Question

The electrochemical equivalent of magnesium is $0.126$$mg/C$. A current of $5A$ is passed in a suitable solution for $1$ hour. The mass of magnesium deposited will be
A. $0.0378$gm
B. $0.227$gm
C. $0.378$ gm
D. $2.27$gm

Answer 1

Hint: When a current is passing through molten an electrolysis reaction occurs. Electrolysis is a process in which chemical reactions occur at the electrodes, dipping in the electrolytes applying current across them. In this case, Faraday’s first law of electrolysis can be applied to evaluate the mass of deposited magnesium.

Complete Step by Step Answer:
Molten magnesium salt has free $M{{g}^{2+}}$ions and respective anions and with these free ions, molten magnesium salt conducts electricity. When an electric current is passed through the cell anions are attracted to the anode (positive electrode) and $M{{g}^{2+}}$ions are attracted to the cathode (negative electrode).

According to Faraday’s law, the mass of an ion discharged during electrolysis is directly proportional to the quantity of electricity passed.
$W$ $\alpha $ $Q$
$Q$ denotes the quantity of electricity passed in the unit of coulombs

Again,$Q=i\times t$
Here $i$ = current in amperes
$t$ = time in seconds
$W$ $\alpha $ $i\times t$
Or, $W=Z\times i\times t$
$Z$ = proportionality constant or electrochemical equivalent in gm/C

Now putting the values in the above formula we can calculate the mass of deposited magnesium.
Given, $Z=0.126$mg/C$=0.126\times {{10}^{-3}}$g
$i=5A$
$t=1$hour $=3600$sec
Thus, $W=0.126\times {{10}^{-3}}\times 5\times 3600$
Or, $W=2.268$gm
Or, $W\approx 2.27$gm
Therefore the mass of magnesium deposited will be $2.27$gm.
Thus, option (D) is correct.

Note: Faraday’s law of electrolysis does not depend on the temperature of the environment. This depends only on the mass of substance deposited at the electrode, time duration of passing the electricity at a uniform rate and also on the amount of current passing through the solution.