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Question #44185

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The Question

An aqueous solution of $\ce{K2Cr2O7}$ at $298\text{ K}$ is subjected to a gradual pH increase from $2.0$ to $11.0$ by the addition of $\ce{NaOH}$ . Which of the following statements correctly describes the thermodynamic, structural, and electronic changes occurring in the predominant chromium-containing species?

Options

A.
The solution color shifts from orange to yellow. The number of equivalent non-bridging $\ce{Cr-O}$ bonds decreases from 6 to 4, and the terminal $\ce{Cr-O}$ bond length increases due to a decrease in the $\ce{Cr-O}$ bond order from approximately 1.67 to 1.50.
B.
The solution color shifts from yellow to orange. The number of equivalent non-bridging $\ce{Cr-O}$ bonds increases from 4 to 6, and the terminal $\ce{Cr-O}$ bond length decreases due to an increase in the $\ce{Cr-O}$ bond order from 1.50 to 1.67.
C.
The solution color shifts from orange to yellow. The number of equivalent non-bridging $\ce{Cr-O}$ bonds decreases from 6 to 4, but the terminal $\ce{Cr-O}$ bond length decreases because the higher symmetry of the tetrahedral chromate ion maximizes $d\pi-p\pi$ back-bonding, increasing the bond order to 2.0.
D.
The solution color shifts from orange to yellow. The transformation is a disproportionation reaction where the oxidation state of chromium changes, and the bridging $\ce{Cr-O-Cr}$ bond is cleaved by $\ce{OH^-}$ nucleophilic attack, yielding species with bond orders of 1.33.

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Mechanism_Trap

Don't get tricked by the process! Learn the mechanical traps used in competitive exam questions.

Concepts Behind This Question

Resonance Stability Criteria|Dichromate-Chromate Equilibrium|Ionic Product of Water (Kw)

Why This Question Is Tricky

Common Mistakes

This question tests the intersection of Le Chatelier's Principle, coordination geometry, and resonance theory.

The 'Chemical Exception' or 'Hidden Variable' is the counter-intuitive bond length change.

Students often assume that the highly symmetric, resonance-stabilized chromate ion ( $\ce{CrO4^{2-}}$ ) has stronger/shorter bonds than the larger, more complex dichromate ion ( $\ce{Cr2O7^{2-}}$ ).

However, calculating the exact fractional bond orders via resonance structures reveals that the terminal bonds in dichromate have a higher bond order (1.67) than the bonds in chromate (1.50).

This leads to an unexpected increase in bond length upon cleavage of the dimer in basic media.

It also traps students who confuse the color change with a redox reaction or misapply $d\pi-p\pi$ back-bonding to assume a bond order of 2.0.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Chemical Bonding and Molecular Structure - Class 11 Part 1
Concept	Resonance Stability Criteria
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free