Calculated the energy required to excite one litre of hydrogen gas at `1atm` and `298K` to the first excited state of atomic hydorgen. The enegry for the dissociation of `H-H` bond is `436 kJ mol^(-1)`.

Answer

`98.17 Kj`

Explanation

Determination of number of moles of hydrogen gas, `n=(PV)/(RT)=(1xx1)/(0.082xx298)=0.0409`
The concerned reaction is `H_(2) rarr 2H, DeltaH=kJ mol^(-1)`
Energy required to bring `0.0409` moles of hydrogen ges to atomic state `=436xx0.0409=17.83 kJ`
`1` mole of `H_(2)` gas has `6.02xx10^(23)` molecules
`0.0409 "mole of" H_(2) "gas"=(6.02xx10^(23))/(1)xx0.0409`
since `1` molecule of `H_(2)` gas has `2` hydrogen atoms
`6.02xx10^(23) xx0.0409` molecules of `H_(2)` gas `=2xx6.02xx10^(23)xx0.0409=4.92xx10^(22)` atoms
energy required to excite an electron from the ground state to the next excited state
`=13.6(1/n_(1)^(2)-1/n_(2)^(2))eV=13.6xx(1/1-1/4)=13.6xx3/4=10.2 eV=1.632xx10^(-21) kJ`
Therefore energy required to excite `4.92xx10^(22)` electrons `=1.632xx10^(-21)xx4.92xx10^(22) kJ`
`=8.03xx10=80.3 kJ`
Therefore total energy required `=17.83+80.3=98.17 kJ`