Accuracy, Repeatability, and Limitations for Determination of Chemical

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Accuracy, Repeatability, and Limitations for Determination of Chemical Activities from Vapor Pressure Osmometry Michael Francis Gray, and Mikael Nilsson Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b03129 • Publication Date (Web): 09 Oct 2018 Downloaded from http://pubs.acs.org on October 14, 2018

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is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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Analytical Chemistry

Accuracy, Repeatability, and Limitations for Determination of Chemical Activities from Vapor Pressure Osmometry

Michael F. Gray1 and Mikael Nilsson1,2

1. Department of Chemical Engineering and Materials Science 2. Department of Chemistry University of California Irvine Irvine, CA, 92697-2575, USA

Abstract Vapor pressure osmometry presents a convenient method to measure chemical activity. The work presented here was carried out to provide confidence in using this technique for a VPO model that does not utilize the ‘hanging-drop’ method. While validation studies are available for certain models of vapor pressure osmometers, none was located for the UIC Jupiter 833 osmometer. This study addresses that need by providing a comparison between original experimental data on sodium chloride, calcium chloride and sodium sulfate solutions to values calculated using the Pitzer equations. A comparison is also made for experimental data on sucrose with a literature correlation. This study briefly reviews the assumptions going into the equation used to relate the osmometer signal to

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the diluent activity in order to identify potential sources of the error and the noise in the data. The experimental data shows that the UIC 833 osmometer yields diluent activity values accurate to an average of 0.02%, allowing calculation of osmotic coefficients and solute activity coefficients. Further studies need to be conducted on the accuracy at concentrations above 1.4 molal. Qualitatively, however, comparison suggests the UIC Jupiter 833 osmometer yields more scatter in the experimental data than the Knauer instruments. Using more uniform mesh caps on the thermistors could possibly reduce that scatter. Finally, we show that replacing the glass thermistors with in-house made thermistors with Teflon incorporated in the structure give reproducible results and that certain modifications to the design are possible without losing accuracy in the measurements.

Keywords: Vapor Pressure Osmometry; Chemical Activities; Osmotic Coefficients; Pitzer Parameters


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Introduction Vapor pressure osmometry (VPO) is a technique to experimentally measure the chemical activity of a volatile diluent in a binary mixture with a semi-dilute, non-volatile solute. Several past experimental studies demonstrate the accuracy of the Knauer1 instrument (a hanging-drop type) vapor pressure osmometer2,3 in measuring chemical activity and osmotic coefficients, but no prior assessment using a UIC Inc. Jupiter 833 vapor pressure osmometer was found in the literature. The goal of the present work is to provide such a study. A vapor pressure osmometer4–6 operates by using a pair of matched thermistors to measure the temperature difference between a drop of a solution and a drop of pure diluent when both are held in a thermostatted chamber that is nearly saturated with diluent vapor. Condensation and evaporation occurs on the solution drop and diluent drop, respectively, leading to a temperature difference between the drops that is directly related to the diluent activity in the solution drop. In turn, the thermistor circuit of the osmometer outputs either a resistance or voltage signal that is directly proportional to that temperature difference. The accuracy of a vapor pressure osmometer can be impacted by a number of conditions including sample dilution, drop size effects, thermistor self-heating, bridge voltage dependency, and solute build up in the resevoir.7–13 The severity of these effects is dependent on the instrument design5,11,14,15 and careful design of the measurement cell and electronics5,6,11 can promote accurate molecular weight determination.11,16 Despite the reported issues, VPO can yield accurate chemical activity values and osmotic coefficents.2,3,9,17,18 In particular, the work of Widera et al.2 demonstrates that VPO can be



