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Application of Electrolysis

Cost of elect...

Question

Cost of electricity for the production of $X$ litres of $H_{2}$ at $N T P$ at the cathode is Rs $X$ , then cost of electricity for the production $X$ litres of $O_{2}$ gas at $N T P$ at the anode will be:

[Assume $1$ mole of electrons as one unit of electricity]

A

2 X

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B

4 X

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C

16 X

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D

32 X

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Solution

The correct option is A $2 X$
Electrolysis of water gives:

$H_{2} O \to H_{2} + \frac{1}{2} O_{2}$

On electrolysis of water, hydrogen, and oxygen formed in the ratio $2 : 1$ .
Since $X$ litres of $H_{2}$ is formed. Amount of $O_{2}$ formed will be $\frac{X}{2}$ . Since cost of production of electricity from $\frac{X}{2}$ litres of $O_{2}$ = Rs $X$

So, cost of production of electricity from $X$ litres of $O_{2}$ = Rs $2 X$ .

So, the correct answer is option $A$ .

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Anode :

H_{2} + 2 O H^{-} \to 2 H_{2} O + 2 e^{-}

O_{2} + 2 H_{2} O + 4 e^{-} \to 4 O H^{-}

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