Cryoscopic Determination of Molecular Weight PDF

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Ruscitti 1

Cryoscopic Determination of Molecular Weight of a Solute Massimo Ruscitti Jaci SilvaSa October 3, 2018

Ruscitti 2 Abstract: In this experiment, the molecular weight of a solute was determined by examining the freezing point depression of a solution. The freezing points of pure cyclohexane and two cyclohexane/naphthalene solutions were compared to assess freezing point depression. From the difference in freezing points, two molecular weights for naphthalene were calculated, which averaged together to make 128.2 g/mol. When compared to the literature value, the percent error of this experimental molecular weight was 0.02341%, indicating that the calculated value was very accurate. Introduction: The main goal of the experiment is to utilize freezing point depression as a way of calculating the molecular weight of a solute, naphthalene. Freezing point depression occurs from the dissolving of a substance into an otherwise pure sample of solvent, as molecules of solute interfere in the solid structure of the solvent, creating a large increase in free energy1. Since freezing point depression is primarily dependent on the number of moles of solute present, it is a colligative property of solvents. In quantitative terms, the freezing point depression, ΔT, is defined below, where kf is the cryoscopic constant of the solvent and m is the molality of the solute: ∆ T =|k f m|=T pure solvent −T solution (1) Alternatively, the freezing point depression could be measured by taking the difference between the freezing point of a pure solvent and the freezing point of the solution, also shown in Eq. (1). From this simple equation, the molar mass, M, of the solute can be easily calculated by a few

Ruscitti 3 substitutions based on the definition of molality, moles of solute divided by kilograms of solvent, and the conversion factor from moles of solute to grams, as shown below in Eq. (2):

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M=

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k f (mass of solute) (2) ∆ T (kg of solvent )

Experimental Method: To begin, the calibration of a computer-interfaced thermocouple temperature probe was checked by immersing the probe in an ice bath. Once it was determined that the probe did not require recalibration, a large beaker was filled with a salt/ice water mixture, which was stirred using a glass rod to ensure that the salt had dissolved completely into the water. Next, a clean test tube was used to accurately weigh a pure sample of cyclohexane on a balance. The temperature probe was placed in the test tube as it was slowly immersed in the salt/ice water bath. As the computer created a temperature vs. time cooling curve for the cyclohexane, the temperature probe was used to gently stir the solvent. Once the cyclohexane solidified, the test tube was pulled out of the salt/ice water bath. After the cyclohexane melted back into a liquid, a small sample of naphthalene was dissolved into the cyclohexane, and the cooling process was repeated for the solution. For the third trial, a second addition of naphthalene was dissolved into the solution, and the test tube was lowered back into the salt/ice water bath. Finally, the computergenerated data was saved onto a flash drive, and the cyclohexane/naphthalene solution was disposed of in the appropriate waste container.

Results:

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The three curves presented in Fig. 1 show the change in temperature of the cyclohexane solution over a 180-second time interval, after which the solution had completely solidified. Evidently, the cooling curves of the solution begin to plateau at significantly lower temperatures as more solute was added to the test tube. This was not surprising, as it merely confirms that the phenomenon of freezing point depression is a colligative property. More importantly, Eq. (2) can be used to solve for the molecular weight of naphthalene by comparing the changes in freezing point from Trial 1 to Trials 2 and 3, respectively. The calculations for the molecular weight of the solute from the experimental data of Trial 2 and Trial 3 can be found in Eqs. 3 and 4, respectively.

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° C∗kg )(0.1016 g) mol g (3) M 2= =125.1 mol (1.06583° C )∗( 0.01554 kg ) (20.4

°C∗kg )(0.2041 g) mol g M 3= (4) =131.4 mol (2.03868° C )∗(0.01554 kg) (20.4

g g +131.4 125.1 g mol mol ´= M =128.2 (5) 2 mol

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128.2 %Error=

g g −128.17 mol mol ∗100 %=0.02341 % (6) g 128.17 mol

Discussion: Overall, the experimental results were proven to be very accurate. Eq. (5) shows the calculation of the average molecular weight of the solute, which was found to have only a 0.02341% error when compared to the literature value for naphthalene’s molecular weight2. For the calculations of ΔT, the temperature values at t = 70 s were picked because they represented a point in the curves where the temperature values began to level off. Given that, the most significant source of error in the experimental results must have occurred in the recording of time/temperature readings for the solutions. The indeterminate errors which could have contributed to the inaccuracy of the cooling curves would probably pertain to an inconsistent stirring technique. In addition, some error could have resulted from addition of water condensation to the test tube. If any water droplets accidentally fell into the solution as it cooled, it would drastically alter the solution’s composition, and thereby affect the cooling curve of the solution. Fortunately, the accuracy of the calculated masses was very high, so none of these potential errors must have occurred to any large degree. Since only two molecular weights were calculated from the experiment, the precision of the results is fairly low. However, this could have been easily remedied by experimenting with more cooling curves, as the additional trials would minimize the standard deviation.

References:

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Garland, Carl W., et al., Experiments in Physical Chemistry Eighth Edition, 179-187, 2009.

Combined Chemical Dictionary, 91-20-3, http://ccd.chemnetbase.com/faces/chemical/ ChemicalSearchResults.xhtml...