Temperature and Pressure Dependence of Liquid Density

Harris KR, Kanakubo M, Woolf LA (2007) Temperature and pressure dependence of the viscosity of the ionic liquid 1-butyl-3-methylimidazolium tetrafluorohorate viscosity and density relationships in ionic liquids. J Chem Eng Data 52 2425-2430... 

The volumes of condensed phases are also much less sensitive to temperature and pressure than gases. The measured values can be adjusted for temperature or pressure changes by using a Taylor series expansion on density. For liquids significantly below the critical temperature and for solids, we can neglect all terms but the first (linear) term of the Taylor expansion. This approach leads to quantification of the temperature and pressure dependencies of volume with the thermal expansion coefficient, j8, and the isothermal compressibility, k, respectively. 

The density of a SCF is typically less than half that of the liquid state, but two orders of magnitude greater than that of a gas. Viscosity and diffusivity are also temperature and pressure dependent. 

The Sanchez-Lacombe equation-of-state provides a good example to help clarify the rather abstract discussion given above. It will now be discussed further. It is given by Equation 3.26 for a pure molecular liquid or gas. The variable r is defined by Equation 3.27, where M is the molecular weight and R is the gas constant. If T, p and p are known, Equation 3.26 can be solved iteratively to estimate the density as a function of temperature and pressure. Since the reduced density p depends on M through the variable r defined by Equation 3.27, it is not equal for all molecules at the same combination of T and p values. Consequently, for ordinary molecules, the Sanchez-Lacombe equation-of-state is not a corresponding states theory. 

Table 4.1 is a comparison of typical values for the physical properties of a pure substance in different phases, including an SCF around the critical point. It can be seen that the density of an SCF is approximately two orders of magnitude higher than that of the gas, but still less than half that of a conventional liquid phase. The viscosity and diffusivity - which are also temperature and pressure dependent - are in general at least an order of magnitude lower and higher, respectively, than for the liquid phase. If a chemical reaction is particularly fast, the diffusion can be the limiting factor an increase in the diffusivity can then lead to reaction rate enhancement. This... 

PRESSURE AND TEMPERATURE DEPENDENCE OF LIQUID DENSITY (continued)... 

The isothermal densities within each of the five groups of esters reveal a significant dependence on the molecular structure. At a constant temperature and pressure, the liquid density of the ester decreases with increasing molecular weight and the successive addition of the methylene groups, (X), even though the concentration of the end-groups remained constant. 

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