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Thermophysical and Thermochemical Properties

Surface Tension and Surface Thermodynamics of Aqueous Inorganic Salt Solutions in the Atmospherically Relevant Temperature Range
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Journal of Chemical & Engineering Data

Cite this: J. Chem. Eng. Data 2025, 70, 12, 4901–4914
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https://doi.org/10.1021/acs.jced.5c00470
Published November 25, 2025

Copyright © 2025 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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The surface tension γ of aqueous solutions of NaCl, NaBr, NaI, LiCl, KCl, MgCl2, and Na2SO4 (0.1 mol·kg–1 to 5 mol·kg–1 in maximum) was investigated within the atmospheric relevant temperature range of 263.15 to 293.15 K. The measured densities ρ of the aqueous inorganic salt solutions between 278.15 and 293.15 K are also reported. From experimental data the excess surface tension Δγ, the concentration (as molality m) and temperature derivatives, (dγ/dm)Tp and (dγ/dT)pm as well as thermodynamic quantities of surface formation such as surface excess entropy Δsσ, surface excess Helmholtz energy Δaσ, surface excess energy Δuσ, and surface excess enthalpy Δhσ were estimated. The surface excess entropy decreases slightly with increasing molality of the inorganic salt, which shows a weak order dependence of the water molecules on the salt concentration. The surface tension data and thermodynamic quantities complement existing data sets especially at temperatures below 283.15 K.

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1. Introduction

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In a huge number of field campaigns and long-term observations, the composition of atmospheric aerosol particles was investigated (e.g. (1−12)). Depending on the altitude, latitude, season, and region (marine, urban, rural, and so on) at which aerosol particles were collected, inorganic as well as a range of organic compounds were identified. Especially in marine aerosol, larger amounts of inorganic components were found that appear as dissolved cations and anions and are mainly Na+, Mg2+, NH4+, Cl, Br, NO3, HSO4, SO42–, among others. (13,14) The organic matter is substantially more complex. (15) So dimethyl sulfide from phytoplankton, as well as different longer chain fatty acids, occur more frequently in marine aerosol or so-called “human-like” species in urban regions or from biomass burning. (16,17) Longer chain organic molecules are typical surfactants that exhibit a hydrophobic and a hydrophilic moiety. Therefore, they tend to adsorb at surfaces and lower the surface tension of the liquid surface. At the so-called critical micelle concentration (CMC), they form micelle aggregates. In the presence of inorganic salts adsorption of surfactants at the liquid surface becomes more intense, and the CMC is shifted to a lower concentration. (18−20) These effects also occur in cloud droplets in the atmosphere, where they can affect the water uptake or adsorption of substances from the gas phase and thus chemical reactions at the droplet surface as well as formation and growth of cloud droplets in a significant manner, and as a consequence, also precipitation and radiative climate forcing are influenced. (21−23) Since inorganic salts play an important role in atmospheric chemistry, their hydration at the air/water interface plays a crucial role in understanding the surface speciation and the reactivity in atmospheric aerosol. Jungwirth and Tobias received surprising results in modeling the air/water interface of aqueous sodium halide solutions, providing a completely new perspective on the distribution of anions and cations in the interfacial region. (24) Larger, polarizable anions showed an enrichment at the air–water interface that was in contrast to the previously regarded depletion of ions in the interfacial region. Depletion or enrichment of substances influences the physicochemical properties of interfaces. An important quantity in the characterization and modeling of a liquid surface is its surface tension as well as its change with the solute concentration (surface tension gradient) and other thermodynamic quantities. (25) Therefore, these parameters are also important in atmospheric cloud formation models. (19,25)
Several studies of thermodynamics of solute adsorption at surfaces and interfaces of liquids, including general formulations, were published by Motomura et al. (26−29) Matubayasi et al. applied these formulations in their own studies concerning the thermodynamic surface excess quantities of aqueous electrolyte solutions. (30−32) The following equations for calculating different thermodynamic quantities are based on these works. All thermodynamic quantities expressed here by lower case letters with the superscript σ represent excess quantities per unit area with reference to the pure solvent as recommended by the International Union of Pure and Applied Chemistry (IUPAC). (33)
Strong electrolytes dissociate completely into ν+ cations and ν anions when they are dissolved in water. The change in surface tension dγ of a salt solution depends on temperature T, pressure p as well as molality m and can be described by the following equation:
=ΔsσdT+vσdp(ν++ν)·R·T·Γσm(1+lnf±lnm)T,pdm
(1)
with the surface excess entropy Δsσ, the volume of surface formation vσ, the stoichiometric coefficient ν, the universal gas constant R, the total surface excess concentration Γσ, and the mean activity coefficient f± of the inorganic salt.
From temperature-dependent surface tension measurements at p, m = const surface excess entropy can be calculated by means of:
Δsσ=(∂γT)p,m
(2)
The thermodynamic quantities surface excess Helmholtz energy Δaσ, surface excess energy Δuσ, surface excess enthalpy Δhσ and surface excess Gibbs energy Δgσ are related as follows:
Δaσ=ΔuσT·Δsσ
(3)
Δuσ=Δhσ+γ=T·Δsσp·Δvσ+γ
(4)
Δgσ=ΔhσT·Δsσ=Δaσγ
(5)
In the case of an ideal surface, no volume work is expected. For a real surface, the contribution from volume work was estimated by Motomura et al., who obtained a value of pΔvσ = −0.0831 mJ·m–2. (29) Compared to those values of γ and T · Δsσ, it is very small and can be neglected. This simplifies eqs 3 to 5 as follows:
Δhσ=T·Δsσ
(6)
Δaσ=γ
(7)
and leads also to Δgσ = 0, which is to be expected for the equilibrium state of the solution surface.
Finally, the values of the surface excess energy and entropy can be determined graphically by linear regression of the γ-T graphs with slope Δsσ and y-intercept Δuσ:
γ=ΔuσT·Δsσ
(8)
The excess surface tension Δγ characterizes the ability of the solute to reduce or raise the surface tension of the solvent γ0 by
Δγ=γγ0
(9)
This work is focused on surface tension data of several aqueous inorganic salt solutions and thermodynamic quantities of their surface in an atmospherically relevant temperature range of 263.15–293.15 K. Most published data refer to measurements at 288.15 K or higher. (31,32,34−40) Only few data sets received at lower temperature are available such as in Shah et al. (41) for several aqueous inorganic salt solutions down to 283.15 K as well as Horibe et al. (42) for NaCl solutions down to 263.15 K. For the qualitative verification of the prepared aqueous inorganic salt solutions (correct molality, possible precipitation of the used salt), density measurements were carried out, which were additionally included in the work. The data represented in this work complement the already existing data and are important for model validation in general and especially in atmospheric science. (24,25,43)

2. Experimental Methods

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2.1. Materials

All salts used are listed in Table 1 and were used without further purification. LiCl is very hygroscopic and was first dried in a desiccator under vacuum. Mass stability was achieved after 24 days (576 h), as shown in Figure S1 in Supporting Information (SI). Thereafter, LiCl and all other salts were stored in tightly closed bottles, additionally sealed with Parafilm (Parafilm M) in a desiccator together with a drying agent to ensure a dry environment. The sealing with Parafilm also avoids possible water loss of the MgCl2 × 6H2O in the presence of a drying agent. The used water was fully demineralized. Additionally, the water was distilled until the conductivity was below 2.5 μS·cm–1.
Table 1. Inorganic Salts Used for Density and Surface Tension Measurementsa
chemicalCASsupplierpurity in mass fraction w
KCl7447-40-7Merck>99.0%
LiCl7447-41-8Fluka>99.0%
MgCl2 × 6H2O7791-18-6Merck>99.0%
NaBr7647-15-6Riedel de Haen>99.0%
NaCl7647-14-5VWR99.9%
NaI7681-82-5Fluka/Merck>99.0%/99.99%
Na2SO47757-82-6Merck99.99%
a

The purity values are provided by the respective supplier.

