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

Titration Analysis of Weak Acid Solutions: Potassium Hydrogen Phthalate and Citric Acid in Fruit Juice

Introduction

The purpose of this lab was to determine the citric acid concentration in commercial fruit juice. This was achieved by titration of a sample of fruit juice with standardized sodium hydroxide. Sodium hydroxide is hygroscopic and had to be standardized, which was achieved using KHP (hydrogen phthalate, KHC₈H₄O₄)(eq 1).

KHC₈H₄O₄(aq) + NaOH(aq) KNaC₈H₄O₄(aq) + H₂O(l) (1)

In the second part of this lab the standardized base was used to determine the concentration of citric acid in lemon juice (eq 2). 

H₃C₆H₅O₇(aq) + 3NaOH(aq) Na₃C₆H₅O₇(aq) + 3H₂O(l) (2)

The neutralization point of the base and acid were found with titration methods.

Procedure

A standard solution of sodium hydroxide was created by dissolving 1.05 g of sodium hydroxide pellets into approximately 500 mL water. Four samples of approximately 0.4 g KHP were weighed and each was put into separate Erlenmeyer flasks. Approximately 50 mL of distilled water and three drops phenolphthalein were added to each sample. The buret filled with the sodium hydroxide solution and it was titrated into each sample until the indicator turned pink. The molarity of each trial was calculated. The average and standard deviation of the values that agreed within 

0.0005 M were calculated.

Distilled water, indicator, and lemon juice were put into Erlenmeyer flasks to create three samples. Each sample was titrated and the amount of sodium hydroxide required to turn the indicator pink was recorded. The molarity of citric acid in the juice sample, the weight/weight percent and the weight/volume percent of citric acid were calculated for each of the trials, along with the averages and standard deviations. A pipet was used to measure 2.00 mL of lemon juice, which was weighed and it’s density calculated.

Detailed procedures can be found in reference 1.

Results 

Table 1 shows the mass of KHP, the initial buret volume, the final buret volumes, and the concentration of sodium hydroxide for each trial done during the standardization of sodium hydroxide.

Table 1. Data collected during standardization of NaOH.

Sample	Mass KHP (g)	Initial Buret Volume (mL)	Final Buret Volume (mL)	[NaOH]
1	0.4178	0.51	44.11	0.04692
2	0.4051	0.41	42.01	0.04768
3	0.4072	0.39	42.38	0.04749
4	0.4097	0.62	42.99	0.04735

The average [NaOH] of samples 2, 3, and 4 was 0.04751 ± 0.00017 M.

Table 2 shows the volumes of juice, the initial buret volumes, and final buret volumes  from the titration of lemon juice with standardized sodium hydroxide.

Table 2.  Data collected during the titration of lemon juice with standardized NaOH.

Sample	Juice Volume (mL)	Initial Buret Volume (mL)	Final Buret Volume (mL)
1	2.00	0.65	32.69
2	2.00	0.97	32.21
3	2.00	0.32	32.28

Table 3 shows the citric acid concentration, the weight/weight percent, and the weight/volume percent of citric acid in the final solution. 

Table 3. Data calculated from titration of lemon juice with standardized NaOH.

Sample	Citric Acid Concentration (mol/L)	Wt/Wt % Citric Acid	Wt/Vol % Citric Acid
1	0.2537	3.891	4.874
2	0.2474	3.794	4.752
3	0.2531	3.881	4.862
Average	0.2514	3.855	4.830
Standard Deviation	0.0034	0.053	0.067

References

1. General Chemistry Experiments: A Manual for Chemistry 204, 205, and 206, Department of Chemistry, Southern Oregon University: Ashland, OR, 20010