E°cell = 0 for symmetric cells.
