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					                               Cryoscopic Determination of Molar Mass

                                        By: Stephanie McKinney
                                       Partners: Billy and Chanel

                                   Experiment Completed: 11-19-09
                                         Submitted: 12-3-09




Abstract

        The experimental molecular mass for naphthalene was determined by adding .6g, .9g, and 1.2g

of the substance into a solvent of cyclohexane and graphically determining the freezing point. Once the

freezing points of the naphthalene were determined to be 2.93±.07 οC, 1.10±.05 οC, -.75±.07 οC

respectively, the respective molar mass values were able to be calculated. The molar mass for the

various amounts of naphthalene were determined to be be 168±5 g/mol, 170±2 g/mol, and 170±4 g/mol

respectively.
Results


          This equation was used in order to determine the density of the cyclohexane because it was

temperature dependant, where the variable t was room temperature.

                                                                                                      1
                                                                                                       Eq 1




          This equation was used to determine the experimental value for the molar mass of naphthalene

where g is the mass of the solute, G is the mass of the solvent, Kf is the molal freezing-point depression

constant, and ΔTf is the difference in the literature value freezing point of cyclohexane and the average

freezing points of the various naphthalene value.

                                                                                                      1
                                                                                                          Eq 2




          This equation was also used to determine the experimental value for the molar mass of

naphthalene where the only different variables were kf which is the correction constant factor.

                                                                                                      1
                                                                                                          Eq 3
Results

          These values were used in coordination with Eq 1 in order to determine the density and

eventually the mass of the cyclohexane used.



Table 1: Determination of Density and Mass of Cyclohexane



                           Room Temp                           Volume
                                ο           Density g/cm3                 Mass g
                                  C                             cm3
                            24.05±.05      0.77477±.00005      25.0±.5   19.4±.4




          These values were the freezing points of the cyclohexane and naphthalene at the various

masses. They were graphically determined in Figure 1-Figure 8 by plotting the temperature versus time

of each trial.



Table 2: Freezing Points of Cyclohexane and Naphthalene




                                        Trial 1 οC          Trial 2 οC        Average οC
                    Cyclohexane         4.10±.05            4.15±.05           4.13±.07
                  .6g Naphthalene       2.80±.05            3.05±.05           2.93±.07
                  .9g Naphthalene       1.10±.05            1.10±.05           1.10±.05
                 1.2g Naphthalene       -.70±.05            -.80±.05           -.75±.07
        These values were determined using Eq 2 and Eq 3 to determine the experimental mass of the

naphthalene at .6g, .9g, and 1.2g. Presented is the literature value of naphthalene along with the

percent deviations.



Table 3;Experimental Molecular Mass of Naphthalene

                             Molar Mass            Molar Mass
                                                                      Literature(g/mol)       % Deviation
                              (g/mol)               (g/mol)
    .6g Naphthalene            168±5                 167±6                  128.17              31±3%
    .9g Naphthalene            170±2                 169±8                  128.17               33±2
    1.2g Naphthalene          170 ±4                170± 20                 128.17              33±3%




Discussion
        The experimental molar masses for .6g, .9g, and 1.2g of naphthalene using Eq 2 were

determined to be 168±5, 170±2, and 170±4 grams per mol respectively. With the correction value for

the molal freezing point depression constant, Eq 3, the molecular weight of naphthalene was calculated

to be 167±6, 169±8, and 170± 20. When comparing the literature value of the naphthalene to those

values calculated from Eq 2 the percent deviations were determined to be 31±3%, 33±2%, and 33±3%

respectively. Once the molar mass values were determined using Eq 2 they were then plotted against

their respective average freezing point of 2.93±.07 οC, 1.10±.05 οC, -.75±.07 οC. A trend line was then

extrapolated back to the y-axis to determine the graphical molar mass of 169.9±.6 grams per mole.

When this value was compared to that of the literature value a percent deviation of 32.6±.7% was

calculated. The most accurate molar mass value was that of the .6g of naphthalene and the least

accurate was that of the 1.2g of naphthalene. This agrees with the predicted trend because if there is

less of the substance within the solvent, the solute is more likely to freeze in its entirety. If there is a

generous amount of the solute in the solvent, there is a more likely hood that the solute would not

entirely freeze giving an inaccurate freezing point, and therefore and inaccurate molar mass value.
        With this experiment there were a few sources of error because all of the data that was

recorded solely depended on the readings from the machines. For example, if the cooling machine

wasn’t at the desired temperature the substance may no freeze completely. If the cooling machine was

reporting a value that was below the freezing point, but it wasn’t actually at that temperature, the

solution may not completely freeze as desired giving an inaccurate recording of the freezing point. The

biggest source of error would be due to the thermistor reading. If there is a loose connection

somewhere throughout the apparatus, the resistance reading would be way off. If the resistance varied

that would then cause the calculated temperature to vary, providing an inaccurate freezing point. Also,

if the machine wasn’t calibrated accurately to the calibrated plot that we were given the values of the

freezing point would also be off. This calibration plot was used in order to determine the temperature of

the substance over time, using the values that were recorded for the resistance.




References
1
Garland, W.C.; Nibler, W.J.; Shoemaker,P.D. Experiments in Physical Chemistry,8; Hodge,L.H.; Thomas

        Timp: New York, 2009; 179-187.

				
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