Question

During the electrolysis of molten sodium chloride, the time required to produce $0.10mol$ of chlorine gas using a current of $3$ ampere is:
A: $55$ minutes
B: $110$ minutes
C: $220$ minutes
D: $330$ minutes

Answer 1

Electrolysis is a process in which chemical substances are decomposed with the passage of electric current. Decomposition refers to the breakdown of a compound into its individual components. Compounds must be ionic for electrolysis.
Formula used: charge$=$current$\times$ time
Charge on one electron$= 96500C$

Complete step by step answer:
In this question we have to find the time taken for the production of $0.10mol$ of chlorine gas using a current of $3$ ampere in the electrolysis of molten sodium chloride. In this electrolysis production of chlorine will be according to the following reaction:
$2C{l^ - }\xrightarrow[{}]{}C{l_2} + 2{e^ - }$
Therefore in the production of one mole of chlorine gas two electrons are required. Charge on one electron is $96500C$. Therefore charge on two electrons will be:
Charge on two electrons$= 2 \times 96500 = 193000C$
Therefore,
Charge required for the production of one mole of chlorine gas$= 193000C$ (explained above)
Therefore, charge required for the production of $0.10mol$ of chlorine gas will be,
Charge required for the production of $0.10mol$ of chlorine gas$= 193000 \times 0.1 = 19300C$
Now, we know the charge required for the production of a given amount of chlorine gas and we know the current as well (given). So, we can calculate the time required using the formula:

Charge$=$current$\times$time
Substituting the values,
$19300 = 3 \times t$
Solving this we get,
$t = 6433.33s$
This is the time required in seconds but the options are given in minutes. To convert this time in seconds we have to divide this time with $60$ (as one minute is equal to $60$ seconds). So,
$t = \dfrac{{6433.33}}{{60}} = 107.22\min .$
This is approximately equal to $110\min .$ so, the time required is $110\min .$
So, the correct answer is option B.

Note:
In electrolysis the cell used is electrolytic. Electrolytic cell is that cell which uses electric energy to make a non-spontaneous redox reaction, spontaneous. Voltaic cell or galvanic cell is that cell which derives electrical energy from a spontaneous reaction that is taking place in the cell.