Question

Calculate the volume of $H_2$ gas at STP which would be produced per minute from radiolysis of water in a 1000 kW reactor, assumimg that 100 eV of energy produces 1 molecule of hydrogen
$2H_{2}O⟶H_2+H_2{O}_2$ $(1eV=1.6\times {10}^{-19}J)$
Plan energy given in kW is to be converted into $J{s}^{-1}$ and thus, volume of $H_2$ gas produced in this reactor can be calculated.

• A. $139.55$ L
• B. $179.55$ L
• C. $149.55$ L
• D. None of these

Answer 1

The correct option is A $139.55$ L

Given $1eV=1.6\times {10}^{-19}J$
$\therefore$ $100eV=100\times 1.6\times {10}^{-19}J$
$=1.6\times {10}^{-17}J$
Also $1000kW=1000\times 1000W$
$=1000\times 1000J{s}^{-1}$
$={10}^{6}J{s}^{-1}$
$=10{-}^6\times 60$ J in one minute (as required)
$1.6\times {10}^{-}17$ J produces $=1$ molecule of $H_2$
$\therefore$ $60\times {10}^6$ J produces $=\frac{60\times {10}^6}{1.6\times {10}^{-17}}$ molecules
$=37.5\times {10}^{23}$ molecules
$=\frac{37.5\times {10}^{23}}{6.02\times {10}^{23}}$ mol $h_2$
$=6.23$ mol $h_2$
1 mol at STP has volume $=22.4$ L
$\therefore$ $6.23$ mol at STP has volume $=139.55$ L