2.2. Experimental Procedure

The aqueous salt solutions were prepared gravimetrically. The concentration is given as the molality. For the calculation of the molality values of MgCl2 x 6H2O solutions, the proportionate mass of the six water molecules per ion pair was added to the mass of the weighed water as solvent. Thus, the molality concerns only the salt and not the hydrate. The concentration range lies between 0.1 and 5 mol·kg–1 (up to 1 mol·kg–1 for Na2SO4, up to 3 mol·kg–1 for MgCl2, and up to 4 mol·kg–1 for KCl). Exact concentration values are given in Tables 2 and 3. Note that the highest concentrated solution of potassium chloride and sodium sulfate is very close to the solubility limit at 293.15 K, which can lead to salting-out effects at lower temperatures. The solubility limits are summarized and compared with the highest concentration of each investigated salt in Tables S2 and S3 in SI. Such salting-out effects can be verified by density or by surface tension, discussed in the corresponding chapters. The combined standard uncertainty of the molality uc(m) is affected by the accuracy of the balance and was obtained from error analysis (see Table S5 in SI). It amounts to uc(m) = 0.0002 mol·kg–1. A more detailed description can be found in Chapter S6 in the SI.
Table 2. Experimental Values of the Density ρ of Aqueous Salt Solutions as a Function of Molality m and Temperature T at a Pressure p = 100,000 Paa
  ρ/kg·m–3
saltm/mol·kg–1278.15 K283.15 K288.15 K293.15 K
NaCl0.0961004.161003.811003.131002.18
 0.2031008.751008.311007.571006.55
 0.4631019.731019.091018.161017.01
 0.7331030.881030.041028.961027.68
 0.9841040.831039.831038.621037.21
 1.4981060.511059.241057.801056.18
 1.9871078.581077.081075.441073.62
 2.9731112.861111.021109.051106.98
 4.0151146.701144.551142.321140.01
 5.0051176.231173.871171.461168.97
NaBr0.1161009.421009.041008.351007.37
 0.2031016.451015.991015.211014.16
 0.4641036.961036.271035.301034.08
 0.7521059.231058.301057.131055.71
 0.9881077.641076.521075.191073.63
 1.4951114.241112.781111.131109.30
 2.9941217.041214.761212.391209.88
 3.9711278.851276.171273.411270.62
 5.0461343.761340.691337.551334.43
NaI0.1111013.001012.611011.891010.89
 0.1431016.801016.371015.631014.58
 0.1971022.631022.141021.341020.27
 0.5131057.921057.101055.991054.66
 0.5301060.771059.931058.801057.46
 0.7471082.941081.801080.431078.89
 0.9941111.851110.541109.011107.30
 0.9971110.051108.751107.231105.52
 1.5301164.641162.891160.941158.88
 2.0851219.621217.441215.111212.64
 2.7721286.161283.481280.711277.84
 3.8331373.571370.341367.021363.64
 4.6641450.341446.641442.931439.17
LiCl0.1061002.761002.451001.811000.89
 0.2021005.011004.681004.021003.07
 0.4991012.171011.741011.011010.01
 0.7481018.001017.491016.711015.70
 1.0141024.031023.461022.621021.56
 1.5611036.961036.251035.321034.18
 2.3631053.701051.841051.831050.62
 2.9851066.201065.281064.201062.98
 4.1411088.051087.011085.861084.59
 4.9201101.731100.651099.451098.16
KCl0.1181005.741005.381004.711003.74
 0.2041009.951009.541008.801007.81
 0.5411025.761025.121024.211023.07
 0.7521035.321034.551033.541032.32
 1.0111046.741045.841044.721043.34
 1.4091063.701062.611061.331059.85
 1.9301084.991083.711082.251080.59
 3.0861132.301130.661128.881127.03
 4.0231160.651158.841156.931154.87
MgCl20.0991007.971007.621006.961006.02
 0.2121016.911016.471015.731014.75
 0.4871038.091037.451036.571035.45
 0.6981053.561052.801051.821050.63
 0.9421071.261070.371069.281068.01
 1.3141096.661095.611094.401093.04
 1.6331117.921116.771115.461114.02
 2.3011158.401158.481157.051155.50
 2.7761187.981186.561185.051183.46
 3.2011211.841210.351208.791207.15
Na2SO40.0881011.891011.431010.661009.65
 0.2351030.561029.831028.841027.60
 0.4951063.551062.351060.391058.54
 0.7301089.891088.521086.951085.25
 0.9301110.961109.341107.561105.63
a

The combined standard uncertainties are as follows: molality values uc(m) = 0.0002 mol·kg–1 and density values uc(ρ) = 0.34 kg·m–3. The standard uncertainty of the temperature is u(T) = 0.01 K. See Chapter S6 in SI for more details.

Table 3. Experimental Values of the Surface Tension γ of Aqueous Salt Solutions as a Function of Molality m and Temperature T at a Pressure p = 100,000 Paa
  γ/mN·m–1
 m/mol·kg–1263.15 K268.15 K271.15 K273.15 K278.15 K283.15 K288.15 K293.15 K
NaCl0.096  75.4975.2974.4673.6873.0472.16
 0.203 76.5576.0675.7374.9374.2073.4772.56
 0.463 77.3176.9476.5675.6475.0574.1573.25
 0.733 77.6277.3176.9175.8575.1774.7073.39
 0.984 78.4377.9377.6476.7075.9474.9473.78
 1.49880.3179.4478.9178.5377.6576.6275.7574.46
 1.987 78.6578.1077.8976.9776.4775.6675.00
 2.97379.8379.2378.9078.4277.8577.2476.3475.55
 4.01582.4881.8881.5381.2780.5580.0979.2878.30
 5.00583.5183.1582.9282.8182.1481.5580.6979.90
NaBr0.116  75.9675.5974.7373.9672.9172.29
 0.203 76.4875.9975.6874.8174.0473.1772.57
 0.464 77.0676.6076.3475.3974.7173.8372.69
 0.752 77.2776.6776.3975.3574.7873.7972.83
 0.988 77.5876.9776.8076.0375.3274.4173.42
 1.49578.6578.1877.7077.4376.5275.6474.7073.42
 2.99479.6679.1178.6478.2777.5576.7975.9275.10
 3.97180.5180.2279.8279.5978.7878.0377.4076.35
 5.04681.5081.1180.8780.6180.0579.4678.7377.84
NaI0.111  76.1775.6574.7873.8672.8971.67
 0.143 75.5475.2175.0074.0273.6172.8771.91
 0.197 76.2475.7675.4474.6573.9173.0572.03
 0.513 76.5976.2176.0675.2274.6073.7172.78
 0.530 77.1676.7876.4675.6074.9574.0973.04
 0.747 76.9176.4576.0575.1874.3773.4672.53
 0.994 76.4376.0075.6975.0674.2773.4172.75
 0.997 77.2376.7876.3475.6474.8673.9072.99
 1.53077.0076.4975.9875.8175.0874.3973.6372.71
 2.08577.2876.6076.2075.8075.1674.4673.5172.66
 2.77276.6676.0875.7075.5175.0474.4573.8473.01
 3.83376.9476.3475.9675.7575.0574.4073.6672.71
 4.66477.4076.7976.4876.2675.3974.9974.2173.29
LiCl0.106  75.9075.5174.5173.8972.9372.14
 0.202 76.5976.0875.8375.0874.4873.6172.72
 0.499 78.8378.2077.9477.1476.5375.7075.17
 0.748 77.8377.4677.1276.0775.5274.6473.75
 1.014 78.7878.2178.0377.3076.5575.7275.01
 1.56178.9178.3577.9477.7576.7675.9875.2074.30
 2.36379.3978.9778.5678.2977.6376.9376.0375.00
 2.98580.9480.5280.1779.8879.1178.6577.8377.12
 4.14182.1581.7881.3981.1180.3880.0179.3778.54
 4.92084.0383.6783.4783.3282.6082.0381.4180.59
KCl0.118  76.1175.8974.9474.3873.6372.90
 0.204 77.3376.9476.5875.7175.0674.1573.40
 0.541 77.2576.8276.7275.8475.2174.4173.60
 0.752 78.3477.9777.7476.8376.2475.6674.89
 1.011 77.5377.1476.8375.9775.3174.3973.42
 1.40979.1878.5378.0977.9177.1076.4675.6575.03
 1.93079.2178.6478.2778.0177.3776.7475.9775.22
 3.08680.3779.9179.5579.3978.6678.0077.4476.80
 4.02381.4580.4680.3180.3979.8779.2578.4877.87
MgCl20.099  77.3377.0176.2675.5474.8274.23
 0.212 77.4876.9576.6775.9775.2774.6273.86
 0.487 77.0677.0876.7375.7975.1374.3573.70
 0.698 77.8277.2777.0076.0975.3074.4673.66
 0.942 78.9678.4478.1977.5976.8976.0075.46
 1.31480.7480.3879.8679.6378.8078.1377.4676.61
 1.63381.5380.9680.6580.3679.5779.0778.2377.59
 2.30184.4883.8383.4783.0482.4781.8781.2180.73
 2.77685.8385.3084.9884.6983.9083.3182.7582.23
 3.20187.6287.0386.8086.5085.8085.3584.5683.89
Na2SO40.088  75.9075.4574.8074.2173.5472.71
 0.235 77.5777.0776.8475.9675.3274.5373.39
 0.495 76.5676.1575.8875.3274.7474.1073.50
 0.730 78.6878.3577.9277.0376.2475.3374.53
 0.930 78.9278.8078.5978.0077.3576.4775.63
a