more precise than direct vapor pressure measurements. One major difference from a hanging-drop type VPO is that the UIC Jupiter 83319 uses standing thermistors with a mesh cap placed on each. The liquid is placed from the top onto the mesh cap. Figure S0 in the ESI show the differences between the instrument used here and a typical hanging-drop VPO. According to the manufacturer “The thermistor design greatly improves reproducibility between users and removes the “technique” variable of other osmometers.” Although this set up is similar to the socalled ‘improved’ instrument described by Dohner6, the performance of the UIC version still requires verification. Seemingly minor changes to the instrument can be expected to impact the accuracy. For example, a change to the geometry of the mesh caps could alter the instrument behavior. Additionally, the repeatability of molecular weight measurements for the UIC Jupiter 833 osmometer was cited to be only within 15%.20 The same research group also noted a substantial variation of the signal between measurements.21 Noticeable signal fall off has also been observed,22 in line with speculation that designs with mesh caps may be more prone to sample dilution compared to the hanging drop design.11 Those reasons spur this attempt to empirically assess the accuracy of chemical activity and osmolality measurements made using the UIC Jupiter 833 osmometer. Studies of chemical activity, osmolality, and aggregation using vapor pressure osmometry can involve relatively high solute concentrations23–26 compared to those recommended in overviews of the technique.4 Over the course of such experiments at higher concentrations, the solute in the liquid reservoir could potentially build up to amounts that may significantly impact the results, as shown by Bersted.14 For molecular


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weight measurements, on the other hand, the vapor pressure reduction due to the solute build up in the reservoir is unlikely to significantly change the accuracy.11 Additionally, the changing viscosity, heat transfer, and diffusion rates in the liquid drop could begin to significantly affect the accuracy of the measurement. While a calibration measurement can empirically correct for some of these changes, the problem would be more pronounced as the properties of the solutions of interest and the calibration solutions diverge. Such issues highlight the need for this experimental assessment of the UIC Jupiter 833 osmometer. The study is all the more relevant as data quality is a recognized issue in experimental thermodynamics.27,28 The analysis in this study also draws attention to the use of VPO at high concentrations without proper validation, a problem prevalent regardless of the instrument used. The lower number of studies conducted with the UIC 833 osmometer likely explains why an assessment has yet to be done. A Google Scholar literature search as of 7/3/2018 for ‘UIC OR Jupiter vapor pressure osmometer’ yields 295 results, whereas a search for ‘Knauer vapor pressure osmometer’ yields 2,890 results. To perform the experimental assessment, data was collected for several wellcharacterized binary aqueous systems. Water activity, the osmotic coefficient and the activity coefficient of the solute were calculated from the experimental data and compared to values from literature correlations. Data for sodium chloride was used to calibrate the instrument. The solutes measured were potassium nitrate, sodium sulfate, calcium chloride and sucrose. Results are compared to activities calculated with the



Pitzer equation for the salt solutions, and a literature correlation29 for the sucrose solution. Experimental All solutions were prepared gravimetrically in Qorpak® sample vials with PolyCone lined phenolic caps using a Mettler Toledo XS105d analytical balance, calibration verified regularly using Mettler Toledo 5g/100g standard weights. Initial stock solutions were prepared by dissolving weighed amounts of each crystalline powder, and subsequent solutions were prepared by dilution. The sucrose, and potassium nitrate were sourced from Fisher Scientific; the sodium chloride and calcium chloride dihydrate were sourced from Macron Fine Chemicals; and the sodium sulfate originated from Ricca Chemical Company. These materials were all ACS reagent grade with a minimum purity of 99%. The water used for all solutions and as the VPO diluent was in-house deionized water further purified by a NANOpure™ 18.2 MΩ unit followed by nitrogen sparging to remove dissolved carbon dioxide. A summary of the solutions and concentrations prepared for the three experiments is presented in Table 1. The exact concentrations tested are tabulated in the ESI. The VPO instrument was a Model 833 Vapor Pressure Osmometer and was obtained from UIC Inc. (Joliet, IL, USA). Two sets of thermistors were used in the experiments. For experiment 1 the stock glass thermistors were used, while for experiment 2 and 3 a set of modified thermistors were used. Between experiments 2 and 3 the modified thermistors were removed, examine for leaks and reinstalled. These modified thermistors had Teflon risers attached to the


