Molar Mass Determination by Freezing Point Depression

Introduction

The purpose of this lab was to use freezing point depression techniques to determine the molar mass of camphor. The pure solvent cyclohexane was cooled to determine its freezing point (T_{f (solvent)}). Then a solution of cyclohexane and camphor was cooled until frozen and its freezing point was determined (T_{f (solution)}).

Equation 1 was used to calculate the freezing point depression (∆T_f).

∆T_f = T_f(solvent) – T_f(solution) (1)

The freezing point depression is equal to the cryoscopic constant (K_f) multiplied by the 

molality (m) of the solute particles (eq 2). 

∆T_f  = K_f m = K_f (mol solute/kg solvent) (2)

Equation 3 was then used to determine the molar mass (mm) of the solvent.

MM= (K_f)(g solute)/(kg solvent)(∆T_f) (3)

Procedure

A test tube was sealed with a rubber stopper and placed in a beaker. It was weighed on a top loading balance and then 0.26 g cyclohexane was added. A salt-ice bath was created and then a temperature probe was placed into the test tube. The data collection was started on Logger Pro and the cyclohexane was stirred with the probe while the test tube was stirred in the salt-ice bath simultaneously. Once the cyclohexane was frozen the data collection was stopped. In Logger Pro lines of linear fit were put onto the cooling and frozen sections of the data and they were interpolated to find the freezing point. Two camphor/cyclohexane solutions were created to do trials one and two, and the same procedure was done with each as the cyclohexane.

With equation 1, the results of the graphical analysis were used to calculate the freezing point depression. The molar mass of camphor was calculated for the two trials using equation 2  and the average molar mass was determined.

Detailed procedures may be found in reference 1.

Results 

The data collected to determine the freezing points of the solvent and solution were put into graphs which can be found in Figures 1, 2, and 3.

Figure 1. Cooling curve of cyclohexane solvent.

Figure 2. Cooling curve of the solution in trial one.

Figure 3. Cooling curve of the solution in trial two.

Equations 1, 3 and the data collected from trials (Table 1) were used to calculate the molar mass for the two trials.

Table 1. Data from cyclohexane/camphor solution trials.

Trial	Mass Cyclohexane (g)	Freezing Point of Solvent (°C)	Mass Camphor (g)	Freezing Point of Solution (°C)
1	5.07	7.335	0.26	1.101
2	5.03	7.335	0.26	1.855

The average molar mass of trials one and two was calculated to be 172 g/mol.

Discussion

The mean molar mass of camphor was calculated to be 172 g/mol, which is higher than the known value of 152.17 g/mol.¹ The most likely cause for this lack of accuracy would be from the freezing point of the solvent, which was used to determine ∆T_f  in the calculations of both trials. A ∆T_f value that is too large would cause the calculated molar mass to also be too large.

The calculated freezing point of cyclohexane 7.0585 °C is larger than the known value of 6.5 °C.¹ This error is likely due to a calibration difference of the temperature probes.

References

1. General Chemistry Experiments: A Manual for Chemistry 204, 205, and 206, Department of Chemistry, Southern Oregon University: Ashland, OR, 2010