Find the energy required to excite `1.10` L of hydrogen gas at `1.0` `Nm^(-2)` and `298`K to the first excited state of atomic hydrogen. The energy required for the dissociation of `H-H` bond is `436 kJ mol^(-1)`. Also calculate the minimum frequency of a photon to break this bond.

Explanation

We know,
Mole of ` H_2` present in one litre `= (PV)/(RT)`
` = ( 1 xx 1)/( 0. 0. 821 xx 298) = 0.04 09`
Thus energy needed to break ` H-H ` bods in ` 0. 0 4 09` mole of ` H_2 = 0. 409 xx 436 = 17 . 83 k J`
Also energy needed tor ecite one H-atom from 1 st to 2nd energy level
` = 13. 6 ( 1 - 1/4 ) eV = 10 . 2 eV`
` = 10 . 2 xx 1.6 xx 10^(-19) J`
` :.` Energy needed to ecite ` 0. 04 09 xx 2 xx 6.02 xx 10^(23)` atoms of h
` = 10 . 2 xx 1.6 xx 10^(-19) xx 0.0409 xx 2xx 6. 02 xx 10^(23) J`
Thus , total energy needed
` = 17 . 83 + 80 . 36 = 98 . 19 k J`
Energy required to break ( H -H ) bond
` = ( 436 xx 10^3)/( 6.03=23 xx 10^(23)) ` joule
` :. (( 436 xx 10^3 )/( 6.023 xx 10^(23)) = 6. 625 xx 10^(-34))v" " ( :. E = hv)`
` :. v = 10 . 93 xx 10^(14) sec ^(-1) or Hz`.