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Question #44067

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The Question

Solid ammonium carbamate, $\ce{NH2COONH4(s)}$ , undergoes reversible dissociation into ammonia and carbon dioxide gases. When excess $\ce{NH2COONH4(s)}$ is introduced into an evacuated rigid vessel at $300\text{ K}$ , the equilibrium total pressure is found to be $0.30\text{ atm}$ .

In a separate experiment, $1.00\text{ mole}$ of $\ce{NH2COONH4(s)}$ is placed in an evacuated $24.63\text{ L}$ vessel at $300\text{ K}$ and allowed to reach equilibrium.

Given $R = 0.0821\text{ L atm K}^{-1}\text{ mol}^{-1}$ and assuming ideal gas behavior, what is the mass of the unreacted $\ce{NH2COONH4(s)}$ at equilibrium in the second experiment? (Molar mass of $\ce{NH2COONH4} = 78\text{ g mol}^{-1}$ )

Options

A.
$70.2\text{ g}$
B.
$55.3\text{ g}$
C.
$65.6\text{ g}$
D.
$7.8\text{ g}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Relationship between Kp and Kc|Homogeneous vs. Heterogeneous Equilibrium

Why This Question Is Tricky

Common Mistakes

This problem tests the rigorous application of the $K_p$ - $K_c$ relationship in heterogeneous equilibria.

The primary trap lies in the calculation of $\Delta n_g$ .

Students often blindly apply $\Delta n_g = \text{moles of products} - \text{moles of reactants}$ without excluding condensed phases (solids/liquids).

If a student incorrectly includes the solid reactant, they calculate $\Delta n_g = 3 - 1 = 2$ , leading to an incorrect $K_c$ and a final unreacted mass of $55.3\text{ g}$ .

Additionally, the problem tests stoichiometric discipline in the $K_c$ expression (forgetting the coefficient 2 leads to $65.6\text{ g}$ ) and reading comprehension (calculating reacted mass instead of unreacted mass yields $7.8\text{ g}$ ).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Relationship between Kp and Kc
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free