Question

\[{C_6}{H_6}\] freezes at \[{5.5^ \circ }C\]. The temperature at which a solution of \[10\]g of \[{C_4}{H_{10}}\] in \[200\] g of \[{C_6}{H_6}\]freeze is……. C
(The molal freezing point depression constant of \[{C_6}{H_6}\] is \[5.12C/m\])

Answer 1

Hint: In this question we determine the molality by first calculating the number of moles of solute than the Van't Hoff factor and the depression at the freezing point is calculated and finally, compute the new freezing point based on the decrease in the freezing point.

Formula used
The freezing point depression is proportional to the solute particle concentration and can be calculated using the equation,
\[\Delta {T_f} = i\,\,m\,\,{k_f}\]
Where \[\Delta {T_f} = \] The freezing point of the solution
\[i = \] Van’t Hoff factor
\[m = \] Molar concentration
\[{k_f} = \] Constant depression of the freezing point (depends on the solvent)

Complete Step by Step Solution:
Now we are given that \[{k_f}\left( {{C_6}{H_6}} \right) = 5.12C/m\]
Molar mass of \[{C_4}{H_{10}}\, = 58\]
And \[10\]g of \[{C_4}{H_{10}}\] is dissolved in \[200\] g of \[{C_6}{H_6}\]
We know that molality can be defined as the ratio of the number of moles of the solute to the total mass of the solvent. Therefore, Molality can be calculated as:
$ m = \dfrac{{\dfrac{{10}}{{58}}}}{{\left( {\dfrac{{200}}{{1000}}} \right)kg}}\,\,mol \\ $
$ = \dfrac{{10 \times 1000}}{{200 \times 58}}\,\,mol \\ $
$ = \dfrac{{10000}}{{11600}}mol \\ $
$ = 0.86\,mol \\ $

Now, the difference in freezing point can be calculated as follows:
$\Delta {T_f} = 1 \times 5.12 \times 0.86 \\ $
$ = 4.4 \\ $

Therefore, the freezing point can be calculated as:
\[{T_f} = \] original freezing point – change in freezing point
$ {T_f} = 5.5 - 4.4 \\ $
$ = 1.1 \\ $

Hence, the freezing point of the solution is \[{1.1^ \circ }C\]

Note: Depression is the phenomenon that describes why adding a solute to a solvent causes the solvent's freezing point to decrease. When a substance freezes, the molecules slow down as the temperature drops, and intermolecular forces take over. Depression is a collaborative property.