Question

A solution of Fe₂(SO₄)₃ is electrolyzed for ‘x’ min with a current of 1.5 A to deposit 0.3482 g of Fe. The value of x is _______. [nearest integer]

Given : 1 F = 96500 C mol^–1. 

Atomic mass of Fe = 56 g mol^–1

Answer 1

Correct Answer: 20

To determine the value of 'x', we need to calculate how long the electrolysis takes to deposit 0.3482 g of Fe using a current of 1.5 A. The deposition of iron (Fe) can be described by the following half-reaction:
Fe³⁺ + 3e^- → Fe

First, we calculate the moles of Fe deposited:
Moles of Fe = \(\frac{{\text{mass}}}{{\text{molar mass}}} = \frac{0.3482 \, \text{g}}{56 \, \text{g mol}^-1} \approx 0.006215 \, \text{mol}\)

According to the half-reaction, depositing 1 mole of Fe requires 3 moles of electrons. Therefore, the moles of electrons (n_e) required are:
n_e = 0.006215 mol × 3 = 0.018645 mol

We use Faraday's laws of electrolysis to find the charge (Q) required:
Q = n_e × F = 0.018645 mol × 96500 C mol^-1 = 1798.9425 C

The charge (Q) is also equal to the product of current (I) and time (t):
Q = I × t → t = \(\frac{Q}{I} = \frac{1798.9425 \, \text{C}}{1.5 \, \text{A}} = 1199.295 \, \text{s}\)

Convert time from seconds to minutes:
t (minutes) = \(\frac{1199.295}{60} \approx 19.98825\) minutes

Rounded to the nearest integer, the value of x is 20. This falls within the expected range of 20 to 20.