Question

A $0.0020M$ aqueous solution of an ionic compound $Co\left(N{H}_3{)}_5\right(N{O}_2)Cl$ freezes at $-{0.00732}^{o}C$. Number of moles of ions which $1$ mole of ionic compound produces on being dissolved in water will be:

$[k_f={1.86}^{o}C/m]$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

$2$

Depression in freezing point $\left(\Delta T_f\right)$ is given by,

$\Delta T_f=i\times K_f\times m$

where,

$i$=Van't Hoff Factor

$i=1+\alpha (n-1)$ for dissociation,

$K_f$=Cryoscopic Constant

(For water value of $K_f$=1.86)

$m$=molality of solution

Here $\Delta T_f=0-(-0.00732)=0.00732$

$i=\frac{\Delta T_f}{K_f\times m}=\frac{0.00732}{1.86\times 0.0020}=1.86\approx 2$

So, This compound, $\left[Co\right(N{H}_3{)}_5\left(N{O}_2\right)]Cl$ in solution will dissociate into ${Cl}^{-}$ and $\left[Co\right(N{H}_3{)}_5\left(N{O}_2\right){]}^{+},n=2$

Therefore two moles of ions are formed.

Hence, the correct option is $B$