Partial molal volume PDF

Title	Partial molal volume
Author	Tafline Sia
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Experiment 4 Partial molal volume Tafline Grace B. Sia Department of Chemistry, Ateneo de Manila University Date Started: 24 November 2020 || Date Completed: 1 December 2020 Results and Discussion Unlike bulk mass, bulk volume is not an additive property. This is because the mixing process is often ...

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Experiment 4

Partial molal volume

Tafline Grace B. Sia Department of Chemistry, Ateneo de Manila University Date Started: 24 November 2020 || Date Completed: 1 December 2020 Results and Discussion Unlike bulk mass, bulk volume is not an additive property. This is because the mixing process is often accompanied by a chemical reaction such as solvation. As such, the molecular packing pattern for real solutions will not be the same as that of the individual substances. For example, while pure water exhibits dipole-dipole interactions among its molecules, ion-dipole interactions are present in an aqueous sodium chloride solution because sodium and chloride ions exist as hexaaqua ions in aqueous media. This means that the bulk densities—and volumes—of sodium chloride solutions will not be equal to that of pure water under the same set of conditions (1). Partial molal volume is a thermodynamic quantity that relates the change in the total volume of a mixture per mole of pure substance added to the mixture (2). Because it is the ratio of infinitesimal changes in two extensive properties, partial molal volume is an intensive property. The partial molal volume of a solute is the volume per mole of solute in the mixture (3). It is usually determined experimentally via the constant T-and-P addition of solute j to a solution (4). A related quantity is the apparent molal volume, which ascribes all changes in the effective volume of the solution to the solute alone. In contrast to this, the partial molal volume accounts for the effects of both the solvent and the solute on the effective volume of the solution (3). Because the apparent molal volume can be measured easily, it is often the measurand of choice in physical chemistry experiments. Experimentally-measured apparent molal volumes can be related to the partial molal volumes of both the solute and the solvent using the experimental parameters molality and density (5). This is done because partial molal volume is a thermodynamic quantity that is of central importance in the field of chemical equilibrium. It helps describe the nature of intermolecular interactions between different components of a mixture (5, 6). As partial molal volumes account for the effect of the molecular environment on the volume that is occupied by solute and solvent molecules, it is both concentration and temperature-dependent. For some mixtures, the addition of the solute decreases the partial molal volume of the solvent, whereas the addition of some types of solute causes an increase in the solvent’s partial molal volume. These are all due to changes in the packing of molecules as a result of differences in ionic charge densities, which in turn affect the strength and nature of ionic interactions in water. The partial molal volume of ionic salts in water is an especially important parameter that allows oceanographers and environmental scientists to understand the physical chemistry of seawater, which is composed mainly of aqueous sodium chloride. This is because knowing the partial molar volume of solute (sodium chloride) in aqueous solution (seawater) helps predict changes in solubility in response to changes in pressure. If the partial molar volume in the solution is less than its molar volume when it is not in solution, then an increase in pressure will result in an increase in the solubility of the solute when it is dissolved in the solvent (7). In this experiment, the apparent molal volumes of five aqueous sodium chloride solutions, each of different concentration, were measured as a function of concentration using density measurements obtained through the use of a pycnometer at constant temperature and pressure. The experiment was divided into three parts. Firstly, approximately 3.0 M of stock sodium chloride solution was prepared using volumetric procedures. Volumetric procedures were then used to prepare solutions of 1/2, 1/4, 1/8, and 1/16 of the initial molarity. Secondly, the pycnometer was calibrated by means of weighing the maximum amount of pure water that the pycnometer could contain. The value obtained was thereafter used as the volume of the solutions. Thirdly, the empty pycnometer was weighed, filled to mark with pure water, and weighed again. It was then emptied and filled to mark with solution, equilibrated at room

temperature, and weighed once more. This was done in duplicate to enable statistical averaging. The procedure was repeated for each of the solutions, and the computed densities (Table 1) were used to determine the apparent molal volume of sodium chloride in aqueous solution as a function of molality. Then the partial molal volume of sodium chloride V 2 in water as a function was calculated using the equation

where ϕ 0 is the apparent molal volume of sodium chloride extrapolated to infinite dilution (where ionic interactions are no longer observed, but only ion-dipole interactions within hydrated ions), √m is the square root of the molality of the solution, and dϕ/d√m is the slope of the apparent molal volume of sodium chloride versus the square root of the molality. The apparent molal volume of NaCl increased along with the molality of the NaCl-water solution (Figure 1, Table 2). This is because strong attractions between the NaCl ions and the water molecules allowed for tight packing of the water molecules in the solvation shells around the NaCl ions, thus decreasing the solution’s volume relative to the volume of the pure solvent (4). A similar trend was observed for the partial molal volume of NaCl in aqueous solution. Additionally, the apparent molal volume of NaCl in aqueous solution decreased sharply as the solution became more diluted (Figure 1). However, the apparent molal volume of NaCl in aqueous solution did not have the strong linear relationship with the square root of the molality that was predicted by the Debye-Huckel theory for dilute solutions. Table 1. Molality of aqueous NaCl solutions Solution

