Partial Molar Volume J. Cayabyab, J.R.L. Cu, A.M.S. Leron Department of Mining Metallurgical and Materials Engineering University of the Philippines Diliman
[email protected] Abstract The determination of the Partial Molar Volume of NaCl solutions using a pycnometer yielded results that were precise but still very susceptible to human error. Experimental data showed positive values of partial molar volume of NaCl in each solution. This was due to the weak attraction between the solute (NaCl) and the solvent (H2O) and also causes increase in mixture volumes.
1. Introduction Generally, the volumes of solution components are not additive. Consider two components in one solution: first, the molecules experience different intermolecular forces compared to that of the pure substance. Those is the intermolecular forces between them, say between two water molecules and two ethanol molecules, is different from the intermolecular forces between a water molecule and an ethanol molecule. Second, the example, water and ethanol, have different sizes and shapes, compared to the pure substance counterpart and consequently, the water and ethanol molecule are going to fit together differently. These factors, differences in intermolecular forces and difference in molecular sizes and shapes cause the molecules to pack together differently in a mixture rather than in pure liquids thus, it is true that the volumes are non-additive. [1] For most organic liquids, the average molar volume V/n varies linearly with composition. Aqueous solutions are often anomalous because of an almost 3% volume change when a water-methanol is made up and a volume shrinkage when an electrolyte solution is made. The explanation lies with the reason that the ions attract water molecules so strongly that the resulting compaction more than compensates for the added volume of ions themselves. [2] The partial molar volume of a substance is an intensive property. It depends on the composition of the solution, but not on the
amount of the solution. Also, the partial molar volume depends on the mole fractions and not on the number of moles. Hence it follows that the partial molar volume of a substance is the molar volume of the substance in a solution at a particular composition. [1] The volume of a solution is dependent on its temperature and pressure and the component used to form the mixture. [3] For a binary system with components A and B, the partial component of A is given by:
Where V is the total volume n A is the number of moles A. Partial volume of A is, therefore, the change in volume per mole A added when an infinitesimal amount of A is added to the solution of constant P and T.
Where Va and VB are the partial molar volumes of A and B, respectively. [4] [ 4] In this experiment, the partial molar volumes of water and alcohol solutions will be determined by density measurements using a pycnometer. A pycnometer is a flask with a tight fitting glass stopper with a fine hole. It is used for measuring the density of a solution upon Partial Molar Volume. Page 1 of 5
comparison to a control. It is important to know the specific gravity first. This is done by accurately measuring the mass of the reference liquid. [5] The specific gravity is determined by:
This experiment is intended to have a direct comparison of partial molar volumes by determining the density of the solution. 2. Methodology
corresponding solution. This procedure was done to all the samples, having two replicates each. 3. Results and Discussion The plots of apparent molar volume vs square root of molality for both replicates were showed in Figure 1 and 2, and were found to be almost linear and with negative slopes. With R 2 values of 0.798(replicate1) and 0.9403(replicate 2), the data can be said as almost precise. The partial molar volume of NaCl and water were computed using the slopes and intercepts of the best fit line on each graphs.
2.1 Solution Preparation
200 mL solutions of 1.5M, 0.75M, 0.375M, 0.1875M, and 0.09375M NaCl solutions were prepared. These solutions could be prepared by successive volumetric dilutions wherein each dilution was done with 100mL of solution into a 200-mL volumetric flask and fill it up to the mark with distilled water. 2.2 Pycnometer calibration
Use a clean and dry pycnometer. An aspirator was used to dry it by suction. Also, few rinses of acetone were used for drying. The pycnometer was weighed until a reading of weight difference ±0.01 grams. The pycnometer was filled with the control, distilled water and then covered. Excess liquid were wiped off around the pynometer joint and then as immersed in water bath just below the cap. The water bath is to let the pycnometer reach equilibrium. After which, the pycnometer was removed from the water bath then wiped off any excess liquid from the capillary tip. Weights were measured using the analytical balance. Two replicates were made. 2.3 Experiment
With the 1.5M calibrated pycnometer solution was discarded The pycnometer was
NaCl solution, the was rinsed and the before filling it again. then filled with the
20 e18 m u16 l o14 v r 12 a l o10 m t 8 n e r 6 a p 4 p A 2 0
y = -0.923x + 19.08 R² = 0.798
1.24466 0.87311 0.6152 0.4344 0.30694
√molality
Fig 1. Apparent molar volume vs square root of molality (R1) 20 e m u 15 l o v r a l o 10 m t n e r a5 p p A
y = -1.116x + 19.53 R² = 0.940
0 1.24465 0.87313 0.61524 0.43439 0.30693 √molality
Fig 2. Apparent molar volume vs square root of molality (R2)
Values for partial molar volumes of NaCl and water for each solution were shown in Partial Molar Volume. Page 2 of 5
Table 1 (see appendix). The positive values of partial molar volume of NaCl in each solution are because of the weak attraction between the solute (NaCl) and the solvent (H2O) which causes increase in mixture volumes. Also, positive partial molar volume indicates that interactions between the solvent molecules (H2O-H2O) are stronger compared to the interactions of unlike molecules (NaCl-H2O) in the solutioni. Based on Table 1, increase in the concentration of NaCl increases the partial molar volume of water while decreases the partial molar volume of the NaCl. Errors in the experiment include; inaccurate preparation of solution, pycnometer was not exactly cooled to room temperature, which may affect the actual density of the water/solutions when weighing was conducted; hand moisture when handling the pycnometer contributed to higher measured weight compared to the actual weight. These errors may be prevented if the pycnometer was place in the bath for longer time for it to reach its equilibrium. Also, use of tissue when handling the pycnometer is recommended for more precise measurements.