The combined standard uncertainty of the molality values amounts to uc(m) = 0.0002 mol·kg–1. The combined standard uncertainty of the surface tension values, uc(γ), are given in Table S6 in SI. The standard uncertainty of the temperature is u(T) = 0.1 K. See Chapter S6 in SI for more details.

2.3. Density Measurements

The density of the aqueous salt solutions was measured as a function of temperature with the density meter DMA 4500 from Anton Paar GmbH by using the oscillating U-tube method. The measurements were carried out at 278.15, 283.15, 288.15, and 293.15 K. The accuracy of the density measurement amounts to ± 0.01 kg·m–3 and the internal temperature control is better than ± 0.01 K. Both values are given by the supplier. Calibration of the density meter was done with air and distilled water by the supplier, and it was verified before each measurement series with distilled water with a conductivity below 2.5 μS·cm–1. Each solution was measured two times and the values were averaged. The combined standard uncertainty amounts to uc(ρ)= 0.34 kg·m–3 (cf., Chapter 6.2 in SI). The results are summarized in Table 2.

2.4. Surface Tension Measurements

The surface tension was measured as a function of temperature as well with the tensiometer SITA online t60 with an upgrade to t100 from SITA GmbH using the bubble pressure method (differential pressure). The capillaries are made of polyetheretherketone (PEEK) and exhibit a diameter of 0.8 mm. Ambient air is dried by passing through a desiccant cartridge at the air inlet before it is pressed through the capillary into the liquid. During bubble formation, the bubble pressure is measured to calculate the surface tension. The maximum bubble formation time amounts to 100 s. To avoid bubble coalescence phenomena, the bubble interval ranges from 1.5 s for a minimum bubble formation time of 1 s to >150 s for a maximum bubble formation time of 100 s. (40) The measurements were performed at 263.15, 268.15, 271.15, 273.15, 278.15, 283.15, 288.15, and 293.15 K. Calibration of the tensiometer was done at 293.15 K with distilled water with a conductivity below 2.5 μS·cm–1 before each temperature-dependent measurement series. The temperature was controlled by a thermostatic bath with an accuracy of ± 0.1 K. The accuracy of the surface tension measurements is given by a value of 0.1 mN·m–1. Each solution was measured two times so that two measurement series were obtained (Figure S2 in SI). The last five values of each measurement series were averaged. The exact procedure is explained in Chapter S4 in the SI. The combined standard uncertainties of the surface tension values uc(γ) are given in Table S6 in the SI. A more detailed description of error analysis can be found in Chapter S6.3 in the SI.

3. Results and Discussion

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3.1. Density

Temperature and salt concentration are the main influencing factors of the density of aqueous salt solutions. The density ρ of the different concentrated aqueous salt solutions was measured as a function of temperature from 278.15 to 293.15 K with an increment of 5 K as presented in Table 2. As expected, the density decreases with increasing temperature (not shown as a diagram). With increasing temperature, the molecular packing, influenced by intermolecular interactions (solvent–solvent and solute–solvent), is reduced due to enhanced molecular mobility in an expanded volume, resulting in a decrease in density. On the other hand, the density increases proportionally with the salt concentration within the investigated temperature range. This behavior is shown in Figure S3 in the SI for the highest and lowest studied temperatures. No deviation from trend was observed, from which one can conclude that there could not have been any precipitation of the used salt between 278.15 and 293.15 K. The observed trend is in good agreement with the expectations based on the molar mass of the salt. A comparison with literature is shown for NaCl at 293.15 K in Figure 1. The density data, received with the same measurement method, agree very well for NaCl (cf. Figure 1), as well as NaBr, LiCl, KCl, MgCl2, and Na2SO4 at 293.15 K, respectively. (44−46) Further graphical comparisons, like in Figure 1, are given in Figures S18 and S19 in the SI. For NaCl, NaBr, LiCl, and KCl, the density values published in Shah et al. (41) are lower, resulting from density measurement with a pycnometer, as a quite different measurement method from that used in this study.

Figure 1

Figure 1. Density ρ of aqueous salt solutions of NaCl as a function of molality m at a temperature T = 293.15 K and at a pressure p = 100,000 Pa for: solid line and × own data (cf. Table 2) in comparison with data from literature: blue ● Hoffert et al., (47) red ▲ Rogers and Pitzer, (48) and gray ◆ Shah et al. (41) Note that the reference data from Rogers and Pitzer are given as specific volumes and were converted into density for comparison.

3.2. Surface Tension

Like in the case of the density, temperature and salt concentration are also the major influencing factors of the surface tension of the aqueous inorganic salt solutions. For all salt solutions, surface tension measurements were possible down to 271.15 K without freezing of the solution. Measurements at 268.15 K were possible for m > 0.14 mol·kg–1 and at 263.15 K for m > 1.3 mol·kg–1, respectively. The data are summarized in Table 3 and the corresponding uncertainty values are listed in Table S6 in the SI. Details concerning the error analysis can be found in Chapter S6.3 in the SI.
In Figure 2 surface tension of 1, 2, and 3 mol·kg–1 NaCl solution as a function of temperature taken from Table 3 is shown in comparison with data from literature at similar molalities. (42) Horibe et al. applied the differential capillary-rise method to measure the static surface tension. (42) To the best of our knowledge, these are the only published surface tension data of aqueous inorganic salt solutions at temperatures below 273.15 K. For all six data sets in Figure 2 the gradient of the surface tension (dγ/dT)pm is similar. Obviously, our values are usually lower than those from Horibe et al., which is due to the different measurement methods. In the case of aqueous inorganic salt solutions, the dynamic surface tension is slightly lower than the static one. In addition, the initial salt content of the water used influences the surface tension. We used water with a very low conductivity (cf. Chapter 2.1). Horibe et al. did not provide any detailed information about sample preparation, especially on water purity. Furthermore, small deviations in the temperature and concentration can also lead to deviations in surface tension, but this effect is considered to be less significant.

