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JEE Main 2017 · Chemistry · Coordination Compounds · medium

The complex [Ti(H2O)6]^3+ is violet because it absorbs light of wavelength 500 nm (the t2g^1→ eg^1 transition). Taking NAhc=1.196×10^5 kJ nm mol^-1…

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The complex [Ti(H2O)6]3+[\mathrm{Ti(H_2O)_6}]^{3+} is violet because it absorbs light of wavelength 500 nm500\ \mathrm{nm} (the t2g1→eg1t_{2g}^1\to e_g^1 transition). Taking NAhc=1.196×105 kJ nm mol−1N_Ahc=1.196\times10^{5}\ \mathrm{kJ\,nm\,mol^{-1}}, the crystal field stabilisation energy of the complex is nearly
  1. A. −239 kJ mol−1-239\ \mathrm{kJ\,mol^{-1}}
  2. B. −95.7 kJ mol−1-95.7\ \mathrm{kJ\,mol^{-1}}
  3. C. −143.5 kJ mol−1-143.5\ \mathrm{kJ\,mol^{-1}}
  4. D. −47.8 kJ mol−1-47.8\ \mathrm{kJ\,mol^{-1}}
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Answer: (B) −95.7 kJ mol−1-95.7\ \mathrm{kJ\,mol^{-1}}

The absorbed energy equals the splitting: Δo=1.196×105500=239.2 kJ mol−1\Delta_o=\dfrac{1.196\times10^5}{500}=239.2\ \mathrm{kJ\,mol^{-1}}. Ti3+\mathrm{Ti^{3+}} is d1d^1, with configuration t2g1t_{2g}^1; each t2gt_{2g} electron contributes −0.4Δo-0.4\Delta_o. CFSE=−0.4×239.2=−95.7 kJ mol−1\mathrm{CFSE}=-0.4\times239.2=-95.7\ \mathrm{kJ\,mol^{-1}}. (−239-239 is Δo\Delta_o itself, and −143.5-143.5 uses −0.6Δo-0.6\Delta_o.)
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