Question

An ammeter reading shows a current of $ 0.50A $ running through the iron hull. How many grams of $ Fe(s) $ are lost in $ 1.0\;h $ ?
A. 0.261 g
B. 0.522 g
C. 1.044 g
D. 0.783 g

Answer 1

Hint: We know that Faraday's laws represent the quantitative relationship between the substance deposited at electrodes and the amount of electricity passed through it. According to Faraday’s first law of electrolysis, the mass of a substance which is deposited at any electrode is directly proportional to the charge passed through it.

Complete answer:
Faraday’s first law of electrolysis can be mathematically expressed as follows:
 $ m \propto Q $
Where, m is the mass (in grams) of the substance deposited at the electrode and Q is the amount of charge (in coulombs) passed through it.
On removing proportionality, a constant is introduced and the equation is represented as follows:
 $ m = ZQ $
Z is the proportionality constant and is known as electrochemical equivalent and is defined as the mass of the substance deposited at electrodes when 1 coulomb of charge is passed through it during electrodes.
Now, we know that one mole of electrons is equal to $ 96500\;C $ which is equal to 1 Faraday. So, if we pass 1 Faraday of charge in an electrolytic cell, then 1 gram equivalent mass of the substance will get deposited and thus, the equation can be represented as follows:
 $ m = \dfrac{{EQ}}{{96500}}\;\;\;\;\;\;\; - (1) $
Where, E is the equivalent mass of the given substance. We know that, amount of electricity passed is equal to the product of current flowing in the solution and the time for which the current is passed i.e., $ Q = I \times T $ . Therefore, equation (1) can be represented as follows:
 $ m = \dfrac{{EIT}}{{96500}} $
Substituting values as per given in question:
 $ m = \dfrac{{28 \times 0.5 \times 60 \times 60}}{{96500}} $
 $ \Rightarrow m = 0.522\;g $
Hence, the mass of $ Fe(s) $ lost is $ 0.522\;g $ . So, option (B) is the correct answer.

Note:
It is important to note that equivalent mass of a substance is the exact mass which will displace or combine with a fixed quantity of another substance and mathematically it is represented as $ E = \dfrac{M}{n} $ where M is the atomic mass and n is the n-factor. In the given process during electrolysis, $ Fe(s) $ is oxidized to $ F{e^{2 + }} $ that means it loses two electrons, so the n-factor for $ Fe(s) $ is 2 and thus, its equivalent mass is 28. Also, remember to substitute the value of time in a unit of seconds.