Question

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

Answer 1

Hint: To solve the given question, first we will write the reaction of electrolysis of molten sodium chloride and then we will write the formula of weight of that compound. And that’s how we will conclude the time during the electrolysis of molten sodium chloride.

Complete step by step answer:
During the electrolysis of molten sodium chloride-
At cathode: $2N{a^ + } + 2{e^ - } \to 2Na$
At anode: $2C{l^ - } \to C{l_2} + 2{e^ - }$
So, the Net reaction is:-
$2N{a^ + } + 2C{l^ - } \to 2Na + C{l_2}$
Now, according to Faraday’s first law of electrolysis,
$
  w = Z \times I \times t \\
   \Rightarrow w = \dfrac{E}{{96500}} \times I \times t \\
 $
$
  \therefore No.{\text{ }}of{\text{ }}moles{\text{ }}of\,C{l_2}gas \times Mol.\,wt.\,of\,C{l_2}gas = \dfrac{{Eq.\,wt.\,of\,C{l_2}gas \times I \times t}}{{96500}} \\
   \Rightarrow 0.10 \times 71 = \dfrac{{35.5 \times 3 \times t}}{{96500}} \\
   \Rightarrow t = \dfrac{{0.10 \times 71 \times 96500}}{{35.5 \times 3}} \\
   \Rightarrow t = 6433.33\sec \\
   \Rightarrow t = 107.22\min \approx 110\min \\
 $
Therefore, the time required to produce $0.10mol$ of chlorine gas using a current of $3amperes$ is 110 minutes.

So, the correct answer is Option d.

Note: Molten (liquid) sodium chloride can be electrolyzed to produce sodium metal and chlorine gas. The electrolytic cell used in the process is called a Down's cell. A Down's cell is used for the electrolysis of molten sodium chloride.