Question

The same amount of electricity was passed through two separate electrolytic cells containing solutions of nickel nitrate [$Ni{\left( {N{O_3}} \right)_2}$​] and chromium nitrate [$Cr{\left( {N{O_3}} \right)_3}$​] respectively. If 0.3 g of nickel was deposited in the first cell, the amount of chromium deposited is (At. Wt. of $Ni = 59$, at. wt. of $Cr = 52$):
A. 0.1 g
B. 0.176 g
C. 0.3 g
D. 0.6 g

Answer 1

Electrolysis is an electrochemical process in which current is passed from one electrode to the other electrode in an ionized solution (i.e. electrolyte). In this phenomenon, cations or positive ions migrate to the cathode i.e. negative electrode whereas anions or negative ions migrate to the anode or positive electrode.

Complete step by step solution:
According to Faraday's second law of electrolysis, if the same quantity of electricity is passed through various electrolytes, the mass of the substances getting deposited are directly proportional to their respective equivalent weight or chemical equivalent.
$\dfrac{{{W_I}}}{{Eq.w{t_I}}} = \dfrac{{{W_{II}}}}{{Eq.w{t_{II}}}} = \dfrac{{{W_{III}}}}{{Eq.w{t_{III}}}} = ....$
Similarly, for the present case, we can write as follows:
$\dfrac{{{W_{Ni}}}}{{Eq.w{t_{Ni}}}} = \dfrac{{{W_{Cr}}}}{{Eq.w{t_{Cr}}}}$
In the question, we are provided with the following information:
$W_{Ni}$=0.3g (Given)
Atomic weight of $Ni = 59$(Given)
Atomic weight of $Cr = 52$ (Given)
Now we need to first calculate the Equivalent weight of Nickel and Chromium.
The equivalent weight of any element is equal to its atomic weight divided by the valence which it assumes in the compounds. In the present case we have $N{i^{ + 2}}{\left( {N{O_3}^{ - 1}} \right)_2}{\text{ and }}C{r^{ + 3}}{\left( {N{O_3}^{ - 1}} \right)_3}$
Thus, substituting the given values,
$\Rightarrow \dfrac{{0.3}}{{\dfrac{{59}}{2}}} = \dfrac{{{W_{Cr}}}}{{\dfrac{{52}}{3}}} \\\ \Rightarrow {W_{Cr}} = \dfrac{{0.3 \times 2}}{{59}} \times \dfrac{{52}}{3} = 0.176 \,g$

**Hence, the correct answer is Option B.

Note:**
We can also determine the equivalent or equivalent weight of a substance by Faraday’s laws of electrolysis and it is defined as the weight of that sub-tenancy which will combine with or displace the unit weight of hydrogen. It should also be noted that the chemical equivalent of hydrogen is unity. Since, the valency of a substance is equal to the number of hydrogen atoms, which can be replaced or combined, the chemical equivalent of a substance may be defined as the ratio of its atomic weight to its valency.