Before You Begin

Question #44849

Difficulty: 8/10 | 🟢 Free

The Question

Consider the outer-sphere redox reaction between a diamagnetic Cobalt(III) complex and a Ruthenium(II) reductant in an aqueous medium at 298 K:

$\ce{[Co(L)6]^{3+} + [Ru(NH3)6]^{2+} -> [Co(L)6]^{2+} + [Ru(NH3)6]^{3+}}$

The standard cell potential is $E^\circ = +0.85\text{ V}$ . The product $\ce{[Co(L)6]^{2+}}$ exhibits a magnetic moment of $\mu_{eff} \approx 4.8\text{ BM}$ . Direct electron transfer is spin-forbidden and possesses an insurmountable Franck-Condon barrier due to the required $t_{2g}^6 \rightarrow t_{2g}^5 e_g^2$ electronic reorganization. Consequently, kinetic studies reveal that the reaction proceeds entirely via a rate-determining thermal spin-crossover of the Co(III) complex to a paramagnetic state ( $\mu_{eff} \approx 4.9\text{ BM}$ ), followed by rapid electron transfer.

Determine the units of the rate constant ( $k$ ) for the overall rate law and the overall order of the reaction.

Options

A.
$s^{-1}$ ; Overall Order = 1
B.
$L \cdot mol^{-1} \cdot s^{-1}$ ; Overall Order = 2
C.
$mol \cdot L^{-1} \cdot s^{-1}$ ; Overall Order = 0
D.
$L^2 \cdot mol^{-2} \cdot s^{-1}$ ; Overall Order = 3

Check Your Answer

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

Units of Rate Constant (k)|E° (M³⁺/M²⁺) Redox Potential|Magnetic Moment Quenching

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to avoid the trap of assuming standard bimolecular collision theory for all redox reactions.

Normally, an outer-sphere electron transfer follows second-order kinetics (Rate = k[Ox][Red]).

However, when a severe Franck-Condon barrier exists due to a required spin-state change (magnetic moment quenching/unquenching), the mechanism shifts.

If the thermal spin-crossover becomes the rate-determining step, the reductant's concentration drops out of the rate law, altering the overall order to 1 and the units of k to s^{-1}.

Students failing to account for the kinetic consequences of crystal field splitting and spin-state reorganization will incorrectly choose the second-order option.

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