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thermistor bead in the place of the glass risers in an attempt to make a set of thermistors not prone to fracture where the thermistor bead joins the riser. More details regarding the thermistors are provided in the ESI Prior to each experiment the cell was cleaned and dried overnight in an oven at 90°C and 45°C for the glass and Teflon thermistors, respectively. After cleaning, the cell was loaded with a new wick, charged with approximately 15ml of water, and equilibrated overnight at 25.3°C. The temperature of all experiments was held constant at 25.3°C using the built-in heating coil and thermostat of the UIC 833 VPO. The room temperature was approximately 19°C during all experiments. The range selector was set at 2, and the bridge current was set at 50 A for all experiments. Samples of pure water were injected in both ports prior to the initial measurements on the aqueous solutions in order to measure the baseline signal that is subtracted from all measurements. This initial baseline was taken as the average of three triplicate measurements. Subsequently, the baseline was measured as a single point between each different aqueous solution tested in order to verify proper operation. The sample port with the thermistor that induces an increase in the voltage signal with increasing temperature relative to the temperature of the other thermistor was used for all the aqueous solutions. The other port was used exclusively for the pure water reference. The instrument was conditioned prior to taking the initial measurement on each sample by injecting small amounts of solution at 30 seconds to 60 second intervals and observing the VPO signal. When the signal at the end of the interval reaches approximately the same value as the prior injection, the conditioning was considered complete.



After conditioning, the sample was measured by injecting a small amount of the pure water onto the reference thermistor, followed by injection of the sample onto the measuring thermistor approximately 30 seconds later. The value for the measurement is taken when the signal levels off after 3-6 minutes. The peak signal was taken to represent the pseudo steady state value in the samples. The signal always exhibited a gradual decrease in the signal after plateauing. Each sample was measured three times in this fashion. The VPO signal was viewed and recorded on a windows PC using the Kaito Electronics, Inc., TekPower multimeter and TekPower Windows software included with the osmometer by UIC Inc. Experiment 1 progressed over two weeks and included the widest range of substances. Data for experiment 2 and 3 were collected over one week each. All experiments included NaCl solutions as the reference, and KNO3 to provide a commonality amongst all runs. The third substance in runs 2 and 3 were selected to provide overlapping data with run 1 for an additional substance.

Table 1. Summary of the three VPO validation experiments. Experiment 1 (glass thermistors) Substance

# of Points

Molality Range (mol/kg solvent)

NaCl

10

0.031 – 2.15

CaCl2

9

0.027 – 1.48


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KNO3

8

0.023 – 1.40

Na2SO4

9

0.022 – 0.38

Sucrose

7

0.060 – 1.07

Experiment 2 (Teflon thermistors) Substance

# of Points


NaCl

10

0.020 – 1.15

KNO3

11

0.027 – 1.23

Sucrose

10

0.039 – 0.96

Experiment 3 (Teflon thermistors) Substance

# of Points


NaCl

10

0.041 – 1.17

KNO3

9

0.055 – 1.22

Na2SO4

10

0.017 – 0.68

Results and Discussion The averages of the triplicate measurements of the VPO signal for the first experiment are plotted in Figure 1. The numerical data for this and the other experiments are tabulated in the ESI. The average standard of deviation for the triplicates was 1.3%



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averaged over all experiments. The error bars in Figure 1 indicate two standard deviations for each point. These error bars fall within or close to the point markers rendering them hard to discern on the plot.

Figure 1. VPO data for experiment 1. The dashed line (--) gives the fit for the machine constant using the Sodium Chloride data (open diamonds). The symbols denote calcium chloride (blue diamonds), potassium nitrate (red squares), sucrose (grey triangles), and sodium sulfate (black circle). Error bars denote two standard deviations for the triplicate averages. The errors are small and are mostly obscured within the markers.

In each experiment the data for sodium chloride was used as a standard to empirically fit for the machine constant, k, in the VPO equation, Equation 1, as an instrument calibration. 1

∆V = k(1 ― a)


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Where V is the VPO signal for each sample, a is the activity of the diluent, and k is the machine constant determined by the calibration. Sodium chloride was chosen as a standard since it has a relatively simple, well described behavior over the concentration range used and water activities for the various sodium chloride concentrations were calculated using the Pitzer equations.30 The equations and parameters are given in the ESI. Using the experimental VPO signal, ΔV, for the sodium chloride solutions along with the calculated water activity based on the molality, the machine constant, k, in Equation 1 can be obtained by a simple fit. The dashed line in figure 1 depicts the result of the fit converted to a molality scale, which yielded a machine constant, k, of 7.62•104 V ± 400 V (95% CI) for experiment 1. The machine constant for each experiment is given in Table 2. Different proportionality constants between the temperature difference and the voltage read out are expected for the glass thermistors in experiment 1 compared to the thermistors in experiment 2 and 3 due to the different electrical resistance of each pair.