Figure 2

Figure 2. Surface tension γ of aqueous salt solutions of NaCl as a function of temperature T at a pressure p = 100,000 Pa for own data at: ■ 2.994 mol·kg–1, blue ● 1.997 mol·kg–1, gray ▲ 0.984 mol·kg–1 (cf. Table 3) and data from literature (42) at: □ 3.020 mol·kg–1, blue ○ 1.901 mol·kg–1, gray △ 0.901 mol·kg–1. The concentrations of the reference data are given in mass fractions and were converted into molality for comparison (cf. Chapter S1 in the SI).

In the following section, we compare our surface tension values with data from literature that were measured under similar conditions (cf. Figures S20 and S21 in SI for graphical comparisons). It has to be mentioned that we concentrated on a temperature of 293.15 K and a concentration of approximately 1 mol·kg–1 for more clarity. Matubayasi et al. published surface tension data for a lot of aqueous salt solutions. (30−32) All data were received via the drop volume method. So, the surface tension amounts to ≈ 74.3 mN·m–1 for NaCl, ≈ 73.8 mN·m–1 for NaI, ≈ 74.2 mN·m–1 for LiCl, as well as ≈ 74.6 mN·m–1 for Na2SO4 (here at 0.9 mol·kg–1). Jarvis and Sheiman (49) measured surface tensions with the duNouy ring method at 298.15 K and obtained values as follows: ≈ 74.0 mN·m–1 for NaCl, ≈ 73.8 mN·m–1 for NaBr, ≈ 73.5 mN·m–1 for NaI, ≈ 73.8 mN·m–1 for LiCl, ≈ 73.5 mN·m–1 for KCl, ≈ 75.6 mN·m–1 for MgCl2, and ≈ 75.0 mN·m–1 for Na2SO4. Since the data from Matubayasi et al. as well as Jarvis and Sheiman are only available in graphical and not tabular form, the values were extracted from the graphs. The surface tension data in Shah et al. (41) were conducted with the stalagmometer method and amounts to 73.96 mN·m–1 for NaCl, 73.81 mN·m–1 for NaBr, 74.08 mN·m–1 for LiCl, and 74.94 mN·m–1 for KCl. In the work of Ozdemir et al. a sessile bubble tensiometer was used for surface tension measurements at a temperature of 296.15 K. (36) The values amounts to 74.05 mN·m–1 for NaCl and 73.77 mN·m–1 for KCl. Note that the concentration is given there as molarity M but a conversion into molality was omitted because of the very low difference in the numerical values at the referred temperatures since water is used as a solvent. Our values are lower by 1.5 mN·m–1 in maximum except for LiCl and Na2SO4, for which our values are larger. Possible reasons for the deviations are already discussed in Figure 2 in the previous section. In case of LiCl a possible explanation can be found in the drying procedure of the hygroscopic salt (see Chapter 2.1 above and Chapter S3 in SI). Since LiCl contains small amounts of water, the real LiCl concentration is lower, and therefore, also the surface tension should be lower. In both articles it is mentioned that the salts were used as received and no further information regarding the preparation of LiCl could be found. (31,41) In the case of Na2SO4 the small concentration differences of the compared solutions may be the explanation for the deviations in surface tension values. For NaI solutions, our measured surface tension values are lower and also show a weaker concentration dependence than the literature data. Regarding to our experiments there is no evidence of contamination of the solutions or of incorrect measurements. Possible explanations can be found in different sample preparation as well as different measurement methods as the most likely reason.
In the following section, all shown graphs represent exemplary results for NaBr solutions. The graphs for the other inorganic salts can be found in Figures S4–S12 in SI. First, Figure 3 depicts the surface tension as a function of temperature for different concentrations of NaBr solutions. Note that not all concentrations are included for better clarity. The graphs of the other salt solutions are given in Figures S4–S9 in SI in the same way. As expected, the surface tension increases linearly with decreasing temperature for all solutions. Only at the two lowest temperatures (268.15 and 263.15 K) do the values deviate slightly from linear behavior. For solutions close to the solubility limit, the decreasing solubility with decreasing temperature may be the cause. Another possible explanation is the slower surface formation during bubble growth at lower temperatures. Thus, it may be that despite the same surface age, the state of the surface is slightly different at different temperatures.

Figure 3

Figure 3. Surface tension γ of aqueous salt solutions of NaBr as a function of temperature T at a pressure p = 100,000 Pa: ■ 0.116 mol·kg–1, gray ● 0.464 mol·kg–1, ▲ 0.988 mol·kg–1, gray ▼ 2.994 mol·kg–1, ◆ 3.971 mol·kg–1, gray ◀ 5.046 mol·kg–1 (cf. Table 3).

Finally, Figure 4 again illustrates the surface tension, this time as a function of molality for all temperatures of NaBr. In general, the surface tension increases with increasing salt concentration at all temperatures, but the increase is less pronounced at 268.15 and 263.15 K. Although the highest concentration is below the solubility limit (cf. Tables S2 and S3 in SI), the surface tension at 268.15 and 263.15 K of the higher concentrated salt solutions seems a little bit too low. A similar behavior was observed for the other salt solutions (cf., Figures S10 to S12 in SI) and a possible explanation is given above in the discussion of Figure 3. Because of the weak concentration dependence of the surface tension in the case of NaI pointed out above, the scatter of data (cf. Figure S10 in SI) is more relevant for calculation of the excess surface tension and surface tension gradient than for the other salts (cf. Chapters 3.3 and 3.4). Therefore, a larger difference of these values compared to comparative data is to be expected. Due to the slight deviations of surface tension data at temperatures below 271.15 K as mentioned in the previous sections, these data were not included into calculation of the surface tension gradient and the thermodynamic quantities.

Figure 4

Figure 4. Surface tension γ of aqueous salt solutions of NaBr as a function of molality m at a pressure p = 100,000 Pa: Solid and dotted lines result from linear fit at ■ 293.15 K, gray ● 288.15 K, ▲ 283.15 K, gray ▼ 278.15 K, ◆ 273.15 K, gray ◀ 271.15 K, ▶ 268.15 K, gray × 263.15 K (cf. Table 3).

At low concentration of NaCl, NaBr, NaI, and LiCl solutions around 0.1 mol·kg–1 a further distinctive feature can be observed. Here the surface tension of solution is lower than those of water, which can be extracted from Table 3 and Table S4 in SI. The latter one exhibits the surface tension of pure water at 293.15 K. Normally, the surface tension is not lowered by adding inorganic salts due to the absence of hydrophobic interactions between the ions and water molecules, which results rather in a depletion of these ions at the surface. The fact that the surface tension decreases despite the addition of small amounts of inorganic salts is known from literature as Jones–Ray effect (50−52) that occurs at typical salt concentrations lower than 0.1 mol·kg–1 and show a minimum in surface tension at concentrations below 0.01 mol·kg–1. (51,53,54) The Jones–Ray effect has been discussed in a very controversial way for decades. Okur et al. proposed in their articles that the Jones–Ray effect results from disturbances in the hydrogen-bond network of water induced by small amounts of inorganic salts. (54,55) Nevertheless, small amounts of surface-active organic molecules as impurity of the untreated salt can also lower the surface tension that becomes prominent in lower concentration ranges. (54) Since this effect is very small with a surface tension reduction of much less than 1 mN·m–1, it can be assumed that the impurity with surface-active organic molecules can be only very low. Otherwise surface tension reduction would be much more concise, since such surfactants are known to be very effective at this.

3.3. Excess Surface Tension

The excess surface tension Δγ was calculated for all salt solutions with eq 9 for a temperature of 293.15 K. The results are summarized in Table S7 and plotted in Figures S16 and S17 in the SI. The excess surface tension data were linearly fitted including the value of pure water (Δγ = 0 mN·m–1). These fits are presented in Figure 5.

