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)
Show Answer
Answer:
Correct Answer: 75. $(98.44$ $ KJ)$
Solution:
- Moles of $H _2=\dfrac{p V}{R T}=\dfrac{1 \times 1}{0.082 \times 298}=0.0409$
$\Rightarrow$ 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 $=2.18 \times 10^{-18}\left(1-\dfrac{1}{4}\right) J$
$=\dfrac{3}{4} \times 2.18 \times 10^{-18} J$
$\Rightarrow$ Total transition energy
$\begin{aligned} & =\dfrac{3}{4} \times 2.18 \times 10^{-18} \times 4.93 \times 10^{22} J \\ & =80.60 \times 10^{3} J=80.60 \hspace{1mm} kJ \end{aligned}$
Therefore, total energy required
$\begin{aligned} & =\text { dissociation energy }+ \text { transition energy } \\ & =(17.84+80.60) kJ=98.44 \hspace{1mm} kJ \end{aligned}$
BETA