Table 2. Machine constant, k, for each experiment. Experiment number

Machine constant, k (V)

1

76,200  400

2

69,200  400

3

69,900  800



The water activity for each of the other solutions was calculated using Equation 1 with the fitted machine constant for each data set. The values shown in subsequent figures include all the data from the different runs overlaid in the figures. For each individual experiment, we refer the reader to the ESI. Figure 2A gives the water activity results for each of the other substances along with water activities calculated using literature correlations. The Pitzer method as presented in Molecular thermodynamics of fluid-phase equilibria30 was used to calculate the water activity for the salt solutions, and the equation of Starzak29 was used for the water activity in the sucrose solutions. The Pitzer equations and the values used are given in the ESI. Figure 2B shows the percent difference between the experimental value of the chemical activity and the theoretical value at each concentration. In general, the accuracy is best below approximately 0.2 mol/kg solvent, as can be seen in the figure.

Figure 2. A: Water activity. B: Percent error compared to literature values. The symbols denote calcium chloride (blue diamonds), potassium nitrate (red squares), sucrose (grey triangles), and sodium sulfate (black circle). The solid lines (—) give the activity calculated using the Pitzer


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equations30 for the salts, and the correlation of Starzak29 for sucrose. Error bars denote two standard deviations.

The chemical activity is matched within 0.13% of the literature values for all data points, as seen in Fig. 2B. On the other hand, the osmotic coefficient shows more deviation as this measure inherently magnifies any differences in activity. Figure. 3A shows the molal osmotic coefficient calculated from the experimental activity (Equation 2) compared to the molal osmotic coefficient determined using Pitzer method30 for the salts and a literature correlation29 for sucrose. The osmotic coefficient, ϕ, was calculated from the water activity values using Equation 2 below. ϕ=―

( )ln a 1000 vmMs

2

In this equation v is the number of ions released by dissociation, m is the molality, Ms is the molar mass of the diluent (water), and a is the activity of the diluent. In addition to experimental data and the calculated osmotic coefficients, figure 3A also presents the fitted smoothing functions (see ESI for details) used with equation 3 to calculate the experimental mean molal ionic activity coefficient of each salt and the activity coefficients for sucrose. Figure 3B shows the percent error between the current experimental data and the literature correlations. In contrast to the water activity values, the percent error is an order of magnitude higher. The average of the absolute value of the percent error is 2.4%.



Figure 3. A: Molal osmotic coefficients. B: Percent error compared to literature values. The symbols denote calcium chloride (blue diamonds), potassium nitrate (red squares), sucrose (grey triangles), and sodium sulfate (black circle). The solid lines (—) give the osmotic coefficient calculated using the Pitzer equations30 for the salts, and the correlation of Starzak29 for sucrose. Sucrose data (x) data from Ref. 23 is included for comparison. The dashed lines (--) are the fits for smoothing functions to the VPO data. Error bars denote one standard deviation.

For the sucrose data, the majority of the experimental osmotic coefficients fall below the literature correlation, suggesting the possibility of a systematic error. Unfortunately, the reference presenting the sucrose correlation29 did not show a plot of the osmotic coefficients for their aggregated data or give a plot showing the variation in the water activity on the scale necessary to judge how the scatter in this VPO experiment compares to those data sets. Indeed, while the correlation clearly performs well over the concentration range as a whole, it is not entirely clear how well it performs specifically in the low concentration range. However, another group also determined the osmotic


