Atomic Structure - Result Question 99
####75. Calculate the energy required to excite $1 L$ 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 $436 kJ mol^{-1}$.
(2000)
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Answer:
Correct Answer: 75. $\left(2.16 \times 10^{20} J /\right.$ atom $)$
Solution:
- Moles of $H _2=\frac{p V}{R T}=\frac{1 \times 1}{0.082 \times 298}=0.0409$
$\Rightarrow$ Bond energy $=0.0409 \times 436=17.84 kJ$ Number of H-atoms produced after dissociation
$$ =2 \times 0.0409 \times 6.023 \times 10^{23}=4.93 \times 10^{22} $$
Transition energy/atom $=2.18 \times 10^{-18}\left(1-\frac{1}{4}\right) J$
$$ =\frac{3}{4} \times 2.18 \times 10^{-18} J $$
$\Rightarrow$ Total transition energy
$$ \begin{aligned} & =\frac{3}{4} \times 2.18 \times 10^{-18} \times 4.93 \times 10^{22} J \ & =80.60 \times 10^{3} J=80.60 kJ \end{aligned} $$
Therefore, total energy required
$$ \begin{aligned} & =\text { dissociation energy }+ \text { transition energy } \ & =(17.84+80.60) kJ=98.44 kJ \end{aligned} $$