Figure 5

Figure 5. Linear fit results of the excess surface tension Δγ of aqueous salt solutions as a function of molality m at a temperature T = 293.15 K and a pressure p = 100,000 Pa of green NaCl, orange NaBr, red NaI, sky blue LiCl, gray KCl, purple MgCl2, and blue Na2SO4. (cf. Figures S16 and S17). See Chapter 10 in the SI for more information on fitting the experimental data.

In the case of NaCl, NaBr, NaI, and LiCl, the excess surface tension also shows negative values at low concentrations (cf. Table S7 in SI). This feature was already discussed in the previous section (cf. 3.2). The negative values were not excluded from the linear fit. Therefore, our values may be slightly smaller than comparable values from the literature. As expected, dissolving inorganic salts in water leads to a general increase in surface tension, which means the excess surface tension is positive. The capability of the different inorganic salts to raise the surface tension is clearly different depending on the adsorption capacity of the salt. A lower excess surface tension value means a stronger adsorption at the air/water interface. Lowest values for a 1 mol·kg–1 solution were received for NaI with Δγ < 0.3 mN·m–1, and highest values for the electrolytes with one divalent ion, MgCl2 and Na2SO4 with Δγ ≈ 3.0 mN·m–1. For the other inorganic salts, the excess surface tension are between 0.7 and 2.2 mN·m–1 for a 1 mol·kg–1 solution. The order of the inorganic salts concerning the power of surface tension raising is in good agreement with the works of Pegram and Record, (56) as well as Weissenborn and Pugh, (39) who have collected a huge amount of experimental data from literature. Their works clearly show a stronger rise in surface tension in the case of electrolytes with divalent anions like Na2SO4 as well as Li2SO4, K2SO4, Cs2SO4, (NH4)2SO4, Na2CO3, and K2CO3, (56) and an even stronger effect for electrolytes with trivalent cations like LaCl3 or Cr(NO3)39 compared to monovalent electrolytes at similar salt concentrations. Based on our measurements, the adsorption capacity of the monovalent sodium halide salts is in the order NaI > NaBr > NaCl. This is consistent with the results from molecular dynamics simulation studies of Jungwirth and Tobias, as already mentioned above. (24) However, there are differences in the magnitude of the values, especially in the case of NaI, for which our values are much lower than those from other experimental works, like in Jarvis and Sheimann (49) or Matubaysai et al., (32) with Δγ ≈ 1.0 mN·m–1 for a 1 mol·kg–1 solution. Possible explanations can be found in Chapter 3.2.

3.4. Surface Tension Gradient

The change in surface tension by adding solutes to the solvent can also be expressed by the gradient (dγ/dm)Tp, which has a similar validity to the excess surface tension but is more common in published studies. The surface tension gradient was calculated by least-squares linear regression analysis at constant temperature. Here, the value of pure water was not included because it was only measured at 293.15 K, and of course, it is not available for 271.15 K. The difference whether the values of water are included or not is far below the calculated uncertainty of the surface tension gradient. Only in the case of NaI, the difference is larger because of the scattering of the surface tension data around that of pure water, combined with the weak increase in surface tension with increasing concentration. The gradients for the different salt solutions at different temperatures are listed in Table 4. Note that the gradient was not calculated for the two lowest temperatures in this work. From Table 4, it can be clearly extracted for the monovalent electrolytes that the gradient is reduced with decreasing temperature, being in agreement with Matubayasi et al. (31,32) For MgCl2 and Na2SO4, our values show a minimum, respectively.
Table 4. Surface Tension Increments of Aqueous Salt Solutions Given as Gradient (dγ/dm)Tp at Temperature T at a Pressure p = 100,000 Paa
 (dγ/dm)Tp/mJ·kg·m–2·mol–1
T/KNaClNaBrNaILiClKClMgCl2Na2SO4
271.151.321 ± 0.1290.966 ± 0.0340.026 ± 0.0901.328 ± 0.1380.969 ± 0.1043.400 ± 0.2273.203 ± 1.114
273.151.345 ± 0.1310.972 ± 0.0440.056 ± 0.0811.346 ± 0.1441.036 ± 0.1033.377 ± 0.2123.311 ± 1.122
278.151.402 ± 0.1181.031 ± 0.0420.090 ± 0.0821.387 ± 0.1491.132 ± 0.1013.301 ± 0.2073.372 ± 0.948
283.151.448 ± 0.1061.043 ± 0.0450.137 ± 0.0751.422 ± 0.1491.124 ± 0.1023.268 ± 0.1913.247 ± 0.909
288.151.419 ± 0.1041.100 ± 0.0490.173 ± 0.0701.475 ± 0.1561.156 ± 0.1203.278 ± 0.1953.003 ± 0.798
293.151.462 ± 0.0831.077 ± 0.0450.199 ± 0.0781.463 ± 0.1791.203 ± 0.1343.426 ± 0.1563.177 ± 0.523
a

The standard uncertainty of the temperature amounts to u(T) = 0.1 K. The standard uncertainties of the gradient values u((dγ/dm)Tp) are taken from least-squares linear regression analysis.

Positive values of the surface tension gradient mean that the solvated ions of the salts are depleted at the air/water interface compared with the bulk phase of the solution. The distribution of anions and cations in the interfacial region can be different, as shown in several molecular dynamics and other theoretical studies, (24,57−61) as well as with X-ray photoelectron spectroscopy (62,63) and ultraviolet second harmonic generation spectroscopy. (64) If this is the case, then the surface properties are dominated by one of the ion types. Jungwirth and Tobias simulated the air/water interface of different aqueous sodium halide solutions at 293.15 K and were the first to publish the results with new insights into the interfacial structure of electrolyte solutions. (24) They could show that smaller, nonpolarizable anions like fluoride or chloride are depleted and larger, polarizable anions like bromide or, in particular, iodide are enriched in the interfacial region. Transferred to the gradient values, it means that it is lower for NaI solutions than for NaCl solutions. This can be seen in Table 4. However, the value for the NaI solution is extremely low, even if the value of water was included in the calculation of the gradient. Nevertheless, the value of NaI should be closer to the value of the NaBr solution, since bromide is also supposed to accumulate at the air/water interface. (24) In a study of Sun et al., a slightly different result was obtained from molecular simulation studies of the same salts. (60) The density profile of bromide in the interfacial region is similar to that of chloride, and bromide seems not so strongly enriched as proposed in earlier studies referenced above. This may be an explanation for our gradient values of NaBr solutions that are closer to the values of NaCl solutions than to those of NaI solutions.
Several surface tension increment values at approximately 293.15 K were extracted from the literature and are summarized in Table 5 for comparison with our data. Note that the data received with the maximum bubble pressure method (mBPM) refer to molarity. These data were also not converted into molality because of the same reasons already given in Chapter 3.2. The summary in Table 5 shows that the data differ. The order of the data is also not always the same, as can be seen based on the example of LiCl and KCl. In the works of Weissenborn and Pugh (39,40) the value of LiCl is larger than for KCl, as in our data, while in Matubayasi et al., (31) the opposite is the case. Considering the uncertainties, our data are in good accordance with the literature data, except for NaI, which is discussed in the previous section and in Chapter 3.2.
Table 5. Surface Tension Increment of Aqueous Salt Solutions Given as Gradient (dγ/dm)Tp Taken from Literaturea
 (dγ/dm)Tp/mJ·kg·m–2·mol–1
methodNaClNaBrNaILiClKClMgCl2Na2SO4
mBPMb2.081.831.231.981.854.062.90
mBPMc1.761.71--1.683.732.99
DVd1.70--1.581.59-2.66
DVe---1.381.49--
DVf1.411.190.97----
WPg1.75-1.21-1.65--
a

Note that the concentration in b and c is given in molarity and is not converted into molality. For this, the gradient is (dγ/dM)Tp/mJ·L·m–2·mol–1. A conversion into molalities was omitted. The abbreviations mean as follows: mBPM – maximum bubble pressure method, DV – drop volume method, WP – Wilhelmy plate method

b

Data from Weissenborn and Pugh (39,40) at T = 294.15–301.15 K and for 0.05–1 mol·l–1 solutions.

c

Data from Henry et al. (38) at T = 293.15 K and for 0.5 to 3 mol·l–1 solutions.

d

Data from Aveyard and Saleem (37) at T = 293.15 K and 0.1–1 mol·kg–1 NaCl solutions, 0.2–1.5 mol·kg–1 KCl solutions, 0.2–1.0 mol·kg–1 Na2SO4 solutions.

e

Data from Matubayasi et al. (31) at T = 293.15 K and 0.1–1 mol·kg–1 solutions.

f

Data from Matubayasi et al. (32) at T = 293.15 K and 0.1–1 mol·kg–1 solutions.

g

Data from Johansson and Eriksson (35) at T = 298.15 K and 0.1–1 mol·kg–1 NaCl and NaI solutions, 0.1–1.5 mol·kg–1 KCl solutions.

