Cost of electricity for the production of $x \mathrm{~L} \mathrm{~H}_{2}$ at STP at cathode is Rs. $x$, then cost of electricity for the production of $x \mathrm{~L} \mathrm{~O}_{2}$ gas at STP at anode will be (assume $1 \mathrm{~mol}$ of electrons as one unit electricity) :

Question

Aicharya · Accepted Answer

$2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{e}^{-} ightarrow \mathrm{H}_{2}+2 \mathrm{OH}^{-}\dots \dots \mathrm{I}$
$2 \mathrm{H}_{2} \mathrm{O} ightarrow \mathrm{O}_{2}+4 \mathrm{H}^{+}+4 \mathrm{e}^{-}\dots \dots \mathrm{II}$
From $\mathrm{I}$ : $1 \mathrm{~mol}$ of $\mathrm{H}_{2}=22.4 \mathrm{~L} \mathrm{H}_{2}$ is obtained by $2$ units
$x \mathrm{~L}$ of $\mathrm{H}_{2}=\frac{2 \mathrm{x}}{22.4}$ units costing Rs. $x$
Thus, $1$ unit costs $=$ Rs. $11.2$
from $\mathrm{II}$ : $22.4 \mathrm{~L} \mathrm{~O}_{2}$ at $\mathrm{NTP}$ costs $=4$ units
$=4 \times 11.2 \mathrm{Rs}$
$x \mathrm{~L}$ costs $=2 \mathrm{x}$ .

Cost of electricity for the production of $x \mathrm{~L} \mathrm{~H}_{2}$ at STP at cathode is Rs. $x$, then…

Solution