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coefficient for aqueous sucrose solutions using VPO,23 and their data shows better agreement to the VPO sucrose data collected in our study than to the correlation by Starzak.29 That data is included in Figure 3A for comparison. Interestingly, the data from the other study shows a definite offset from the literature correlation. That common offset suggests it is due to the VPO technique rather than the specific instrument. Another noteworthy aspect to the sucrose data is the visually lower scatter in the data from reference 23. This data was collected on the Knauer instrument compared to the UIC model used in our work. Not only has the UIC model been cited for variability,20,21 but some additional studies using the Knauer osmometers seem to show lower relative scatter compared to the current result.2,31 These observations provide strong anecdotal support to a performance difference between the instruments in regards to repeatability. In contrast to the sucrose data, the calcium chloride data appears to have a small upward shift compared to the correlation result. With the shift in the opposite direction of the potential sucrose shift, it is unlikely that the changes are due to an offset in the machine constant. In that case, the shift would be in the same direction for both substances. Although less definite due to the scatter, the sodium sulfate data may also show a small upwards shift. The reason the offset is in the opposite direction for sucrose versus the salts may be due to differing physical properties of the liquid drops for a given VPO signal. Due the lower molar mass and dissociation of the salts, a sucrose solution requires a significantly higher mass fraction of solute to yield the same VPO signal. For example, a 1 molal sucrose solution gives roughly the same signal as a 0.3 molal calcium chloride solution and the mass fractions will be 25% and 4%, respectively. The thermal conductivity in that calcium chloride solution will only be about 2-3%32 less than pure



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water, but the thermal conductivity in the sucrose drop will be about 13%33 less than pure water. Thus, the differing solution properties of the sucrose drop compared to the drops of salt solution, including the calibration standard, at a given VPO signal may explain the different directions of the offsets. Subsequent to calculating the osmotic coefficients, activity coefficients of the minor components could also be determined. The activity coefficients of the minor components were computed based on Equation 3.30 mϕ - 1 m dm

ln γ = ϕ -1 + ∫0

3

In order to solve this equation a number of substitutions and smoothing functions are needed and are shown in the ESI. The results from the calculations of the activity coefficients are shown in Figure 4. The scatter present in the osmotic coefficients is averaged out by the smoothing functions, but the offsets for sucrose and calcium chloride compared to the Pitzer model remain. Despite the offset, however, the data shows reasonably accurate activity coefficients for the solutes over the tested concentration ranges. Figure 4 also show experimental data from other previous studies for the different salts for comparison with our results. The experimental data for sucrose is from an isopiestic vapor pressure measurement reported by Robinson and Stokes.34 This data is shown as a grey dash-dot line in the figure and was obtained by using the data in their study combined with their reported equation for calculating activity coefficients for sucrose. The experimental data for potassium nitrate, red open squares, was taken from a compilation of data35 and is also reported in a comparative study by Hamer and Wu.36 In the range shown here the data is most likely


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based on isopiestic measurements.37 The data for sodium sulfate, black circles, is taken from suggested data by Whitfield.38 In the paper by Whitfield the author refers to experimental data from Platford and Dafoe39 most likely using an ion selective electrode, i.e. electromotive force (EMF) measurements. The experimental data for calcium chloride was taken from two separate sources both cited in a study by Staples and Nuttall40 where a wide range of experimental data for calcium chloride were compared. The black crosses are data from Briggs and Liley41 while the blue diamonds are experimental data from Scatchard and Tefft.42 Both these studies use EMF measurements. The authors of the comparative study40 make the observation that the data at higher concentration of calcium chloride, shown as solid blue diamonds in figure 4, is questionable. As shown in figure 4, the data at higher concentrations of CaCl2 compare poorly to the Pitzer model as well as our data.



Figure 4. Activity coefficients of the different solutes tested in this study. The dotted lines are based on the experimental VPO data calculated using equation 3. The solid lines give the activity coefficient calculated using the Pitzer equations30 for the salts, and the correlation of Starzak29 for sucrose. Experimental data from previous studies are included as comparison. The grey dash-dot line for sucrose are based on isopiestic measurements.34 The open red squares are isopiestic measurements.35-37 Black circles are based on EMF measurements.38-39 The calcium chloride data, black crosses and blue diamonds, are based on EMF measurements with data taken from two separate experimental studies.41,42

While our data shows agreement with the Pitzer model, as well as reasonable agreement with previous experimental data by other groups over the concentration ranges tested,


