Calculate the energy required to excite one litre 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 . (mark the answer in KJ)

Step-by-step solution

For n moles of an ideal gas PV = nRT , n = PV RT = 1 1 0.0821 298 =0.0409 Energy required to effect dissociation of 0.0409 mole of hydrogen =436 0.0409=17.83 ~kJ . Energy required to excite one hydrogen atom to the first excited state =13.6 (1- 1 4 )=10.2 eV =10.2 1.6 10⁻¹⁹ ~kJ =1.632 10⁻²¹ ~kJ No. of H-atoms in the sample =0.0409 2 6.02 10²³ So energy required for the excitation =1.632 10⁻²¹ 0.0409 2 6.02 10²³=80.36 ~kJ The energy required =17.83+80.36=98.19 ~kJ