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Question #44850

Difficulty: 8/10 | 🟢 Free

The Question

A rigid reactor of volume $8.0 \text{ L}$ contains a solid tungsten catalyst with a total active surface area of $40.0 \text{ cm}^2$ . The decomposition of \ce{NH3(g)} on the catalyst surface at $1000 \text{ K}$ and an initial pressure of $50 \text{ atm}$ follows zero-order kinetics due to complete surface saturation (Langmuir-Hinshelwood mechanism).

The catalyst surface has a site density of $1.5 \times 10^{19} \text{ active sites m}^{-2}$ . The rate-determining step is the decomposition of adsorbed \ce{NH3}, which occurs with a transition state vibrational frequency of $\nu = 4.0 \times 10^{12} \text{ s}^{-1}$ .

Given the activation energy for the surface reaction is $E_a = 23.03 RT$ , calculate the magnitude of the initial rate of change of the partial pressure of \ce{NH3(g)} in the reactor.

(Assume ideal gas behavior, $N_A = 6.0 \times 10^{23} \text{ mol}^{-1}$ , $R = 0.08 \text{ L atm K}^{-1} \text{ mol}^{-1}$ , and $e^{-23.03} = 10^{-10}$ . Each active site decomposes one \ce{NH3} molecule per effective vibration.)

Options

A.
$4.0 \times 10^{-4} \text{ atm s}^{-1}$
B.
$8.0 \times 10^{-1} \text{ atm s}^{-1}$
C.
$4.0 \text{ atm s}^{-1}$
D.
$4.0 \times 10^{-5} \text{ atm s}^{-1}$

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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

Units of Rate Constant (k)|Collision Frequency vs. Effective Collisions|Zero Order Rate Integration

Why This Question Is Tricky

Common Mistakes

The problem tests the 'Hidden Variable' of dimensionality in heterogeneous catalysis.

Students often memorize the Arrhenius equation and zero-order kinetics in terms of volumetric concentration ( $\text{mol L}^{-1} \text{ s}^{-1}$ ).

Here, the 'effective collision' frequency is limited by the 2D surface site saturation, meaning the pre-exponential factor $A$ and rate constant $k$ must be defined per unit area ( $\text{mol m}^{-2} \text{ s}^{-1}$ ).

Failing to account for the catalyst's surface area or incorrectly treating $A$ as a volumetric parameter leads to massive dimensional and numerical errors (as seen in the distractors).

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Kinetics - Class 12
Concept	Units of Rate Constant (k)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free