Question

$3gm$ of a metal is deposited in $50$ minutes by passing a current of $2.5$ amperes through its respective electrolyte solution. The equivalent mass of metal is:
A. $38.6$
B. $51$
C. $16.5$
D. $74.6$

Answer 1

Hint: The deposited mass “W” as a result of current “I” overtime in grams is given by the formula $W=\dfrac{I\times t\times e}{96500}$, where ‘e’ is the charge equivalent mass of the given element. With this relation, try to calculate the equivalent mass of the metal in the given question. $50\times 60=3000$

Complete step by step solution:
We know that; $1\text{ Faraday}=96500\text{ coulomb}$.
Given that,
$3gm$ (W) of a metal is deposited in $50$ minutes ($50\times 60=3000$ seconds, consider as “t”) by passing a current of $2.5$ amperes (I) through an electrolysis process.
By applying a simple formula representing a relationship between current, time, equivalent weight and the mass of a substance; we can get the equivalent weight of the metal.
The formula is given as:
$W=\dfrac{I\times t\times e}{96500}$, where
W is the mass given,
I is the current,
e is the equivalent weight of the substance, and
it is the time.
By putting the values given, we will get:
$3=\dfrac{2.5\times 3000\times e}{96500}$
Then, $e=\dfrac{3\times 96500}{2.5\times 3000}=38.6$
Therefore, we can conclude that the equivalent mass of the metal is $36.8g$.

Hence, the correct option is A.

Note: It is important to note that molar mass and equivalent mass of a compound is completely different. The above formula is one of the equations taken from Faraday's law of electrolysis.