what is the energy required to excite 1 litre of hydrogen gas and 298k to the first excited state of atomic hydrogen.the energy for dissociation of H-H bond is 436KJ/mol

Answer 1

1 LITER OF H2 at 298 K and 1 atm pressure contains n = PV/RT moles of H2 molecules

n = 1 atm * 1 L / 0.0821 L-atm/molK * 298 K = 0.0409 moles (correct sig.figs is 0.04 moles)

dissociation energy is 436 kJ/mol * 0.0409 mol = 17.8 kJ (20 kJ sig figs)

0.0409 moles of dissociated H2 contains 0.0409 x 2 = 0.0818 moles of atomic H (0.08 sf)

0.0818 moles of H * 6.022*10^23 atoms/mole = 4.93*10^22 H atoms (5 * 10^22 sf)

ionization energy to remove 1st energy level electron from 1s orbital is

E = -2.178 x 10^-18 J (1/infinity - 1/1) = 2.178 x 10^-18 J/atom (from Rydberg equation for changing electron quantum levels)

ionization energy = 2.178*10^-18 J/atom * 4.93*10^22 atoms = 1.07 * 10^5 J = 107 kJ (100 kJ sf)

total energy to ionize 1 liter of H2 molecules at 298 K is 107 kJ + 17.8 kJ = 125 kJ (100 kJ if 1 sig fig)