Step 1: Understanding Faraday’s Laws of Electrolysis
Faraday’s first law of electrolysis states that the mass of metal deposited on the cathode is directly proportional to the charge passed: \[ m = \frac{ZQ}{F} \] where: \( m \) is the mass of the deposited metal,
\( Z \) is the electrochemical equivalent of the metal,
\( Q \) is the charge passed (constant for all solutions),
\( F \) is Faraday’s constant \( 96500 \) C/mol.
Step 2: Electrochemical Equivalent and Equivalent Weight
The electrochemical equivalent (\( Z \)) is calculated as: \[ Z = \frac{{Atomic weight}}{{Valency} \times F} \] A higher electrochemical equivalent (\( Z \)) results in a greater mass of metal deposited.
The equivalent weight is calculated as:
\[ {Equivalent weight} = \frac{{Atomic weight}}{{Valency}} \]
Step 3: Calculating Equivalent Weights for Given Options
Zn from ZnSO$_4$ - Atomic weight of Zn = 65 - Valency = 2 - Equivalent weight = \( \frac{65}{2} = 32.5 \)
Fe from FeCl$_3$ - Atomic weight of Fe = 56 - Valency = 3 - Equivalent weight = \( \frac{56}{3} \approx 18.67 \)
Ag from AgNO$_3$ - Atomic weight of Ag = 108 - Valency = 1 - Equivalent weight = \( \frac{108}{1} = 108 \)
Ni from NiCl$_2$ - Atomic weight of Ni = 58.7 - Valency = 2 - Equivalent weight = \( \frac{58.7}{2} = 29.35 \)
Step 4: Identifying the Metal Deposited in Maximum Amount
- The mass deposited is directly proportional to the equivalent weight; therefore, the metal with the highest equivalent weight will be deposited in the maximum amount. - Silver (Ag) has the highest equivalent weight (108 g/mol), indicating it will be deposited in the greatest amount. Consequently, the correct answer is (C) AgNO$_3$.
A particle is moving in a straight line. The variation of position $ x $ as a function of time $ t $ is given as:
$ x = t^3 - 6t^2 + 20t + 15 $.
The velocity of the body when its acceleration becomes zero is: