Question

How long will it take to deposit 1.0 g of chromium when a current of 1.25 A flows through a solution of chromium (III) sulphate?
(Molar mass of Cr = 52)
(A) 1.24 min
(B) 1.24 hr
(C) 1.24 s
(D) None of these

Answer 1

Hint: To solve this question using the Faraday's law of electrolysis. The formula to find the time is time = $\dfrac{mFz}{{MIt}}$. Equation of chromium to solve this question is,
\[C{{r}^{3+}}\,+\,3{{e}^{-}}\to \,Cr(s)\], so the valency number of ions is 3.

Complete step by step solution:
As you have learned about the Faraday's law of electrolysis from your chemistry lessons. Faraday's first law state that mass of substance deposited is directly proportional to the amount of charge passes through an electrode, the mathematical representation of law is ,
 \[m\alpha Q\]
\[m=ZQ\].......... (1)
Where Z is the proportionality constant
Q= Charge (C) and
m=mass of a substance deposited (g)
Faraday also observed that one Faraday of charge (96500 C) liberated one gram equivalent of substance at the electrode. This shows the relation of Z= Equivalent weight /96500 C
Now put the value of Z in the first equation, then it can be written as
\[m=\dfrac{E}{96500}\times Q=\dfrac{E}{96500}\times I\times t\](Q can also be written as I×t)………..(2)
Where I= Current
And t= time
Now the second law of Faraday states that When the same amount of electricity passes through several electrolytes the deposition of mass is proportional to their respective equivalent weight. And the formula to find the equivalent weight is,
Equivalent weight (E) =$\dfrac{Atomic\,weight}{valency}$=\[\dfrac{M}{z}\]
So, by putting the value of equivalent weight in equation three we will get,
 \[m=\dfrac{M}{z\times 96500}\times I\times t\](96500 is the value of F or Faraday constant)
Now if we will write this formula in respect to time it can be written as,
 \[t=\dfrac{m\times 96500\times z}{M\times I}\] ...............(3)
Now the values that are given in question are m = 1g, I= 1.23A, M= 52 and the value of valency will be 3 ,since chromium uses only three mole of electrons combined with other atoms.
\[C{{r}^{3+}}\,+\,3{{e}^{-}}\to \,Cr(s)\]
Now by putting all the values in the equation (3), we will get,
\[t=\dfrac{m\times 96500\times 3}{M\times I}=\dfrac{1\times 96500\times 3}{52\times 1.25}=4453.84\,\sec =1.24\,hr\]

Thus the correct option will be (B).

Note: The value of one Faraday or for Faraday constant is 96500 C/mol. In the solution, 'Z' represents the proportionality constant and 'z' represents the valency so do not confuse between them. If the time is given in seconds and you have converted it in hours then divide it by 3600.