Actual molarity of solution (M)

Average mass of solution (g)

Volume of solution (mL)

Density of solution (g/mL)

Molality (m)

1

3.015 ± 0.008

124.9 ± 0.1

113.7 ± 0.1

1.099 ± 0.001

3.270 ± 0.010

1/2

1.508 ± 0.008

120.2 ± 0.1

113.7 ± 0.1

1.057 ± 0.001

1.557 ± 0.008

1/4

0.754 ± 0.008

117.3 ± 0.1

113.7 ± 0.1

1.031 ± 0.001

0.764 ± 0.008

1/8

0.377 ± 0.008

116.5 ± 0.1

113.7 ± 0.1

1.024 ± 0.001

0.376 ± 0.008

1/16

0.188 ± 0.008

114.8 ± 0.1

113.7 ± 0.1

1.009 ± 0.001

0.189 ± 0.008

Figure 1. Apparent molal volume of sodium chloride as a function of molality. As evinced by the correlation coefficient R2 , there was a moderately strong positive linear relationship between the apparent molal volume of sodium chloride and the molality of the solution.

Table 2. Apparent molal volumes of NaCl in NaCl-water mixtures of varying compositions Solution

Molality m (m)

Apparent molal volume Φ of NaCl in NaCl-water mixture (cm3/mol)

1

3.270 ± 0.010

9.641 ± 0.293

1/2

1.557 ± 0.008

-11.656 ± 0.711

1/4

0.764 ± 0.008

-56.144 ± 1.891

1/8

0.376 ± 0.008

-147.117 ± 5.943

1/16

0.189 ± 0.008

-267.019 ± 17.868

Using extrapolation, the partial molal volume of NaCl at infinite dilution at a temperature of 31.0°C was found to be -274.264 ± 66.908 cm3/mol (Figure 2), while that of water was found to be 18.069 ± 66.908 (Figure 3). In comparison, the literature value for the former is 16.62 ± 0.04 cm3/mol at 25.0°C and 17.28 ± 0.05 cm3/mol at 35.0°C (8). The large discrepancy can be said to be the result of several factors. Firstly, extrapolation to infinite dilution requires very accurate determinations of densities at low concentrations of NaCl because the densities of such solutions are only very slightly different from the density of pure water. However, the makeshift polypropylene pycnometer used in the experiment was such that accurate density measurements were very difficult to obtain. This is because unlike glassware, certain types of plastic containers, especially those made of polypropylene, can expand to accommodate more fluid (9). As such, the amount of fluid the pycnometer could contain was likely not constant throughout the experiment. This would have resulted in inaccurate density measurements and significant scatter to the data. Additionally, the digital balance used in the experiment was uncalibrated and readable only up to the first decimal place. All these prevented density measurements of the required level of accuracy from being taken.

Figure 2. Partial molal volume of sodium chloride as a function of molality.

Figure 3. Partial molal volume of water as a function of molality.

Another factor that could have contributed to the discrepancy between the experimental data and the literature values was the presence of impurities in the salt. Due to practical limitations, the starting sodium chloride that was used to prepare the aqueous sodium chloride solutions was not of analytical grade. Instead, it was merely crude rock salt that was filtered using a cloth filter. Thus it is highly probable that it contained other trace minerals that were dissolved in water along with the sodium chloride. This meant that the mixture was most probably not a two-component system. Since the formulas used for the calculation of the partial molal volume of NaCl was for binary solutions only, this would have meant that significant errors were introduced to the data due to the inappropriate use of formulas. Lastly, the moisture content of the sodium chloride that was used in the preparation of the aqueous sodium chloride solutions was not known. However, the formulas for the partial molal volume of NaCl in aqueous solution operated under the assumption that the reagents used were 100% pure. It is possible that there was a significant amount of starting water that was present as an impurity in the sodium chloride which was unaccounted for in the calculations. Despite the large discrepancy between the experimental data and the literature values, the curves of the partial molal volumes of the solute (Figure 2) and that of the solvent (Figure 3) behaved in accordance with the Gibbs-Duhem equation, which states that the partial molar derivative of a component in a mixture cannot change without causing a change in the partial molar derivative of the other components. Therefore, for a binary mixture, an increase in one component’s partial molar volume relative to its molal volume as a pure substance must be accompanied by a decrease in the other component’s partial molal volume in solution (10, 11). As shown in Figures 2 and 3, the higher the molality, the higher the partial molal volume of sodium chloride and the lower the partial molal volume of water in aqueous sodium chloride solution. Calculations Part A. Calibration of pycnometer

