Question

Calculate mass of a divalent metal produced at cathode by passing 5 amp current through its salt solution for 100 minute.

(Molar mass of metal = x)

• A. $\frac{193}{30}x$
• B. $\frac{30}{193}x$
• C. $\frac{15}{193}x$
• D. $\frac{193}{15}x$

Answer 1

Answer: (B)

$\frac{30}{193}x$

Answer 2

Solution:

1. Calculate total charge (Q):

   Time = 100 minutes = 6000 s

   $Q = I \times t = 5 \text{ A} \times 6000 \text{ s} = 30000 \text{ C}$

2. Determine moles of electrons transferred:

   For a divalent metal:

   $M^{+2} + 2e^- \rightarrow M$

   Moles of electrons = $Q / F = 30000 / 96500$

   Moles of metal deposited = $(Q / F) / 2 = 30000 / (2 \times 96500) = 30000 / 193000 = 30/193$

3. Calculate mass deposited:

   Mass = (Moles of metal) × (Molar mass) = $(30/193) \times x$

Thus, the mass of the metal produced is $\frac{30}{193}x$.