Question

A current of 3 A is passed through a molten calcium salt for 1 hr 47 min 13 sec. The mass of calcium deposited is:

• A. 6.0 g
• B. 2.0 g
• C. 8.0 g
• D. 4.0 g

Hint:

The hint involves using the formula w= Eit/96500 to calculate the amount of substance produced during electrolysis.

Answer 1

The Correct Option is D

To solve the given problem of finding out the mass of calcium deposited, we need to use Faraday's laws of electrolysis. The relevant concepts involved here are:

1. The amount of substance deposited during electrolysis is directly proportional to the charge passed through the electrolyte.

Let's proceed with the solution:

1. Determine the total charge (Q) passed through the electrolyte: The charge passed can be calculated using the formula: \(Q = I \times t\), where \(I\) is the current and \(t\) is the time in seconds.
   • Current, \(I = 3 \, \text{A}\)
   • Time, \(t = 1 \, \text{hour} \, 47 \, \text{minutes} \, 13 \, \text{seconds}\) 
   • Convert the time into seconds:
     • \(1 \, \text{hour} = 3600 \, \text{seconds}\)
     • \(47 \, \text{minutes} = 47 \times 60 = 2820 \, \text{seconds}\)
     • Total time \(= 3600 + 2820 + 13 = 6433 \, \text{seconds}\)
2. Calculate the charge:
   • \(Q = 3 \, \text{A} \times 6433 \, \text{s} = 19299 \, \text{C}\)
3. Use Faraday's second law to find the mass of calcium deposited: The mass deposited is calculated using the formula: \(m = \frac{Q \cdot M}{n \cdot F}\) where:
   • \(m\) is the mass deposited,
   • \(Q\) is the charge (19299 C),
   • \(M\) is the molar mass of calcium (40.08 g/mol),
   • \(n\) is the number of electrons exchanged (2 for calcium, as \(\text{Ca}^{2+}\) will gain two electrons to form Ca),
   • \(F\) is Faraday's constant (approximately 96500 C/mol).
4. Calculate the mass of calcium deposited:
   • \(m = \frac{19299 \times 40.08}{2 \times 96500} \approx 4.0 \, \text{g}\)

Thus, the mass of calcium deposited is 4.0 g, confirming that the correct answer is the option "4.0 g".