Question

Calculate the energy required to excite one litre of hydrogen gas at 1 $atm$ and 300 K to the first excited state of atomic hydrogen. The energy for the dissociation of $H-H$ bond is $436kJmo{l}^{-1}$.
Given : $R=\frac{1}{12}atmLmo{l}^{-1}{K}^{-1}$
$N_A=6\times {10}^{23}mo{l}^{-1}$

• A. 95.78 $kJ$
• B. 75.12 $kJ$
• C. 240.4 $kJ$
• D. 105.2 $kJ$

Answer 1

The correct option is A 95.78 $kJ$

For n moles of an ideal gas
$PV=nRT$
$n=\frac{PV}{RT}$

$n=\frac{1\times 1}{\frac{1}{12}\times 300}=0.04mol$

Energy required to effect the dissociation of 0.04 mol of hydrogen = $436\times 0.04=17.44kJ$

Energy required to excite one hydrogen atom to the first excited state
= $13.6(1-\frac{1}{4})=10.2eV$
= $10.2\times 1.6\times {10}^{-19}J$
= $1.632\times {10}^{-21}kJ$

Number of hydrogen atoms in the sample = $0.04\times 2\times 6\times {10}^{23}$

So energy required for the excitation = $1.632\times {10}^{-21}\times 0.04\times 2\times 6\times {10}^{23}=78.34kJ$

Energy required = $17.44+78.34=95.78kJ$