3.5. Thermodynamic Quantities of Surface Formation

The surface excess entropy Δsσ and surface excess energy Δuσ given in Table 6 were estimated by least-squares linear regression analysis of the temperature-dependent surface tension data (cf. eq 8 and description in Chapter 1). As described above, the values at 263.15 and 268.15 K were not included in the regression analysis. The surface excess enthalpy Δhσ at a temperature of 293.15 K was calculated with eq 6. First of all, it should be noted that the changes in the excess quantities are associated with the adsorption capacity of the dissolved substance.
Table 6. From Experimental Data Calculated Values of Surface Excess Entropy Δsσ, Surface Excess Energy Δuσ, and Surface Excess Enthalpy Δhσ of Aqueous Salt Solutions as a Function of Molality m at a Pressure p = 100,000 Paa
saltm/mol·kg–1Δsσ/mJ·K–1·m–2Δuσ/mJ·m–2Δhσ/mJ·m–2
NaCl0.0960.1509±0.0038116.4433±1.082544.2345±1.1434
 0.2030.1560±0.0016118.3353±0.443345.7342±0.4778
 0.4630.1635±0.0032121.2163±0.906147.9206±0.9609
 0.7330.1638±0.0097121.5607±2.738948.0049±2.8731
 0.9840.1816±0.0050127.1595±1.418553.2297±1.4980
 1.4980.1944±0.0063131.6060±1.773156.9840±1.8686
 1.9870.1413±0.0031116.4144±0.867641.4261±0.9183
 2.9730.1433±0.0055117.6466±1.551842.0164±1.6331
 4.0150.1387±0.0067119.1521±1.886940.6633±1.9813
 5.0050.1366±0.0066120.0873±1.861340.0578±1.9536
NaBr0.1160.1667±0.0040121.0866±1.128148.8646±1.1929
 0.2030.1582±0.0037118.8695±1.033046.3885±1.0924
 0.4640.1725±0.0051123.4361±1.439650.5688±1.5173
 0.7520.1684±0.0037122.2627±1.037949.3651±1.0997
 0.9880.1583±0.0057119.9938±1.592046.4065±1.6753
 1.4950.1865±0.0069128.3121±1.938454.6743±2.0400
 2.9940.1559±0.0034120.8511±0.946845.6965±1.0028
 3.9710.1511±0.0055120.8056±1.555944.3081±1.6375
 5.0460.1309±0.0059116.3658±1.660838.3648±1.7451
NaI0.1110.1970±0.0046129.5423±1.281457.7419±1.3554
 0.1430.1445±0.0069114.3908±1.942842.3523±2.0393
 0.1970.1669±0.0040121.0629±1.111848.9205±1.1754
 0.5130.1537±0.0052117.9655±1.462645.0625±1.5403
 0.5300.1616±0.0044120.5451±1.229447.3609±1.2983
 0.7470.1698±0.0021122.3612±0.587749.7820±0.6303
 0.9940.1475±0.0040115.9751±1.127243.2261±1.1899
 0.9970.1638±0.0047121.0817±1.311648.0146±1.3850
 1.5300.1447±0.0049115.2674±1.367042.4283±1.4400
 2.0850.1554±0.0050118.3054±1.393245.5624±1.4684
 2.7720.1181±0.0063107.7911±1.780134.6292±1.8679
 3.8330.1419±0.0055114.4380±1.546841.5853±1.6277
 4.6640.1379±0.0054113.8483±1.508540.4203±1.5869
LiCl0.1060.1711±0.0026122.2650±0.736750.1435±0.7845
 0.2020.1512±0.0038117.1506±1.071844.3276±1.1322
 0.4990.1410±0.0043116.4026±1.202241.3199±1.2673
 0.7480.1677±0.0035122.9118±0.975249.1579±1.0330
 1.0140.1468±0.0028118.0374±0.790443.0213±0.8390
 1.5610.1656±0.0034122.8650±0.946848.5391±1.0036
 2.3630.1565±0.0077121.0421±2.162445.8661±2.2704
 2.9850.1359±0.0031116.9841±0.864939.8466±0.9156
 4.1410.1210±0.0038114.1376±1.078035.4588±1.1358
 4.9200.1303±0.0034118.8528±0.948038.2061±1.0018
KCl0.1180.1462±0.0020115.7361±0.566442.8459±0.6050
 0.2040.1581±0.0029119.7337±0.822046.3380±0.8728
 0.5410.1459±0.0027116.4182±0.748042.7572±0.7941
 0.7520.1361±0.0036114.8167±1.003539.9121±1.0600
 1.0110.1599±0.0047120.4518±1.324646.8833±1.3972
 1.4090.1404±0.0027116.1949±0.748841.1679±0.7943
 1.9300.1323±0.0039114.0987±1.100038.7942±1.1608
 3.0860.1253±0.0018113.5204±0.501736.7453±0.5359
 4.0230.1146±0.0093111.5716±2.627933.5971±2.7514
MgCl20.0990.1419±0.0030115.7444±0.833941.5889±0.8835
 0.2120.1418±0.0011115.4515±0.302641.5779±0.3294
 0.4870.1540±0.0039118.7758±1.110645.1433±1.1725
 0.6980.1642±0.0019121.7893±0.540348.1280±0.5795
 0.9420.1369±0.0046115.5453±1.288240.1329±1.3578
 1.3140.1424±0.0033118.4270±0.926141.7465±0.9800
 1.6330.1361±0.0007117.5042±0.191439.9118±0.2132
 2.3010.1197±0.0036115.7778±1.000635.0887±1.0550
 2.7760.1221±0.0026117.9685±0.740535.7913±0.7841
 3.2010.1272±0.0030121.2133±0.846537.2762±0.8955
Na2SO40.0880.1383±0.0036113.3197±1.019440.5521±1.0765
 0.2350.1600±0.0061120.4811±1.704346.9052±1.7933
 0.4950.1175±0.0025107.9805±0.708534.4392±0.7501
 0.7300.1648±0.0023122.8768±0.664048.3184±0.7037
 0.9300.1407±0.0070117.0263±1.979541.2489±2.0777
a

The surface excess enthalpy was calculated for a temperature of 293.15 K. The combined standard uncertainty of the molality values amounts to uc(m) = 0.0002 mol·kg–1. The combined standard uncertainties of the surface excess enthalpy uchσ) are estimated via error calculation. See Chapter S6 in SI for more detail. The standard uncertainties of the surface excess entropy usσ) and the surface excess energy uuσ) are taken from least-squares linear regression analysis.

