Question

A current of $9.65{\text{A}}$ is passed through an aqueous solution of $NaCl$ using suitable electrodes for $1000\sec $. Given that 1 faraday equals $96500$coulombs the amount of $NaOH\left( {{\text{mol wt}}{\text{. 40}}} \right)$formed on electrolysis is:
A.${\text{2}}{\text{.0 g}}$
B.$8.0{\text{ g}}$
C.${\text{4}}{\text{.0 g}}$
D.$1.0{\text{ g}}$

Answer 1

Hint:To solve this question, you must recall the formula for Faraday’s first law of electrolysis. It states that the amount of substance produced, released or deposited during electrolysis at any electrode is directly proportional to the amount of charge passed through the electrolyte solution.
Formula used: ${\text{w}} = {\text{ZIt}}$
Where, ${\text{w}}$is the amount of substance liberated or deposited.
${\text{I}}$ is the current that is passed through the solution
${\text{t}}$ is the time for which current is passed through the solution.
And, ${\text{Z}}$ is the electrochemical equivalent of a substance
${\text{Z}}$ is given by $\dfrac{E}{{96500}}$.
Where \[{\text{E}}\] is the equivalent weight of the substance liberated or deposited.
This gives the equation as: ${\text{w}} = \dfrac{{{\text{EIt}}}}{{96500}}$.

Complete step by step answer:
We are given the current passed as $9.65{\text{ C}}$ and the time is $1000\sec $. The substance produced during the reaction, i.e., $NaOH$ has equivalent weight $E = 40{\text{ g/mol}}$.
Substituting the values in the formula given by the first law, ${\text{w}} = \dfrac{{{\text{EIt}}}}{{96500}}$, we get,
$w = \dfrac{{40}}{{96500}} \times 9.65 \times 1000$
$\therefore w = 4g$

Thus, the correct answer is C.
Additional information: Electrolysis is the breaking down of an electrolyte due to the supply of electricity. In electrolysis we need to supply external energy to initiate chemical reaction which is non-spontaneous in nature otherwise. The second law of Faraday states that when the same amount of energy is passed through the electrolytic solution of a number of substances then and the equivalent weight of electrolyte in each solution will be in a ratio to each other.

Note:
The electrochemical equivalent of a substance is the amount of substance deposited or liberated during the electrolysis by the passage of quantity of electricity equal to 1 Faraday which is given as 96500 coulombs per mole. Equivalent weight of an element or compound depends upon the reaction in which that species is involved.