Calculate the energy required to excited one liter 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 436 kJ mol –1 . Also calculate the minimum frequency of photon to break this bond.
Text Solution
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Mole of H 2 present in one liter = 
= 
= 0.0409
Thus, energy needed to break H–H bonds in 0.0409 mole of H 2 = 0.0409 × 436 = 17.83 kJ.
Also energy needed to excite one H atom from 1st to 2nd energy level
= 13.6 
eV = 10.2 eV = 10.2 × 1.6 × 10 –19 J
∴ Energy needed to excite 0.0409 × 2 × 6.02 × 10 23 atoms of H
= 10.2 × 1.6 × 10 –19 × 0.0409 × 2 × 6.02 × 10 23 J = 80.36 kJ
Thus, total energy needed = 17.83 + 80.36 = 98.19 kJ
Energy required to break (H–H) bond = 
joule
E = h ν
∴ 
= 6.625 × 10 –34 ν
ν = 10.93 × 10 14 sec –1 or Hz.
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