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higher concentrations require further verification. Literature guidance on appropriate concentration ranges is limited. One overview of the technique claims VPO is typically used for concentrations up to 0.5 mol/kg solvent for aqueous solutions,4 but does not give reasoning behind that. In contrast, the Knauer1 instrument manual states the range is 0.001 molal to 15 molal, but without discussion or justification of that high range. Similarly, the manual for the UIC19 osmometer does not discuss appropriate concentration ranges. Despite the limited info on suitable concentration ranges, VPO has seen use at up to nearly 10% mole percent, giving solute mass fractions of over 50%.23 Neither the current evaluation nor earlier literature evaluations extend to those relatively high concentrations.2,3,9,17 Lacking an empirical assessment, examining the theoretical model can bring awareness to some of the concentration dependent assumptions in the VPO technique. The VPO equation, Equation 1, can be derived from a mass and heat transfer balance on the thermistors with several simplifying assumptions. Equation 4 below shows the result of that derivation for the steady state VPO signal from the work of Kamide et al.43 This extended form of Equation 1 shows the sources of inaccuracy clearer, and also illustrates the difficulty in quantifying them.

(ac - as) ∆V = ∆T = (Ts - Tr) = β k1sA1s + k2sA2s 1 k3sA1s

P∆H

-

+ as•

(ac - 1)

∆H k1rA1r + k2rA2r 1 ∆H + k3rA1r P∆H RT2c RT2c 4



Table 3. Symbols used in Equation 4. Symbol

Description

T

Temperature

T

Temperature difference between the sample and reference thermistors

V

VPO signal, the bridge voltage difference due to T



Proportionality between the temperature difference (T) and the voltage signal (V)

a

Activity of the diluent

P

Pure diluent vapor pressure at the temperature, Tc

H

Enthalpy of vaporization of the diluent at temperature Tc

R

Universal gas constant

k1

Heat transfer coefficient at the vapor-liquid interface of the liquid drop

k2

Heat transfer coefficient of the drop to thermistor interface

k3

Mass transfer coefficient at the vapor-liquid interface of the drop

A1

Surface area of the vapor-liquid interface of the drop

A2

Area of the boundary between the drop and the thermistor

Subscript

Indicates the quantity refers to the reference thermistor. E.g. ‘Tr’ is the

‘r’

temperature of the reference thermistor.


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Subscript

Indicates the quantity refers to the reference thermistor. E.g. ‘as’ is the

‘s’

activity of the diluent on the sample thermistor.

Subscript

Indicates the quantity refers to the VPO cell. E.g. ‘Tc’ is the temperature of

‘c’

the VPO cell, i.e. the thermistor surroundings.

Equation 4 can be transformed into Equation 1 by treating both denominators on the right-hand side as equal and constant with respect to concentration, allowing them to be lumped into the machine constant, k, in Equation 1. This constant also included the proportionality between the temperature change and voltage change, β. However, these two assumptions about the denominators are approximations, and results in a decrease of accuracy as the concentration changes. That limitation, along with the influence of dilution, restricts the accuracy of VPO to low concentrations. The terms in Equation 4 also show that the accuracy is dependent on the temperature, the diluent properties, and the specific geometry of both the thermistors and the solution drops. The purpose of Equation 1 is to determine the diluent activity of a series of solutions, but to arrive at it, one treats the diluent activity appearing in the denominator, as, as constant. Attempts to quantify the effects of the two previous assumptions for the UIC instrument show that from 0 to 2.2 mole percent of hexadecane in heptane, the denominator varies by at most 0.74% due to the activity term in the denominator, leading to a 0.015% error of the chemical activity of the diluent.22 In light of this data, the assumption that the diluent activity is constant causes relatively minor inaccuracies.



The assumption that the geometry and mass transfer characteristics are identical for both thermistors may be more of a problem. In the case of the UIC Jupiter 833 osmometer, the design includes a feature intended to help ensure those characteristics are as close as possible. Mesh caps on the thermistors are supposed to maintain a constant drop volume, minimizing the differences in surface areas. The Knauer osmometer, on the other hand, does not use these caps, but provides a viewing window for the operator to visually balance drops of equal size on the hanging thermistors. As the results in this study seem to show more scatter in the data compared to studies using the Knauer osmometers, it may be that the mesh caps do not adequately regulate the drop size. Although the mesh caps in the improved instrument described by Dohner et al.6 are portrayed as being cylinders with a hemispherical top that fit smoothly and uniformly over each thermistor, the mesh caps provided with the UIC instrument are not so uniform. The caps are made from a fine stainless steel mesh that has been rolled into a cylinder and then had the top folded in. The folds add non-uniformity and extra material at the tips of the matched thermistor probes. That non-uniformity is where the thermistor bead is located. Thus, the cap design may be behind some of the variability in the signal from drop to drop, and as the concentration in the reservoir changes. However, comparing the data between the three separate experiments carried out in this study where different thermistors, and hence different mesh-caps, were used indicate good agreement in the calculated activities. The assumption of identical geometries and physical properties becomes more impactful as solute builds up in the chamber solution. As the vapor moves further from saturation, a significant amount of the temperature difference between the thermistors will arise from


