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Question #44881

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The Question

An aqueous solution of $0.1 \text{ M } H_2SO_4$ is electrolyzed at $273 \text{ K}$ and $1 \text{ atm}$ using a Platinum anode and a Palladium ( $Pd$ ) cathode. The mass of the Palladium cathode is $10.64 \text{ g}$ . A constant current of $9.65 \text{ A}$ is passed through the cell for $2000 \text{ s}$ . During the electrolysis, the Palladium cathode absorbs atomic hydrogen to form an interstitial hydride with the limiting composition $PdH_{0.60}$ before any hydrogen gas is evolved. Assuming $100\%$ current efficiency for the reduction of $H^+$ and that the cathode reaches its maximum hydrogen absorption capacity, what is the volume of $H_2(g)$ evolved at the cathode?\n\n(Given: Atomic mass of $Pd = 106.4 \text{ g/mol}$ , $1 \text{ F} = 96500 \text{ C/mol}$ , Molar volume of an ideal gas at $273 \text{ K}$ and $1 \text{ atm} = 22.4 \text{ L/mol}$ )

Options

A.
1.568 L
B.
2.240 L
C.
0.896 L
D.
1.120 L

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

Interstital Compound Formation|Electrolysis Product Prediction

Why This Question Is Tricky

Common Mistakes

This problem tests the intersection of Faraday's Laws of Electrolysis and solid-state chemistry (interstitial compounds).

The 'Textbook Rule' assumes 100% of the cathodic current yields H2(g).

The 'Hidden Variable' is the kinetic partitioning of adsorbed hydrogen (H_ads) into the Palladium lattice to form a non-stoichiometric interstitial hydride (PdH_x) before Volmer-Tafel recombination into H2(g) occurs.

Students commonly fall into the trap of calculating the theoretical Faradaic yield of H2 gas (2.240 L, Option B) without subtracting the moles of atomic hydrogen occluded by the cathode.

Another trap (Option C) involves confusing the stoichiometry of the hydride, erroneously subtracting 0.06 mol of H2 molecules instead of atomic H.

Option D is the volume of O2 gas evolved at the anode.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	D and F Block Elements - Class 12
Concept	Interstital Compound Formation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free