------------------------------------------------------------------------------------------------------------------------Part B. Molarity of solution 1

------------------------------------------------------------------------------------------------------------------------Part C. Molality of solution 1

-------------------------------------------------------------------------------------------------------------------------

Part D. Apparent molal volume of NaCl in solution 1

------------------------------------------------------------------------------------------------------------------------Part E. Partial molal volume of NaCl in solution 1

Part F. Partial molal volume of water in solution 1

Conclusion The objectives of the experiment were to measure the partial molal volumes of aqueous sodium chloride solutions at ambient temperature and pressure. As shown by the experimental results, these objectives were fulfilled using the appropriate laboratory and statistical methods. However, as mentioned in the preceding paragraph, there was a relatively high degree of uncertainty associated with the measurements. Given this, it is recommended that future runs of the experiment employ the use of a calibrated analytical balance for mass determinations. Additionally, in order to increase the accuracy of the experimental data, it is crucial that a pycnometer with walls that are relatively inflexible (such as those made of glass) be used instead of a flexible one like the polypropylene sauce container used in the experiment. Finally, it is suggested that reagent-grade sodium chloride with known moisture content and purity be used to prepare the aqueous sodium chloride solutions for the experimental determination of partial molal volumes through density measurements. References (1) Perkins, R. Assumptions: Part 1 — Preparing solutions, 2017. University of Waterloo. https://uwa terloo.ca/chem13-news-magazine/november-2017/feature/assumptions-part-1-preparing-solut ions (accessed November 23, 2020). (2) Atkins, P.; de Paula, J. Simple mixtures. Physical Chemistry, 10th ed.; W.H. Freeman and Company: New York, N.Y., 2014; pp 178-243. (3) Colby College. Partial Molal Volume, 2006. Department of Chemistry, Colby College. https:// www.colby.edu/chemistry/PChem/lab/PartMolalV.pdf (accessed November 23, 2020).

(4) Levine, I. N. Solutions. Physical Chemistry, 6th ed.; McGraw-Hill: New York, N.Y., 2009; pp 263-293. (5) Sime, R. J. Physical Chemistry: Methods, Techniques, and Experiments; Holt Rinehart & Winston: New York, N.Y., 1990. (6) Vilseck, J. Z.; Tirado-Rives, J.; Jorgensen, W. L. Determination of partial molar volumes from free energy perturbation theory. Phys. Chem. Chem. Phys. [Online] 2015, 17(13), 8407-8415. https://pubmed.ncbi.nlm.nih.gov/25589343/ (accessed December 8, 2020). (7) Garland, C. W.; Nibler, J. W.; Shoemaker, D. P. Solutions. Experiments in Physical Chemistry, 8th ed.; McGraw-Hill: New York, N.Y., 2009; pp. 172-198. (8) Millero, F. The apparent and partial molal volume of aqueous sodium chloride solutions at various temperatures. J. Phys. Chem. [Online] 1970, 74(2), 356-362. https://pubs.acs.org/doi/abs/10.1021/j100697a022 (accessed December 1, 2020). (9) British Plastics Federation. Polypropylene (PP). British Plastics Federation. https://www.bpf. co.uk/plastipedia/polymers/pp.aspx (accessed December 8, 2020). (10) Grima, J. Chemical potential, simple mixtures, chemical reactions and equilibria, 2007. University of Malta.http://staff.um.edu.mt/jgri1/teaching/che2372/notes/05/02/01/gibbs_ duhem.html#:~:text=The%20significance%20of%20the%20Gibbs,increases%2C%20the%20 other%20must%20decrease (accessed December 8, 2020). (11) Fleming, P. Chemical Potential, 2020. ChemLibreTexts. https://chem.libretexts.org/Bookshelves /Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Physical_Chemistry_(Fle ming)/07%3A_Mixtures_and_Solutions/7.03%3A_Chemical_Potential (accessed December 8, 2020)....