Question

Calculate the energy required to excite two litre of hydrogen gas at 1 atm and 298 k to the first excited state of atomic hydrogen. The energy for the disassociation of H${}_2$ bond is 436 kJ mol${}^{-1}$.

• A. 195.62 kJ
• B. 225.25 kJ
• C. 391.24 kJ
• D. None of these

Answer 1

The correct option is A 195.62 kJ

Number of moles of $H_2$ present = $\frac{PV}{RT}$

$\Rightarrow$ $\frac{1\times 2}{0.0821\times 298}$ = 0.0817 moles

Energy need to break $H-H$ bonds $=0.0817\times 436=35.641KJ$

Energy needed to excite $H$ from ground state to first excited state = $13.6(1-1/4)eV=10.2eV=10.2\times 1.6\times {10}^{-19}J$

Therefore total energy needed to excite $0.0817$ moles of molecules = $2\times 10.2\times 1.6\times {10}^{-19}\times 6.022\times {10}^{23}J=160.58KJ$

Therefore total energy needed = $160.58+35.64=195.62KJ$