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Solution Molecular Weight of Small Molecules

Module by: Tawana Robinson, Andrew R. Barron. E-mail the authorsEdited By: Andrew R. Barron

Introduction

The cryoscopic method was formally introduced in the 1880’s when François-Marie Raoult (Figure 1) published how solutes depressed the freezing points of various solvents such as benzene, water, and formic acid. He concluded from his experimentation “if one molecule of a substance can be dissolved in one-hundred molecules of any given solvent then the solvent temperature is lowered by a specific temperature increment”. Based on Raoult’s research, Ernst Otto Beckmann (Figure 2) invented the Beckmann thermometer and the associated freezing - point apparatus (Figure 3), which was a significant improvement in measuring freezing - point depression values for a pure solvent. The simplicity, ease, and accuracy of this apparatus has allowed it to remain as a current standard with few modifications for molecular weight determination of unknown compounds.

Figure 1: French chemist François-Marie Raoult (1830 - 1901).
Figure 1 (Picture 15.png)
Figure 2: German chemist Ernst Otto Beckmann (1853 - 1923).
Figure 2 (Picture 16.png)
Figure 3: Beckmann differential thermometer and freezing point depression apparatus
Figure 3 (graphics1.png)

The historical significance of Raoult and Beckmann’s research, among many other investigators, has revolutionized a physical chemistry technique that is currently applied to a vast range of disciplines from food science to petroleum fluids. For example, measured cryoscopic molecular weights of crude oil are used to predict the viscosity and surface tension for necessary fluid flow calculations in pipeline.

Freezing point depression

Freezing point depression is a colligative property in which the freezing temperature of a pure solvent decreases in proportion to the number of solute molecules dissolved in the solvent. The known mass of the added solute and the freezing point of the pure solvent information permit an accurate calculation of the molecular weight of the solute.

In Equation 1 the freezing point depression of a non-ionic solution is described. Where ∆Tf is the change in the initial and final temperature of the pure solvent, Kf is the freezing point depression constant for the pure solvent, and m (moles solute/kg solvent) is the molality of the solution.

Eq48.jpg
(1)

For an ionic solution shown in Equation 2, the dissociation particles must be accounted for with the number of solute particles per formula unit, i (the van’t Hoff factor).

Eq49.jpg
(2)

Cryoscopic procedure

Cryoscopic apparatus

For cryoscopy, the apparatus to measure freezing point depression of a pure solvent may be representative of the Beckmann apparatus previously shown in Figure 3. The apparatus consists of a test tube containing the solute dissolved in a pure solvent, stir bar or magnetic wire and closed with a rubber stopper encasing a mercury thermometer. The test tube component is immersed in an ice-water bath in a beaker. An example of the apparatus is shown in (Reference). The rubber stopper and stir bar/wire stirrer are not shown in the figure.

Figure 4: An example of a cryoscopic apparatus. Adapted from http://www.lahc.cc.ca.us/classes/chemistry/arias/Exp%2012%20-%20Freezing%20Point.pdf
Figure 4 (Picture1X.jpg)

Sample and solvent selection

The cryoscopic method may be used for a wide range of samples with various degrees of polarity. The solute and solvent selection should follow the premise of like dissolved like or in terms of Raoult’s principle of the dissolution of one molecule of solute in one-hundred molecules of a solvent. The most common solvents such as benzene are generally selected because it is unreactive, volatile, and miscible with many compounds. Table 1 shows the cryoscopic constants (Kf) for the common solvents used for cryoscopy. A complete list of Kf values are available in Knovel Critical Tables.

Table 1: Cryoscopic constants (Kf) for common solvents used for cryoscopy.
Compound Kf
Acetic Acid 3.90
Benzene 5.12
Camphor 39.7
Carbon disulfide 3.8
Carbon tetrachloride 30
Chloroform 4.68
Cyclohexane 20.2
Ethanol 1.99
Naphthalene 6.80
Phenol 7.27
Water 1.86

Cryoscopic Method

The detailed information about the procedure used for cryoscopy is shown below:

