Question

Calculate the energy required to excite $1$ L of hydrogen gas at $1$ atm and $298$K to the first excited state of atomic hydrogen. The energy for the dissociation of $H-H$ bond is $436kJmo{l}^{-1}$.

Answer 1

Mole of $H_2$ present in one litre $=PV/RT$

$=1\times 1/0.0821\times 298$

$=0.0409$

Thus energy needed to break $H-H$ bonds in 0.0409 mole of $H_2=0.0409\times 436=17.83KJ$

Also energy needed to excite on $H-$atom from 1st to 2nd energy level$=13.6(1-1/4)eV$

$=10.2eV$

$=10.2\times 1.6\times {10}^{-19}J$

Energy needed to excite $0.0409\times 2\times 6.02\times {10}^{23}$ atoms of H$=10.2\times 1.6\times {10}^{-19}\times 0.0409\times 2\times 6.02\times {10}^{23}J$

$=80.36KJ$

Total energy needed$=17.83+80.36$ $=98.19KJ$