Question

The energy required to excite $1L$ of hydrogen gas at $1atm$ and $298K$ to the first excited state of atomic hydrogen. The energy for the dissociation of $H—H$ bond is $436kJmo{l}^{-1}$ is:

• A. $89.44kJ$
• B. $98.44kJ$
• C. $89.44kJ$
• D. $98.44J$

Answer 1

The correct option is B $98.44kJ$

Moles of $H_2$ gas:
Using formula of ideal gase: $pV=nRT$
where, $p$ = pressure, $V$ = volume, $n$ = moles, $T$ = temperature of $H_2$ and $R$ = $0.0821Latm{K}^{-1}mo{l}^{-1}$
$\Rightarrow$ Bond energy = $0.0409\times 6.023\times {10}^{23}$
= $4.93\times {10}^{22}$
Transition energy per atom = $2.18\times {10}^{-18}[1-\frac{1}{4}]J$
= $\frac{3}{4}\times 2.18\times {10}^{-18}J$
$\Rightarrow$ total transition energy:
= $\frac{3}{4}\times 2.18\times {10}^{-18}\times 4.93\times {10}^{22}J$
= $80.60\times {10}^{3}J$
= $80.60kJ$

Therefore, total energy required:
= dissociation energy + transition energy
= $(17.84+80.60)kJ$
= $98.44kJ$