The surface excess entropy is plotted for the monovalent electrolytes in Figures 6 and 7. The data of NaCl show larger variation than those for the other salts, which was also observed in the works of Matubayasi et al. (32) and Shah et al. (41) These variations may result from slight deviations in the temperature dependence of the surface tension, leading to deviations in the slope value for calculation of the surface excess entropy. Nevertheless, considering the uncertainties, a decrease in the surface excess entropy with increasing salt concentration can be observed. This is in accordance with published data and complements, at larger concentrations, the trend in the data there in a comprehensible way. (30−32,41) It should be pointed out that the decrease in surface excess entropy is much smaller than for typical surfactants, like, for example, sodium taurodeoxycholate (NaTDC), a bihydroxy bile salt. (65) Since the entropy is a quantity of disordering of a system, this is not surprising. In general, entropy increases by adding solutes to the solvent, leading to larger entropy values of solutions (bulk and surface) compared to the pure solvent. A decrease in surface excess entropy with increasing concentration means a higher degree of orientation of the molecules at the surface with an increasing number of solute molecules. Typical surfactants tend to adsorb strongly at the air/water interface, which leads to a more or less ordered arrangement of the molecules at the water surface that becomes more prominent with increasing concentration until a highly ordered surfactant film is formed at the water surface. The high degree of order of these surfactant films results from their molecular structure. Surfactants are amphiphilic molecules with a hydrophilic headgroup and a hydrophobic tail. While the interactions between the polar headgroups of the surfactants and the polar water molecules are attractive, the interactions between the hydrophobic tails and the water molecules are repulsive, leading to an orientation of the hydrophobic tails out of the surface. The water molecules also have a higher degree of orientation in the interfacial region as a result of their interaction with the polar headgroups of the surfactant molecules, which is why the surface excess entropy decreases again and can even show negative values. (27) In the case of inorganic salts, the situation at the air/water interface is already discussed in Chapter 3.4. Larger, polarizable, not fully solvated ions also adsorb at the air/water interface, leading to a larger degree of organization of water molecules with an increasing number of ions due to electrostatic interactions between them. Compared to surfactant solutions, the organization of the water molecules there occurs to a much weaker extent due to the absence of repulsive interactions between them and the ions. This can be stated by an approximately reduction of surface excess entropy from 0.16 mJ·K–1.m–2 for a 1 mol·kg–1 salt solution to 0.13 mJ·K–1.m–2 for a 5 mol·kg–1 salt solution in comparison to an approximately reduction from 0.16 mJ·K–1.m–2 for a < 1 mmol·kg–1 NaTDC solution to <0.01 mJ·K–1.m–2 for a 4 mmol·kg–1 NaTDC solution (extracted from graphs in Matubayasi et al. (65)). Smaller, nonpolarizable ions are fully solvated and are arranged in the subsurface region. They may also lead to a slightly higher degree of organization of the water molecules at the air/water interface with an increasing number of ions for the same reasons as described before. The difference between the different ions concerning the enrichment or depletion at the water surface seems to be small, so that no clear differences could be observed in the surface excess entropy data. A value of approximately 0.16 mJ·K–1.m–2 for a 1 mol·kg–1 salt solution is also in good agreement with literature data. (30−32,41) Johansson and Eriksson did not directly calculate the surface excess entropy, but the slope of the temperature-dependent surface tension data provided a value of approximately −0.16 mJ·K–1.m–2 for NaCl, NaI, and KCl that also agrees very well with our data. (35) Conclusions concerning the dependence of the surface excess entropy on the hydration radius or polarizability of the ions cannot be drawn, because of the small differences and the larger uncertainties in the data.

Figure 6

Figure 6. Surface excess entropy Δsσ of aqueous salt solutions as a function of molality m at a pressure p = 100,000 Pa of: ■ NaCl, ○ NaBr, gray ▲ NaI (cf. Table 6).

Figure 7

Figure 7. Surface excess entropy Δsσ of aqueous salt solutions as a function of molality m at a pressure p = 100,000 Pa of: ■ NaCl (again for comparison), ○ LiCl, gray ▲ KCl (cf. Table 6).

Further thermodynamic quantities as a function of molality are represented exemplarily for NaBr in Figure 8. The graphs for the other inorganic salts can be found in Figures S13–S15 in the SI. Regarding the small number of data points, the data for Na2SO4 are not representative and are therefore not shown. The surface excess energy Δuσ as well as the surface excess enthalpy Δhσ are also given in Table 6, and the surface excess Helmholtz energy Δaσ is equal to the surface tension (cf. eq 7). The fact that the surface excess Helmholtz energy is increasing with increasing concentration results directly from surface tension and does not need to be further discussed. The surface excess enthalpy is always lower than 60 mJ·m–2 and decreases with increasing concentration but remains positive, which can already be concluded from the positive values of the surface excess entropy (cf. eq 6). Positive values of the surface excess enthalpy indicate that the transfer of solvated or partially solvated ions from the electrolyte solution to the air/water interface is endothermic. For typical surfactants, the decrease of surface excess enthalpy is much stronger and can reach negative values. (27) An explanation is already given in the discussion of the surface excess entropy. The surface excess energy amounts to approximately 120 mJ·m–2 for all salt solutions and shows the weakest concentration dependence, with also a very slight decrease with increasing concentration. Thus, the adsorption of ions at the surface of aqueous inorganic salt solutions is neither particularly less favored nor particularly favored energetically. This is contrary to the adsorption behavior of typical surfactants. Like for the already discussed thermodynamic quantities, the surface excess energy in these systems can also become negative, (27) which means that the adsorption of the surfactant molecules at the water surface is energetically more favorable than their remaining in the bulk.

Figure 8

Figure 8. Thermodynamic quantities of aqueous salt solutions of NaBr as a function of molality m and their linear fits at a pressure p = 100,000 Pa: ▲ surface excess energy Δuσ(cf. Table 6), gray ■ surface excess Helmholtz energy Δaσ at T = 293.15 K (cf. Table 3), ○ surface excess enthalpy Δhσ at T = 293.15 K (cf. Table 6). The error bars correspond to the uncertainties of Δuσ and Δhσ given in Table 6. The uncertainties of Δaσ are too small to depict, but they are equal to those of the surface tension given in Table S6 in SI.

The values and the behavior of these thermodynamic quantities are in agreement with the data from Matubayasi et al. (30,31) and Shah et al. (41) It has to be mentioned that all changes of these thermodynamic quantities of the inorganic salt solutions are very small compared to surfactant solutions. (65) This can be expected based on the weak concentration dependence of the surface tension itself and the surface excess entropy due to the much weaker adsorption of the solvated or partially solvated ions at the air/water interface compared to typical surfactants, as already discussed in detail. The weaker adsorption means that no continuous or closely packed solute film forms at the interface. As a result, the changes in the excess quantities with increasing salt concentration are generally not as significant.

4. Conclusions

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In the present work, new experimental surface tension data of aqueous inorganic salt solutions of NaCl, NaBr, NaI, LiCl, KCl, MgCl2, and Na2SO4 in an atmospherically relevant temperature range of 263.15–293.15 K were presented. The concentration range was set from 0.1 to 5 mol·kg–1 (up to 1 mol·kg–1 for Na2SO4, up to 3 mol·kg–1 for MgCl2, as well as up to 4 mol·kg–1 for KCl). From these data, the excess surface tension, the surface tension gradient, and several thermodynamic quantities like surface excess entropy, surface excess energy, surface excess enthalpy, and surface excess Helmholtz energy were calculated. The concentration-dependent surface excess entropy, as a quantity giving information about the degree of ordering of the solvent molecules at the air/water interface, slightly decreases with a growing number of dissolved ions. A decrease in surface excess entropy from approximately 0.16 mJ·K–1.m–2 for a 1 mol·kg–1 salt solution to 0.13 mJ·K–1.m–2 for a 5 mol·kg–1 salt solution shows a very small order dependence of the water molecules on the concentration of the inorganic salt solutions compared to typical surfactants. From an energetic point of view, the adsorption of ions at the water surface is endothermic based on the positive values of the surface excess enthalpy and is not the clearly preferred process as can be extracted from the positive and nearly constant values of the surface excess energy. This can be explained by the attractive interactions between the ions and the water molecules in aqueous inorganic salt solutions. The thermodynamic quantities are in good agreement with the literature and complement this, especially for salt concentrations higher than 1 mol·kg–1.

