Question

With the help of CFT number of unpaired electron in a compound can be calculated and we can calculate its paramagnetic moment (due to spin only), by the formula :

$\mu ,=\sqrt{n(n+2)}$ Bohr magneton (BM), where 'n' is the number of unpaired electron in the complex. For spectral analysis the separation between $t_{2g}$ and $e_g$ orbitals, called ligand field splitting parameter ${\Delta }_0$ (for octahedral complexes) should be known to us, which can be easily calculated by observing the absorption spectrum of one $e^{-}$ complex figure shows the optical absorptions spectrum of the $d^1$ hexaaqatitanium (III) ion $\left[Ti\right(H_{2}O{)}_6{]}^{3+}$. The CFT assigns the first absorption maximum at 20,300 $c{m}^{-1}$ to the transition $e_g\leftarrow t_{2g}$. For multielectronic $\left(d^{2}to{d}^{10}\right)$ system, the calculation of ${\Delta }_0$ by absorption spectrum is not that easy as the absorption spectrum will also be affected by electron-electron repulsions.

The crystal field stabilization energy (CFSE) for complex given in the passage, $\left[Ti\right(H_{2}O{)}_6^{3+}$ will be (in kJ / mol) :

• A. 243 kJ / mole
• B. 97 kJ / mole
• C. 194 kJ / mole
• D. 143 kJ / mole

Answer 1

Answer: (B)

97 kJ / mole

${\Delta }_O=hc\overline{\nu }$

${\Delta }_O=6.625\times {10}^{-34}\times 3\times {10}^{10}\times 20300=4.0\times {10}^{-19}J/molecule$

${\Delta }_O=6.023\times {10}^{23}\times 4.0\times {10}^{-19}=243005J/mol=243kJ/mol$

$CFSE=0.4{\Delta }_O=0.4\times 243=97kJ/mol$

[because Ti(III) contains 1 unpaired electron].