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Question #44699

Difficulty: 8/10 | 🟢 Free

The Question

A reaction vessel at $298 \text{ K}$ contains $0.50 \text{ moles}$ of a gaseous dimer $\ce{X2}$ and $0.60 \text{ moles}$ of a monoatomic gas $\ce{Y}$ . They are ignited to react completely according to the following balanced stoichiometric equation:

$\ce{3 X2(g) + 4 Y(g) -> 2 X^{3+} (n=4) + 4 XY(g)}$

where $\ce{X^{3+}}$ is the hydrogen-like beryllium ion ( $\ce{Be^{3+}}$ ). Immediately after formation, all the excited $\ce{Be^{3+}}$ ions undergo an electronic transition to the first excited state. Given the ionization energy of a hydrogen atom is $1312 \text{ kJ mol}^{-1}$ , what is the total energy emitted by the sample in the form of photons during this specific transition?

Options

A.
$1180.8 \text{ kJ}$
B.
$1312.0 \text{ kJ}$
C.
$2361.6 \text{ kJ}$
D.
$5904.0 \text{ kJ}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Rydberg Equation Constants|Stoichiometric Coefficient Division

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of macroscopic reaction stoichiometry and microscopic quantum transitions.

It features three distinct traps.

Trap 1: Failing to identify the limiting reagent and using the $0.50$ moles of X2, which yields $1312.0$ kJ.

Trap 2: Ignoring the stoichiometric coefficient division (assuming 1 mole of Y gives 1 mole of excited ions), yielding $2361.6$ kJ.

Trap 3: A terminology trap where students misinterpret 'first excited state' as the ground state ( $n=1$ ), leading to the calculation of a Lyman-equivalent transition and an incorrect energy of $5904.0$ kJ.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Structure of Atom - Class 11 Part 1
Concept	Rydberg Equation Constants
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free