Excessive molar volume

Figure 7.5 Comparison of excess molar volumes for four mixtures as follows Curve 1 . y,C 0H22 +. y2c-C6H,2 at 7=313.15 K.

AV is then the excess molar volume of products over that of reactants, in their standard states. For dilute solutions, where activity corrections may be neglected, and where Kx is expressed in mole fraction units... 

In this chapter, we shall consider the methods by which values of partial molar quantities and excess molar quantities can be obtained from experimental data. Most of the methods are applicable to any thermodynamic property J, but special emphasis will be placed on the partial molar volume and the partial molar enthalpy, which are needed to determine the pressure and temperature coefficients of the chemical potential, and on the excess molar volume and the excess molar enthalpy, which are needed to determine the pressure and temperature coefficients of the excess Gibbs function. Furthermore, the volume is tangible and easy to visualize hence, it serves well in an initial exposition of partial molar quantities and excess molar quantities. 

Chandrasekhar, G., Venkatesu, P., and Rao, M.V.P. Excess molar volumes and speed of sound of ethyl acetate and butyl acetate with 2-alkoxyethanols at 308.15 K, J. Chem. Eng. Data, 45(4) 590-593, 2000. 

Comelli, F. and Francesconi, R. Isothermal vapor-liquid equilibria measurements, excess molar enthalpies, and excess molar volumes of dimethyl carbonate + methanol. + ethanol, and propan-l -ol at 313.15 K. J. Chem. Eng. Data, 42(4) 705-709, 1997. 

Lu, H., Wang, J., Zhao, Y., Xuan, X., and Zhuo, K. Excess molar volumes and viscosities for binary rtrixtrrres of y-butyrolactone with methyl formate, ethyl formate, methyl acetate, ethyl acetate, and acetonitrile at 298.15 K,J. Chem. Eng. Data, 46(3) 631-634, 2001. 

Resa, J.M., Gonzalez, C., de Eandaluce, S.O., and Eanz, J. Densities, excess molar volumes, and refractive indices of ethyl acetate and aromatic hydrocarbon binary mixtures. J. Chem. Thermodyn, 34(7) 995-1004. 2002. 

Tanaka. R. and Toyama, S. Excess molar volumes and excess molar heat capacities for binary mixtures of ethanol with chlorocyclohexane, 1-nitropropane, dibutyl ether, and ethyl acetate at the temperature of 298.15 K. 7 Chem. Eng. Data, 41(6) 1455-1458,1996. 

Less negative values of the excess molar volumes were obtained for the IL with the longer alkyl chain in the cation for the same alcohol. The structure of [C4CiIm][CiS04] is less H-bonded than [CiCiIm][CiSOJ in the pure state. 

The excess molar volumes for [C0CiIm][BF4] + 1-butanol, or 1-pentanol were found very small and negative in the alcohol-rich range of the mixture composition and positive in the alcohol-poor range [62]. More positive values were observed for 1-pentanol ( (max) = 0-92 cm moD at equimolar composition and 298.15 K). 

The influence of temperature and pressure on the excess molar volume is not very well known. For ILs the values were observed more negative at higher temperature [60,63]. Increasing the pressure from 0.1 to 20 MPa at the same temperature, less negative values of were observed [63]. The influence of temperature on the values at the pressure 15 MPa for [CiCiIm][CiS04] -t methanol is presented in Figure 1.4. 

Strong intermolecular interactions between the hydroxyl group and the IL lead to the negative values of excess molar volumes,, and excess molar enthalpies The strongly negative curve for [CiQlm][QS04] + water, ... 

Zafarani-Moattar, M.T. and Shekaari, H. Volumetric and speed of sound of ionic liquid, l-butyl-3-methylimidazolium hexafluorophosphate with acetonitrile and methanol at T = (298.15 to 318.15) K, /. Chem., Eng. Data, 50,1694,2005. Wang, J. et al.. Excess molar volumes and excess logarithm viscosities for binary mixtures of the ionic liquid l-butyl-3-methylimidazolium hexafluorophosphate with some organic solvents, /. Solution Chem., 34, 585, 2005. 

Heintz, A. et al.. Excess molar volumes and liquid-liquid equilibria of the ionic liquid l-methyl-3-octyl-imidazolium tetrafluoroborate mixed with butan-l-ol and pentan-l-ol, /. Solution Chem., 34,1135, 2005. 

The excess molar volumes of 10-40 mol % methanol/C02 mixtures at 26°C as a function of pressure has been determined. The excess molar volumes varied with composition and pressure significant interaction between CO2 and methanol was noted from the observed excess molar volumes. To better characterize the interaction and its effect on analyte solubility, the partial molar volume of naphthalene at infinite dilution in liquid 10 and 40 mol % methanol/C02 mixtures was determined. The variation of the partial molar volume at infinite dilution with pressure correlated well with isothermal compressibility of the methanol/C02 mixtures (Souvignet and Olesik, 1995). 

