Question

Identify the correct trend given below (Atomic number, $Ti=22,Cr=24$ and $Mo=42$ )

• A. ${\Delta }_o$ of ${\left[Cr{\left(H_{2}O\right)}_6\right]}^{2+}<{\left[Mo{\left(H_{2}O\right)}_6\right]}^{2+}$ and ${\Delta }_o$ of ${\left[Ti{\left(H_{2}O\right)}_6\right]}^{3+}<{\left[Ti{\left(H_{2}O\right)}_6\right]}^{2+}$
• B. ${\Delta }_o$ of ${\left[Cr{\left(H_{2}O\right)}_6\right]}^{2+}>{\left[Mo{\left(H_{2}O\right)}_6\right]}^{2+}$ and ${\Delta }_o$ of ${\left(Ti{\left(H_{2}O\right)}_6\right)}^{2+}>{\left[Mo{\left(H_{2}O\right)}_6\right]}^{2+}$
• C. ${\Delta }_o$ of ${\left[Cr{\left(H_{2}O\right)}_6\right]}^{2+}>{\left[Mo{\left(H_{2}O\right)}_6\right]}^{2+}$ and ${\Delta }_o$ of ${\left[Ti{\left(H_{2}O\right)}_6\right]}^{2+}<{\left[Mo{\left(H_{2}O\right)}_6\right]}^{2+}$
• D. ${\Delta }_o$ of ${\left[Cr{\left(H_{2}O\right)}_6\right]}^{2+}<{\left[Mo{\left(H_{2}O\right)}_6\right]}^{2+}$ and ${\Delta }_o$ of ${\left[\mathrm{Ti}{\left(H_{2}O\right)}_6\right]}^{3+}>{\left[\mathrm{Ti}{\left(H_{2}O\right)}_6\right]}^{2+}$

Answer 1

Answer: (B)

For ${\left[Cr{\left(H_{2}O\right)}_6\right]}^{2+}$ and $C{r}^{2+}=[Ar],3d^4$

As $H_{2}O$ is a weak field lignad, so pairing of electrons does not occur.
$CFSE$ for ${\left[Cr{\left(H_{2}O\right)}_6\right]}^{2+}=3\left(-0.4{\Delta }_o\right)+1\left(0.6{\Delta }_o\right)=-0.6{\Delta }_o$ Similarly,

Complex	Metal ion	Electronic configuration	$CFSE$
${\left[Mo{\left(H_{2}O\right)}_6\right]}^{2+}$	$M{o}^{2+}$	$t_{2g}^3,e_g^1$	$-0.6{\Delta }_o$
${\left[Ti{\left(H_{2}O\right)}_6\right]}^{3+}$	$T{i}^{3+}$	$t_{2g}^1,e_g^0$	$-0.4{\Delta }_o$
${\left[Ti{\left(H_{2}O\right)}_6\right]}^{2+}$	$T{i}^{2+}$	$t_{2g}^2,e_g^0$	$-0.8{\Delta }_o$

${\Delta }_o\propto$ Crystal Field Stabilisation Energy $(CFSE)$
${\Delta }_o$ depends on $Z_{eff}$ and for $3d$-series, $Z_{eff}$ is less than $4d$-series.
Hence, ${\Delta }_o$ of ${\left[Cr{\left(H_{2}O\right)}_6\right]}^{2+}>{\left[Mo{\left(H_{2}O\right)}_6\right]}^{2+}$
From above table,
${\Delta }_o\text{ of }{\left[Ti{\left(H_{2}O\right)}_6\right]}^{3+}>{\Delta }_o\text{ of }{\left[Ti{\left(H_{2}O\right)}_6\right]}^{2+}$