Chapter 16, Problem 101A

Interpretation Introduction

Interpretation: An experiment based on the concept of freezing-point depression to get the molar mass needs to be designed for an unknown compound. The laboratory measurements and calculations required need to be determined.

Concept Introduction: The relation between change in freezing point and molality of a solution is as follows:

  $\Delta T_f=K_{f}m$

Here, $K_f$ is the freezing point constant of water and $m$ is the molality of the solution.

Explanation of Solution

The given known compound needs to be identified by means of its molar mass. To do so, the following experiment can be identified:

The known mass of an unknown compound is first dissolved in water of known mass. After that its freezing point is determined by checking at which temperature it gets frozen. The freezing point of water is known that is $0{}^{\text{o}}\text{C}$ . Also, the freezing constant of water is $1.86{}^{\text{o}}\text{C/m}$ . Now, the relation between the change in freezing point and the molality of the solution is as follows:

  $\Delta T_f=K_{f}m$

Here, $K_f$ is the freezing point constant of water and $m$ is the molality of the solution.

From the change in freezing point and freezing constant of water, the molality of the solution can be determined as follows:

  $m=\frac{\Delta T_f}{K_f}$

Here, molality can be calculated using the above formula.

Now, the molality of the solution is related to the number of moles and mass of solvent (in kg) as follows:

  $m=\frac{n_{\text{solute}}}{M_{\text{solvent}}\left(\text{kg}\right)}$

Here, the mass of solvent is known as this is mass of water taken in the experiment to dissolve the known mass of an unknown compound.

Now, from the known molality and mass of the solvent, the number of moles of the unknown compound (solute) can be determined. The number of moles is related to mass and molar mass as follows:

  $n=\frac{m}{M}$

Here, m is mass and M is the molar mass of the unknown compound.

Since the mass of the unknown compound is known as this is the mass dissolved in water. The molar mass can be calculated from the number of moles and mass as follows:

  $M=n\times m$

Thus, the molar mass of the unknown compound can be determined by performing an experiment based on the concept of freezing-point depression.