Tzou TZ. Density, excess molar volume, and vapor pressure of propellant mixtures in metered-dose inhalers deviation from ideal mixtures. Respir Drug Delivery YI, Int Symp 1998 439-443. 

Figure 17.4 Excess molar volumes at T= 298.15 K and p = 0.1 MPa for (a) (xiCmH2m + 2+ 2C-C6H 2) and (b) (xiCmH2m + 2 + x2n-C6Hi4). The numbers on the graph give m, the number of carbon atoms in the n-alkane.

Figure 17.5 Derived thermodynamic properties at T — 298.15 K and p = 0.1 MPa for (2Cic-CfiHi2 + X2n-CjHi4) (a) excess molar heat capacities obtained from the excess molar enthalpies (b) relative partial molar heat capacities obtained from the excess molar heat capacities (c) change of the excess molar volume with temperature obtained from the excess molar volumes and (d) change of the excess molar enthalpies with pressure obtained from the excess molar volumes.

Figure 17.6 Excess molar properties at p = 0.1 MPa for (X111-C7H16 +X2I-C4H9CI) (a) gives the excess molar enthalpies. The solid line represents values at T= 298.15 K, while the dashed line gives values changed to T = 323.15 K, using the excess molar heat capacities at T = 298.15 K shown in (b). The excess molar volumes at T= 298.15 K are shown in (c).

Remark 2 The reacting mixture is assumed to be an ideal solution (i.e., zero excess solution property). As a result of this assumption we do not need data of the excess molar volume as a function of the reacting components. 

For an ideal mixture, the enthalpy of mixing is zero and so a measured molar enthalpy of mixing is the excess value, HE. The literature concerning HE -values is more extensive than for GE-values because calorimetric measurements are more readily made. The dependence of HE on temperature yields the excess molar heat capacity, while combination of HE and GE values yields SE, the molar excess entropy of mixing. The dependences of GE, HE and T- SE on composition are conveniently summarized in the same diagram. The definition of an ideal mixture also requires that the molar volume is given by the sum, Xj V + x2 V2, so that the molar volume of a real mixture can be expressed in terms of an excess molar volume VE (Battino, 1971). 

Experimental determination of excess molar quantities such as excess molar enthalpy and excess molar volume is very important for the discussion of solution properties of binary liquids. Recently, calculation of these thermodynamic quantities becomes possible by computer simulation of molecular dynamics (MD) and Monte Carlo (MC) methods. On the other hand, the integral equation theory has played an essential role in the statistical thermodynamics of solution. The simulation and the integral equation theory may be complementary but the integral equation theory has the great advantage over simulation that it is computationally easier to handle and it permits us to estimate the differential thermodynamic quantities. 

In the two component systems, MCI-UCI3, evidence of chloroanion formation from excess molar volume changes was obtained when the cation M was large, M = K, Rb, or Cs (245-248), but not with M = Li or Na (248-251). 

The excess Gibbs energy of the ternary mixture was expressed through the Wilson [38], NRTL [39] and Zielkiewicz [32] expressions. Because of the agreement between the latter two expressions, detailed results are presented only for the more simple NRTL expression. The parameters in the NRTL equation were found by htting x-P (the composition of liquid phase-pressure) experimental data [32]. The derivatives (9 i/9xi) c2 ( IX2/dx2)xi and (diX2/dxi)x2 in the ternary mixture were found by the analytical differentiation of the NRTL equation. The excess molar volume (V ) in the binary mixtures (i-j) was expressed via the Redlich-Kister equation... 

Ci being parameters provided by [33]. The derivatives of the excess molar volumes in binary and ternary mixtures can be calculated using Eqs. (24)-(26) and thus the partial molar volumes can be obtained. 

However, none of the expressions available, including eq 25, can represent the extremum in the mixed Henryfs constant found in some experiments at low alcohol concentrations. Perhaps only very accurate representations of the activity coefficients and excess molar volume of the mixed solvent in the dilute region can explain this anomaly. 

The aim of this appendix is to evaluate the sensitivity of the integral in Eq. (12) to the ideality assumption of the molar volume. For this purpose, the composition dependence of (In y )/(V ) for the mixture water/l,4-dioxane at 25 °C was calculated for two cases (1) y = 0 (V being the excess molar volume) and (2) V 0 (the mixture water/1,4-dioxane was selected because it is the most frequently used mixed solvent considered in the present paper). The activity coefficient of water in water/1,4-dioxane mixture was calculated using the Wilson equation with the parameters provided by the Gmehling VLE compilation (Gmehling and Onken, 1977). The molar volume of the mixed solvent was calculated using the expression ... 

The composition dependence of the excess molar volume of the mixture water/1,4-dioxane at 25 °C was found in a paper by Aminabhavi and Gopalakrishna (1995). 

Bhujrajh P, Deenadayalu N. Liquid densities and excess molar volumes for binary systems (ionic liquids plus methanol or water) at 298.15, 303.15 and 313.15K, and at atmospheric pressure. J. Solut. Chem. 2007. 36, 631-642. 

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