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evaporation of diluent on the reference thermistor. In this case, any differences in the thermistor heat and mass transfer characteristics will lead to VPO signal changes that are not necessarily accounted for by the empirical calibration procedure. The equation derivation also assumes that a steady state, or constant VPO signal over time, is attainable. For low concentration samples, the dilution due to the condensation is not apparent over the measurement interval, but for more concentrated samples there is a noticeably decreasing signal. Although both dilution and volatile contaminants in the sample cell have been cited to cause decreasing signal in VPO,7,8 the correlation with sample concentration suggests dilution is the more probable explanation. Normally the sample is injected and the signal rapidly increases and then levels off to a plateau. In the more dilute samples this plateau remains stable over the several minute measuring period. However, for the more concentrated samples, the signal plateaus and then decreases slowly over time at a constant rate. Samples at approximately 0.1 molal for each of the solutes did not show a discernable decrease in the signal, while samples of 1.03 molal calcium chloride showed a decrease corresponding to a dilution of 0.5% per minute in the example. These two cases are shown in Figure 5.



Figure 5. VPO signal behavior for a measurement of 0.111 molal calcium chloride (A) compared to a measurement on 1.03 molal calcium chloride (B). The VPO signal rapidly increases after the sample is injected, reaching a plateau. The plateau is steady for lower concentration samples, but for higher concentrations the plateau slowly decreases, as seen here at a rate of 0.5% of the overall signal per minute.

Despite these assumptions and caveats built into the VPO equation, empirically determining the machine constant can compensate for these effects over a useful concentration range. The accurate data for potassium nitrate and sodium sulfate demonstrates validity over the concentration ranges tested. Nonetheless, these affects lead to increasing systematic errors as concentration increases, so the technique requires further evaluation at higher concentrations. Due to the potential of the drops physical properties to affect the signal, the calibration standard material should give close properties to the investigated solutions at the same VPO signals. As the analysis of the VPO equation indicates the importance of having identical and reproducible geometries


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for the sample drops, an easy improvement to the off the shelf UIC osmometer may be to make more uniform mesh caps.

Conclusions

The experimental assessment of the UIC 833 Jupiter vapor pressure osmometer indicates that it performs adequately in measuring diluent activity. Qualitatively, however, this instrument may yield nosier data than the more commonly used Knauer vapor pressure osmometer. The design of the mesh caps was identified as a potential cause of that disparity. Nonetheless, reasonable activity coefficients of the minor component can be obtained up to 1.4 molal. The instrument produced repeatable data even after the thermistors were replaced and Teflon risers were used instead of the standard glass. Further studies may be needed to qualify both models of osmometer at the higher concentrations seen in the literature. That need was highlighted by a discussion of the assumptions in a derivation of the VPO equation relating the osmometer signal to diluent activity.

Acknowledgements This work was funded in part under subcontract number 107827 with the Idaho National Laboratory, Fuel Cycle Research and Development program (FCR&D), U.S. DOE,



Office of Nuclear Energy. The authors are not affiliated with or have received any financial support from UIC Inc.

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For Table of Contents Only



Figure 4. Activity coefficients of the different solutes tested in this study. The dotted lines are based on the experimental VPO data calculated using equation 3. The solid lines give the activity coefficient calculated using the Pitzer equations30 for the salts, and the correlation of Starzak29 for sucrose. Experimental data from previous studies are included as comparison. The grey dash-dot line for sucrose are based on isopiestic measurements.34 The open red squares are isopiestic measurements.35-37 Black circles are based on EMF measurements.38-39 The calcium chloride data, black crosses and blue diamonds, are based on EMF measurements with data taken from two separate experimental studies.41,42 203x152mm (300 x 300 DPI)


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Accuracy, Repeatability, and Limitations for Determination of Chemical

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