  1. Step 1. Weigh (15 to 20 grams) of the pure solvent in a test tube and record the measured weight value of the pure solvent.
  2. Step 2. Place a stir bar or wire stirrer in the test tube and close with a rubber stopper that has a hole to encase a mercury thermometer.
  3. Step 3. Place a mercury thermometer in the rubber stopper hole.
  4. Step 4. Immerse the test tube apparatus in an ice-water bath.
  5. Step 5. Allow the solvent to stir continuously and equilibrate to a few degrees below the freezing point of the solvent.
  6. Step 6. Record the temperature at which the solvent reaches the freezing point, which remains at a constant temperature reading.
  7. Step 7. Repeat the freezing point data collection for at least two more measurements without a difference less than 0.5 °C between the measurements.
  8. Step 8. Weigh a quantity of the solute for investigation and record the measured value.
  9. Step 9. Add the weighed solute to the test tube containing the pure solvent.
  10. Step 10. Re - close the test tube with a rubber stopper encasing a mercury thermometer.
  11. Step 11. Re-immerse the test tube in an ice water bath and allow the mixture to stir to fully dissolve the solute in the pure solvent.
  12. Step 12. Measure the freezing point and record the temperature value.

Note:

Allow the solution to stir continuously to avoid supercooling.

The observed freezing point of the solution is when the temperature reading remains constant.

Sample calculation to determine molecular weight

Sample data set

Table 2 represents an example of a data set collection for cryoscopy.

Table 2: Example of a data set collection for cryoscopy
Parameter Trial 1 Trial 2 Trial 3 Avg
Mass of cyclohexane (g) 9.05 9.00 9.04 9.03
Mass of unknown solute (g) 0.4000 0.4101 0.4050 0.4050
Freezing point of cyclohexane (°C) 6.5 °C 6.5 °C 6.5 °C 6.5 °C .
Freezing point of cyclohexane mixed with unknown solute (°C) 4.2 °C 4.3 °C 4.2 °C 4.2 °C

Calculation of molecular weight using the freezing point depression equation

Calculate the freezing point (Fpt) depression of the solution, 

TΔf (from Table 2).

Eq52X.jpg
(3)
Eq51.jpg
(4)
Eq52.jpg
(5)

Calculate the molal concentration, m, of the solution using the freezing point depression and Kf (see Table 1 and Table 2).

Eq53.jpg
(6)
Eq54.jpg
(7)
Eq55.jpg
(8)

Note:

Eq55X.jpg

Calculate the MW of the unknown sample.

Note:

i = 1 for covalent compounds in Equation 2.
Eq56.jpg
(9)
Eq57.jpg
(10)
Eq58.jpg
(11)

Exercise 1

Nicotine Figure 5 is an extracted pale yellow oil from tobacco leaves that dissolves in water at temperatures less than 60 °C. What is the molality of nicotine in an aqueous solution that begins to freeze at -0.445 °C? See Table 1 for Kf values.

Figure 5: The chemical structure of nicotine.
Figure 5 (nicotine.jpg)
Solution
Eq59.jpg
(12)
Eq60.jpg
(13)
Eq61.jpg
(14)

Exercise 2

If the solution used in Exercise 1 is obtained by dissolving 1.200 g of nicotine in 30.56 g of water, what is the molar mass of nicotine?

Solution
Eq62.jpg
(15)
Eq63.jpg
(16)
Eq64.jpg
(17)

Exercise 3

What would be the freezing point depression when 0.500 molal of Ca(NO3)2 is dissolved in 60 g of water?

Solution
Eq65.jpg
(18)
Eq66.jpg
(19)
Eq67.jpg
(20)

Exercise 4

Calculate the number of weighed grams of Ca(NO3)2 added to the 60 g of water to achieve the freezing point depression from Exercise 3? The MW of Ca(NO3)2 is 164.088 g/moles.

Solution
Eq68.jpg
(21)
Eq69.jpg
(22)
Eq70.jpg
(23)

Bibliography

  • Knovel Critical Tables, 2nd Ed., Knovel, New York (2008).
  • http://www.lahc.cc.ca.us/classes/chemistry/arias/Exp%2012%20-%20Freezing%20Point.pdf
  • H. C. Jones, The Modern Theory of Solutions: Memoirs by Pfeffer, Van't Hoff, Arrhenius, and Raoult, Harper and Brothers, New York (1899).
  • E. Beckmann, Z. Anorg. Allg. Chem., 1910, 67, 17.
  • H. P. Ronningsen. Energ. Fuel., 1993, 7, 565.
  • D. A McQuarrie, P. A Rock, and E. B. Gallogly, General Chemistry, University Science Books, Mill Valley (2011).

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