Chapter 14.4, Problem 47PP

Interpretation Introduction

Interpretation:

The freezing point depression constant (K_f) of a 0.045 m solution needs to be determined. The solvent also needs to be identified.

Concept introduction:

Depression of freezing point is calculated as follows:

$\Delta {\mathrm{T}}_f=K_f\times m$

Here, m is molality of the solution.

Answer to Problem 47PP

The freezing point depression constant (K_f) of a 0.045 m solution is 1.8 °C/m. It is most likely water because the calculated value is closest to 1.86 °C/m

Depression of freezing point $\Delta {\mathrm{T}}_f=K_f\times m$

Data given: molality of the solution = 0.045 m

The freezing point depression ? T_f = 0.08 °C

$\begin{array}{l}\Delta {\mathrm{T}}_f=K_f\times m\\ {\mathrm{K}}_f=\frac{\Delta {\mathrm{T}}_f}{\mathrm{m}}\\ K_f=\frac{0.08°C}{0.045m}\\ =1.8°C/m\end{array}$

It is most likely water because the calculated value is closest to 1.86°C/m

Explanation of Solution

Depression of freezing point $\Delta {\mathrm{T}}_f=K_f\times m$

Data given: molality of the solution = 0.045 m

The freezing point depression ? T_f = 0.08 °C

$\begin{array}{l}\Delta {\mathrm{T}}_f=K_f\times m\\ {\mathrm{K}}_f=\frac{\Delta {\mathrm{T}}_f}{\mathrm{m}}\\ K_f=\frac{0.08°C}{0.045m}\\ =1.8°C/m\end{array}$

It is most likely water because the calculated value is closest to 1.86°C/m