frequency. Reading of the frequency fluctuates when sample is introduced into the system. The measured data, frequency, is then converted to density. [9] 5. References 1.
Perona (Spring 2010) Partial Molar Volumes. Chem 4012
2.
Adamson, A.W., A Textbook of Physical Chemistry. 1980: J. Chem Educ.
3.
Jaltig Measurement of Partial Molar Volumes. Physical Chemistry Laboratory.
4.
Anonymous Experiment 5Determination of Partial Molar Quantities. Chem 356, 1-9.
5.
Anonymous Experiment 1: partial Molar Volumes. ChE 121 Physical Chemistry 1 Laboratory.
6.
J.P. O’Connell, J.M. Haile
7.
Anton Paar. (n.d.). Density Meter. Österreich.
8.
Stabinger, H. (1994). Density Measurement using modern oscillating transducers.
9.
University of Delaware. (2006). Physical Chemistry Laboratory. Newark.
4. Conclusion and Recommendation The use of pycnometer is the traditional way of determining the partial molar volume of a solution. [8] Therefore, this method can only be reliable at a laboratory scale. Using this method on a large amount of sample might result to erroneous data. However, this method of measuring is very prone to human error. Machines for density determination have been developed such as the DMA 4500 Density Meter which can accurately give data for the concentration and density of the sample and uses and oscillating U-tube. [7] Density meters have high precision than that of pycnometers since such apparatus involves a hollow glass tube which vibrates at a certain
(2005). Thermodynamics: Fundamentals for Applications. Cambridge University Press
Partial Molar Volume. Page 3 of 5
Appendix
Table 1. Derived values for molarity, molality, density, partial molar volume of water and partial molar volume of NaCl 1.5 M NaCl
0.75 M NaCl
0.375 M NaCl
0.1875 M NaCl
0.09375 M NaCl
R1
R2
R1
R2
R1
R2
R1
R2
R1
R2
d (g/cm)
1.05592
1.05593
1.02767
1.02763
1.01274
1.01261
1.00457
1.00461
1.00059
1.00067
m (kg/mol)
1.54917
1.54915
0.76232
0.76235
0.37847
0.37852
0.18870
0.18870
0.09421
0.09420
V NaCl
17.35878
17.45196
17.87318
18.07434
18.23026
18.50635
18.48057
18.80930
18.65704
19.02284
V water
18.08503
18.08840
18.07453
18.07570
18.07094
18.07134
18.06968
18.06982
18.06924
18.06929
Table 2. Experimental data for weight of pycnometer at 27 degree Celsius Empty pycnometer
Pycnometer with water
Trial 1
22.3128
47.6305
Trial 2
22.3129
47.6310
Trial 3
22.3129
47.6305
Mean
22.31287
47.6307
Table 3. Experimental data for weight of each solution 1.5 M NaCl
0.75 M NaCl
0.375 M NaCl
0.1875 M NaCl
0.09375 M NaCl
R1
R2
R1
R2
R1
R2
R1
R2
R1
R2
Trial 1
49.1401
49.1406
48.4246
48.4215
48.0440
48.0399
47.8355
47.8365
47.7338
47.7293
Trial 2
49.1400
49.1406
48.4215
48.4215
48.0433
48.0396
47.8356
47.8362
47.7346
47.7292
Trial 3
49.1403
49.1399
48.4211
48.4211
48.0420
48.0395
47.8355
47.8365
47.7344
47.7394
Mean
49.1402
49.1404
48.4224
48.4214
48.0431
48.0397
47.8355
47.8364
47.7343
47.7326
Sample Calculations:
1. Volume of pycnometer:
2. Density of each solution:
Partial Molar Volume. Page 4 of 5
3. Molality of each solution:
4. Apparent molar volume each solution:
where: W = weight of pycnometer filled to mark with solution W0 = weight of pycnometer filled to mark with pure water We = weight of empty pycnometer M = solute molecular weight
5. Partial Molar Volume of NaCl:
6. Partial Molar Volume of water:
Partial Molar Volume. Page 5 of 5
