Density of normal and associated liquids
Graphical abstract
Highlights
► Formula of liquids density obtained on the basis of liquids distribution function. ► Regularities of changes of density in ranks of ordinary liquids were determined. ► Associated liquids do not obey the regularities detected for ordinary liquids.
Introduction
The liquid density is measured often for two reasons. The first one is a qualitative evaluation of a liquid. The measurements of liquid density aim at the conformity with quality standards and possible assessment of the liquid. For example, in works [1], [2], [3], [4] the estimation of the density scaling of the diffusivity, liquid dynamics and excess volumes of viscous liquids was carried out. The Tait or Tait-like equations [5] relating liquid density to pressure were tested in [6], [7], [8]. The improvement of solvent collection system for a dispersive liquid–liquid microextraction of organochlorine pesticides from water using low-density organic solvent was shown in work [9]. Redlich–Kister polynomial relations [10] are useful to calculate the azeotropic point coordinates in the temperature and pressure ranges studied in [11]. Thermodynamic functions of a liquid crystal were studied through density measurements in [12].
At present, the mixed solvents [13], [14], [15], which have anticipatorily planned physicochemical properties including density, have been studied widely. In most cases, such measurements are carried out in laboratories using laboratory densitometers [16], [17], [18], [19], [20], [21].
The second reason for measuring density is the estimation of density to evaluate the mass of a liquid. Because the mass of a liquid is a stable parameter, the amount of liquid can be calculated in many fields not on the basis of volume (liters) but according to mass (kilograms). The density of a liquid should be measured to calculate its mass, what is successfully done with density measuring devices for liquids.According to Continuity Hypothesis, a liquid is considered as a deformable system of material particles, which continuously fills the space it is moving in [22]. The particle of a liquid makes up a very little volume containing a great deal of molecules of liquid. For example, if we take into consideration a cube of water with sides of 0.001 cm, there will be 3.3 × 1013 of molecules within the volume. The particle of a liquid is considered very small in comparison to size of the area taken by a moving liquid. Based on such assumption, a liquid can be in general considered a continuum, a continuous medium steadily filling the space, e.g. it is presumed that there are no gaps and emptiness in a liquid, all characteristics of a liquid are continuous functions having continuous partial derivatives with respect to their arguments [23]. The continuous medium can be considered a model which is successfully used in research on the patterns of rest and motion of a liquid [24], [25]. The density determines distribution of mass M of a liquid in volume W. In any point A of a liquid, the densitywhere ΔM is the mass contained in the volume ΔV contractible to the point A.
The density of a homogeneous liquid is equal to the ratio of the mass of M a liquid to its volume V:The density ρ at all points of a homogeneous liquid is equal.
In general, the density can change from point to point in the volume taken by the liquid and at any point of the volume in time [26].
The density of liquids ρ is determined by thermodynamical factors (p and T) and properties of constituent particles of the body – their size, mass, form, dipole moment, polarizability [27]. The formulas suggested for density [28], [29]:where M is molecular mass, mz is the mass of hydrogen atom, v is the volume calculated for one molecule in liquid, ρs is density at the boiling point, σ is molecular diameter, Ks is constant do not take into account the direct influence of temperature, interaction forces between the particles in a liquid, form of a molecule; the formula (3) estimates the influence of own molecular size in an inconsistent way. That is why a more precise dependence can be obtained on the basis of the kinetic theory of liquids [30] from the sum-of-states function for a liquid:
At present, Flory's statistical theory of binary liquid mixtures [31] has been applied successfully to multicomponent liquid mixtures [32], [33], [34] what confirms the correctness of the research on liquids carried out on the basis of the kinetic molecular and statistical theories of liquids.
Section snippets
Theory
For liquids in the structured state, the free molar volume Vf can be considered equal to [35]where V is the molar volume of liquid, NA is the Avogadro number, vM is the molecular volume, C is the coefficient equal to 1.911 if the molecules have a spherical form and the position of neighbors of the central molecule is fixed. In fact, molecules have different diameters, and the neighbors of the central molecule are steady moving; C is the coefficient dependent both on the
Chemicals
The list of associated liquids used in this study is as follows: [2-nitrophenol], MERCK, grade >0.995 mass fraction; [3-nitrophenol], MERCK, grade >0.995 mass fraction; [4-nitrophenol], MERCK, grade >0.995 mass fraction; [2-Nitroanisole], MERCK, grade >0.99 mass fraction; [3-nitroanisole], MERCK, grade >0.99 mass fraction; [4-nitroanisole], MERCK, grade >0.99 mass fraction; [2-hydroxybenzaldehyde], MERCK, grade >0.99 mass fraction; [3-hydroxybenzaldehyde] MERCK, grade >0.995 mass fraction;
Density of associated liquids
When additive schemes of molar volume are created, in some cases the special atomic value is attributed to hydroxyl oxygen what shows the anomaly of density for associated liquids [46]. Indeed, spirits, phenols, and carbon acids as members of appropriate ranks do not obey the aforementioned regularities for ordinary liquids. Hence, isologs containing a hydroxyl group show much higher density than it may be concluded from the mass of their molecules. In case of phenol, its density is higher than
Conclusions
The formula of liquids density obtained on the basis of distribution function of liquids allows to estimate the density of ordinary liquids more precisely. The regularities of changes of density in different ranks of ordinary liquids (homological, metamer, and isotopic compounds, isologs) were determined.
During transition into associated liquids, the spirits, phenols, and carbon acids as members of the appropriate ranks do not obey the regularities detected for ordinary liquids. It was shown
Acknowledgement
Financial support of the US National Science Foundation, grant CHE-1050405 is gratefully acknowledged.
- A
A = RT = const
- C
coefficient in Eq. (6)
- h
Planck's constant = 6.626068 × 10−34 m2 kg/s
- k
Boltzmann constant = 1.38066 × 10−23 J/K
- Ks
constant in Eq. (4)
- mz
mass of hydrogen atom
- M
molecular mass (g mol−1)
- Munsub
molecular mass of non-substituted compound
- Mw
molecular weight (g mol−1)
- m
mass of one molecule
- N
number of molecules in unit of volume
- NA
Avogadro number
- P
pressure
- Ql
sum-of-states function for liquid
- R
gas constant (8.31451 J mol
List of symbols
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Cited by (1)
On viscosity of selected normal and associated liquids
2013, Journal of Molecular LiquidsCitation Excerpt :The purity grade and viscosities of pure components are given in Table 1, showing good agreement with the literature data [26,27]. The densities of compounds under study are given in Ref. [28]. The viscometer was calibrated with spectroscopic grade 1-butanol and doubly distilled water at the experimental temperature.