Question

Calculate the energy required to excite one litre of hydrogen gas at 1 atm pressure and 298K to the first excited state of atomic hydrogen. The energy for the dissociation of H-H is 436 kJ ${mol}^{-1}$.

• A. $0.585KJ$
• B. $5\times {10}^{23}eV$
• C. $80.36KJ$
• D. none of these

Answer 1

The correct option is D none of these

Determination of number of moles of $H$ gas,

$N=\frac{PV}{RT}=1\times \frac{1}{0.082}\times 298=0.0409$

The concerned reaction is $H_2\to 2H$, $deltaH=436$ Kj/mol

Energy required to bring $0.0409$ moles of $H$ gas to atomic state $=436\times 0.0409=17.83$ $kJ$

$1$ mole of $H_2$ gas has $6.022\times {10}^{23}$ molecules

Since, $1$ molecule of $H_2$ gas has $2H$ atom $=6.022\times {10}^{23}\times 0.0409$

$=2\times 6.022\times {10}^{23}\times 0.0409=4.92\times {10}^{22}$ atoms of $H$

$E=13.6(\frac{1}{n_1^2}-\frac{1}{n_2^2})eV=13.6\times (\frac{1}{1}-\frac{1}{4})=13.6\times \frac{3}{4}=10.2eV$

$=1.632\times {10}^{-21}Kj$

Therefore energy required to excited $4.92\times {10}^{22}$ electrons

$=1.632\times {10}^{-21}\times 4.92\times {10}^{-22}Kj$

$=8.03\times 10=80.3Kj$

Therefore total energy required $=17.83+80.3=98.17kJ$