If 0.5 amp current is passed through acidified silver nitrate solution...
Given:
- Current (I) = 0.5 A
- Time (t) = 100 minutes
- Equivalent weight of silver nitrate (AgNO3) = 108 g/mol
Calculating the amount of charge passed:
- Charge (Q) = Current (I) × Time (t)
- Substituting the given values, Q = 0.5 A × 100 minutes
Converting time to seconds:
- 1 minute = 60 seconds
- Therefore, 100 minutes = 100 × 60 seconds = 6000 seconds
Substituting the values:
- Q = 0.5 A × 6000 seconds
Calculating the amount of silver deposited:
- The amount of charge passed (Q) is directly proportional to the amount of silver deposited.
- The ratio of charge to the amount of silver deposited is given by the Faraday's law of electrolysis:
- Q = n × F
- Where n is the number of moles of electrons transferred and F is Faraday's constant.
- The Faraday's constant is given by 1 Faraday = 96485 C/mol.
Calculating the number of moles of electrons transferred:
- n = Q / F
- Substituting the values, n = (0.5 A × 6000 seconds) / 96485 C/mol
Calculating the mass of silver deposited:
- The number of moles (n) is directly proportional to the mass of silver deposited.
- The ratio of moles to mass is given by the molar mass of silver (Ag).
- The molar mass of silver is 107.87 g/mol.
Calculating the mass of silver:
- Mass of silver = n × molar mass of silver
- Substituting the values, Mass of silver = (0.5 A × 6000 seconds / 96485 C/mol) × 107.87 g/mol
Simplifying the equation:
- Mass of silver = (0.5 A × 6000 seconds × 107.87 g) / 96485 C
Calculating the mass of silver (approximated to four decimal places):
- Mass of silver ≈ 3.3575 g
The mass of silver deposited on the cathode is approximately 3.3575 g. Therefore, the correct answer is option (B).