Question

Which compound will have an equal freezing point as $0.1$Methanol?

• A. $0.1\mathrm{M}{\mathrm{Na}}_2{\mathrm{SO}}_4$
• B. $0.1\mathrm{M}{\mathrm{Ba}}_3{\left({\mathrm{PO}}_4\right)}_2$
• C. $0.1\mathrm{M}\mathrm{HCl}$
• D. $0.1\mathrm{M}{\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$

Answer 1

The correct option is D

$0.1\mathrm{M}{\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$

Explanation for the correct options:

Depression in freezing point: Raoult's law says, adding a non-volatile solute lowers the solvent's vapor pressure, making it equivalent to that of a solid solvent at lower temperatures. This lowers the solvent's freezing point. The decrease in the freezing point is known as depression at the freezing point.

$∆{\mathrm{T}}_{\mathrm{f}}={\mathrm{ik}}_{\mathrm{f}}\mathrm{m}$

where $∆\mathrm{T}=$is the freezing point depression,

• i is the Van’t Hoff factor,
• m is the molality.
• K_f is the cryoscopic constant

Option D is correct.

(D) 0.1M

Van't Hoff factor 1 is present in glucose.0.1M. Van't Hoff factor 1 is also present in methanol.

Both solutions have the same molality, and Kf is a constant. As a result, the value of the depression at the freezing point is solely determined by the van't Hoff factor.

The Van't Hoff factor is proportional to the number of solute particles. Because glucose and methanol are covalent molecules, they do not produce ions when they dissociate.

As a result, Van't Hoff (i) has a value of 1.

Explanation for the incorrect options:

(A)

$$\begin{gathered} 0.1\mathrm{M}{\mathrm{Na}}_2{\mathrm{SO}}_4: \\ {\mathrm{Na}}_2{\mathrm{SO}}_4\left(\mathrm{aq}\right)\rightleftharpoons 2{\mathrm{Na}}^{+}\left(\mathrm{aq}\right)+{{\mathrm{SO}}_4}^{2-}\left(\mathrm{aq}\right) \end{gathered}$$

The Van't Hoff factor (i) has a value of 3.

(B) $0.1\mathrm{M}{\mathrm{Ba}}_3{\left({\mathrm{PO}}_4\right)}_2$:

${\mathrm{Ba}}_3{\left({\mathrm{PO}}_4\right)}_2\left(\mathrm{aq}\right)\leftrightharpoons 3{\mathrm{Ba}}^{+}\left(\mathrm{aq}\right)+2{{\mathrm{PO}}_4}^{3-}\left(\mathrm{aq}\right)$

The Van't Hoff factor (i) has a value of 5.

(C) $0.1\mathrm{M}\mathrm{HCl}$

$\mathrm{HCl}\left(\mathrm{aq}\right)\rightleftharpoons {\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)$

The Van't Hoff factor (i) has a value of 2.

Therefore, Option D is the correct answer.