Supporting Information

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The following files are available free of charge. The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jced.5c00470.

  • Conversion of mass fraction to molality (Chapter S1, Table S1); solubility of the inorganic salts (Chapter S2, Tables S2 and S3); preparation of LiCl (Chapter S3, Figure S1); estimation of the surface tension from time series (Chapter S4, Figure S2); surface tension of water including uncertainties (Chapter S5, Table S4); calculation of the combined standard uncertainty of the molality (Chapter S6.1, Table S5); calculation of the combined standard uncertainty of the density (Chapter S6.2); calculation of the combined standard uncertainty of the surface tension (Chapter S6.3, Table S6); calculation of the combined standard uncertainty of the excess surface tension (Chapter S6.4); calculation of the combined standard uncertainty of the surface excess enthalpy (Chapter S6.5); density values at 293.15 and 278.15 K (Chapter S7 and Figure S3); surface tension as a function of the temperature of NaCl, NaI, LiCl, KCl, MgCl2, and Na2SO4 solution (Chapter S8 and Figures S4–S9); surface tension as a function of the molality of NaCl, NaI, LiCl, KCl, MgCl2, and Na2SO4 solution (Chapter S9 and Figures S10–S12); thermodynamic quantities such as surface excess energy, surface excess Helmholtz energy, and surface excess enthalpy at 293.15 K of NaCl, NaI, LiCl, KCl, MgCl2, and Na2SO4 solution (Chapter S10 and Figures S13 to S15); excess surface tension including fits for all aqueous inorganic salt solutions at 293.15 K (Chapter S11, Table S7, and Figures S16 and S17); graphical comparison of the density values with literature data (Chapter S12, Figures S18 and S19); graphical comparison of the surface tension values with literature data (Chapter S13, Figures S20 and S21) (PDF)

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Author Information

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  • Corresponding Author
  • Author
    • Alexandra Giermann - Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstraße 2, 04103 Leipzig, Germany
  • Author Contributions

    The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript. M. R.: Conceptualization, methodology, experiment, investigation, data evaluation, formal analysis, validation, visualization, writing – original draft, and writing – review and editing. A. G.: Experiment, investigation, data evaluation, and writing – review and editing.

  • Funding

    The research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) project 321027174 (Spectroscopic Characterization of Salt Dissolution in Microhydrated Cluster Ions and at the Water/Vapor Interface).

  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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We thank Prof. Dr. Jonas Warneke for his discussions and critical comments on the manuscript.

References

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  • Abstract

    Figure 1

    Figure 1. Density ρ of aqueous salt solutions of NaCl as a function of molality m at a temperature T = 293.15 K and at a pressure p = 100,000 Pa for: solid line and × own data (cf. Table 2) in comparison with data from literature: blue ● Hoffert et al., (47) red ▲ Rogers and Pitzer, (48) and gray ◆ Shah et al. (41) Note that the reference data from Rogers and Pitzer are given as specific volumes and were converted into density for comparison.

    Figure 2

    Figure 2. Surface tension γ of aqueous salt solutions of NaCl as a function of temperature T at a pressure p = 100,000 Pa for own data at: ■ 2.994 mol·kg–1, blue ● 1.997 mol·kg–1, gray ▲ 0.984 mol·kg–1 (cf. Table 3) and data from literature (42) at: □ 3.020 mol·kg–1, blue ○ 1.901 mol·kg–1, gray △ 0.901 mol·kg–1. The concentrations of the reference data are given in mass fractions and were converted into molality for comparison (cf. Chapter S1 in the SI).

    Figure 3

    Figure 3. Surface tension γ of aqueous salt solutions of NaBr as a function of temperature T at a pressure p = 100,000 Pa: ■ 0.116 mol·kg–1, gray ● 0.464 mol·kg–1, ▲ 0.988 mol·kg–1, gray ▼ 2.994 mol·kg–1, ◆ 3.971 mol·kg–1, gray ◀ 5.046 mol·kg–1 (cf. Table 3).

    Figure 4

    Figure 4. Surface tension γ of aqueous salt solutions of NaBr as a function of molality m at a pressure p = 100,000 Pa: Solid and dotted lines result from linear fit at ■ 293.15 K, gray ● 288.15 K, ▲ 283.15 K, gray ▼ 278.15 K, ◆ 273.15 K, gray ◀ 271.15 K, ▶ 268.15 K, gray × 263.15 K (cf. Table 3).

    Figure 5

    Figure 5. Linear fit results of the excess surface tension Δγ of aqueous salt solutions as a function of molality m at a temperature T = 293.15 K and a pressure p = 100,000 Pa of green NaCl, orange NaBr, red NaI, sky blue LiCl, gray KCl, purple MgCl2, and blue Na2SO4. (cf. Figures S16 and S17). See Chapter 10 in the SI for more information on fitting the experimental data.

    Figure 6

    Figure 6. Surface excess entropy Δsσ of aqueous salt solutions as a function of molality m at a pressure p = 100,000 Pa of: ■ NaCl, ○ NaBr, gray ▲ NaI (cf. Table 6).

    Figure 7

    Figure 7. Surface excess entropy Δsσ of aqueous salt solutions as a function of molality m at a pressure p = 100,000 Pa of: ■ NaCl (again for comparison), ○ LiCl, gray ▲ KCl (cf. Table 6).

    Figure 8

    Figure 8. Thermodynamic quantities of aqueous salt solutions of NaBr as a function of molality m and their linear fits at a pressure p = 100,000 Pa: ▲ surface excess energy Δuσ(cf. Table 6), gray ■ surface excess Helmholtz energy Δaσ at T = 293.15 K (cf. Table 3), ○ surface excess enthalpy Δhσ at T = 293.15 K (cf. Table 6). The error bars correspond to the uncertainties of Δuσ and Δhσ given in Table 6. The uncertainties of Δaσ are too small to depict, but they are equal to those of the surface tension given in Table S6 in SI.

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  • Supporting Information

    Supporting Information


    The following files are available free of charge. The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jced.5c00470.

    • Conversion of mass fraction to molality (Chapter S1, Table S1); solubility of the inorganic salts (Chapter S2, Tables S2 and S3); preparation of LiCl (Chapter S3, Figure S1); estimation of the surface tension from time series (Chapter S4, Figure S2); surface tension of water including uncertainties (Chapter S5, Table S4); calculation of the combined standard uncertainty of the molality (Chapter S6.1, Table S5); calculation of the combined standard uncertainty of the density (Chapter S6.2); calculation of the combined standard uncertainty of the surface tension (Chapter S6.3, Table S6); calculation of the combined standard uncertainty of the excess surface tension (Chapter S6.4); calculation of the combined standard uncertainty of the surface excess enthalpy (Chapter S6.5); density values at 293.15 and 278.15 K (Chapter S7 and Figure S3); surface tension as a function of the temperature of NaCl, NaI, LiCl, KCl, MgCl2, and Na2SO4 solution (Chapter S8 and Figures S4–S9); surface tension as a function of the molality of NaCl, NaI, LiCl, KCl, MgCl2, and Na2SO4 solution (Chapter S9 and Figures S10–S12); thermodynamic quantities such as surface excess energy, surface excess Helmholtz energy, and surface excess enthalpy at 293.15 K of NaCl, NaI, LiCl, KCl, MgCl2, and Na2SO4 solution (Chapter S10 and Figures S13 to S15); excess surface tension including fits for all aqueous inorganic salt solutions at 293.15 K (Chapter S11, Table S7, and Figures S16 and S17); graphical comparison of the density values with literature data (Chapter S12, Figures S18 and S19); graphical comparison of the surface tension values with literature data (Chapter S13, Figures S20 and S21) (PDF)


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