Solute partial molar volume density

Figure 5 Calculated and experimental (1) solute partial molar volume ys. density at T = 1.37.

Problem 3.10 Osmotic pressure measurement was made at 27°C on an aqueous solution of a globular protein believed to be spherical in shape. For a solution of concentration 1 mg/cm the osmotic head was 1.64 mm water and for 5 mg/cm it was 8.31 mm water. The number average molecular weight of the protein is 1,56,500 and its specific volume is 0.75 cm g. Calculate the excluded volume of the protein and compare your result with the partial molar volume. Density of water at 27°C is 0.996 g/cm. ... 

When a component A is added to a solvent, there is a volume change usually the volume increases but occasionally it decreases. The volume change on adding 1 mol of A is termed the partial molar volume, and it is denoted by It is dependent on all the thermodynamic conditions the temperature, the pressure, the nature of the solvent, the concentration of A, the concentration of all the other solutes, and any other pertinent thermodynamic variables. Measuring is equivalent to measuring the solution density at specified conditions, a measurement that can be made quite accurately. For stable solutes, partial molar volumes are frequently quoted to a precision of 0.01 cm mol It often suffices to consider only the partial molar volume at... 

The effect of pressure on chemical equilibria and rates of reactions can be described by the well-known equations resulting from the pressure dependence of the Gibbs enthalpy of reaction and activation, respectively, shown in Scheme 1. The volume of reaction (AV) corresponds to the difference between the partial molar volumes of reactants and products. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state (TS) with respect to the partial molar volumes of the reactants. Volumes of reaction can be determined in three ways (a) from the pressure dependence of the equilibrium constant (from the plot of In K vs p) (b) from the measurement of partial molar volumes of all reactants and products derived from the densities, d, of the solution of each individual component measured at various concentrations, c, and extrapolation of the apparent molar volume 4>... 

Table 18.6 show the experimental results of Gucker et al. [10] for the molar concentration of urea, the density p of the solutions in grams per liter, and the partial molar volume of urea in cm calculated from the density data. 

Previous experimental and theoretical studies have found what appears to be clear evidence for cluster formation, or local density enhancement, in near critical solutions (7t12t42-45). These include experimental optical absorption, fluorescence and partial molar volume measurements as well as theoretical simulation studies. These offer compelling evidence for local solvent density enhancement in near critical binary SCF systems. Theoretical models suggest that local density enhancement should be strongly dependent on the relative size and attractive force interactions strengths of the solute and solvent species as well as on bulk density and temperature (7,44). 

The reaction volume may be of interest in itself, and furthermore its determination can provide a route to the volume of activation in the reverse direction if that parameter is not experimentally accessible and when AV for the reaction in the forward direction is known. As indicated above, AV may be determined from the dependence upon pressure of the equilibrium constant. It may also be obtained under certain circumstances from the partial molar volumes of the reactants and products. Density measurements d are made on several solutions of different concentrations of the reactant(s) and the product(s). The following equation is used to obtain the apparent molar volume of each species, tp, at each molar concentration c. 

The density of the solvent is d0 and MW is the molar mass of the solute. The values of the apparent molar volume are plotted against concentration and the partial molar volume of a species is the value obtained by extrapolation to zero concentration. 

Molar concentration units were converted into molal units using the partial molar volume of the salt. (W e assume that RNA and other buffer components are present in such low concentrations that the density of the solution is not significantly different than a solution of water and salt alone.) The formula is... 

The effect of temperature, pressure and density on solute retention (k1) in supercritical fluid chromatography (SFC) has been well studied.(1-6) Retention in SFC depends upon both solute solubility in the fluid and solute interaction with the stationary phase. The functional relationship between retention and pressure at constant temperature has been described by Van Wasen and Schneider. ( 1 ) The trend in retention is seen to depend on the partial molar volume of... 

Careful consideration was taken in the parameterization process to insure that the parameters were deemed reasonable for the atom types, using the OPLS-AA force field atom types as a comparison. As one of the goals of this project was to ensure that robustness was achieved in many different calculated properties of the newly developed model, several sets of simulations were also performed to ensure that the parameters could achieve a reasonable agreement with experiment. Some of the properties calculated included the gas phase density, the partial molar volume in aqueous solution, and the bulk solvent structure as well. The calculation of the solubility was discussed in the previous section for the parameterization process and the viewing of these results, the solubility will be reported in log S values, as many of the literature values are reported as log S values, and therefore, the comparison would not lose any sensitivity due to rounding error from the log value. 

In this experiment the partial molar volumes of sodium chloride solutions will be calculated as a function of concentration from densities measured with a pycnometer. 

This equation tells one that the density of the solution that gives for a series of concentrations gives the partial molar volume t/ at any value of n - Knowing from and / , Eq. (2.7) can be used to obtain as a function of n - Extrapolation of Vto /ij = 0 gives the partial molar volume of the electrolyte at infinite dilution, V (i.e., free of interionic effects). 

The densities of aqueous NaCl solutions at 25°C are given as a function of NaCl molality in Table P.5, (a) Obtain a graph for the partial molar volumes of both water V, and NaCl V2, as a function of NaCl molality. Compare the limiting cases V, (m 0), (m sat) with those of pure water and pure NaCl molar volumes, Vj and V, respectively, (b) Calculate Vj for m = 0.5 and m = 2. (Mussini)... 

Table P.6 gives the density of a number of solutions of AgCl. Find the apparent molar volume of the electrolyte at each concentration. Then, by using the method described in the text, find the partial molar volume of the electrolyte at infinite dissolution. 

The magnitude of the fluctuations in volume (dilatation) and density (condensation) associated with US wave is controlled by the properties of the medium and the applied forces. The velocity of sound in mixtures and suspensions will therefore be controlled by the mean density and mean compressibility as expressed by the Urick equation (see Eq.9.7-9.10). The equation can be formulated in terms of partial molar volumes by forming an identity between the volume fraction of the solute, its partial volume Vm2), the mean molar volume of the solution Vm) and the mole fraction Cm) as follows ... 

The composition dependence of the total volume of a solution at constant temperature and pressure is expressed in terms of the partial molar volumes of the solute and the solvent. Since we are concerned with solvation properties, the quantities which we need to discuss are the partial molar volumes in infinite dilution of the solute so that solute-solute interactions make no contribution. In practice, partial molar volumes are obtained indirectly from precise density measurements. The partial molar volumes at infinite dilution of the amino acids are compiled in Table 2 [7]. It is apparent from these data that an approximately linear correlation exists between the partial molar volume and the number of carbon atoms in the backbone. The data indicate volume contributions from the polar head group (NH, COj) and from the CH2 group and to be about... 

Source of Data. There are only a few local density data, and partial molar volumes of solutes at infinite dilution are scarce as well. Only two systems could be identified for which data for the calculation of the correlation volume are available CO2 + naphthalene and CO2 + pyrene. The augmented local density data in these systems were taken from ref 24 and the partial molar volume of the solute at infinite dilution in CO2 + naphthalene system from ref 8. Because the partial molar volume of the solute at infinite dilution for the CO2 + pyrene system was not available, it was taken equal to that for the CO2 + phenanthrene. The density and compressibility of the pure SCR CO2 were taken from refs 1 and 24, respectively, and the solubilities of naphthalene and p)rene in SCR CO2 from refs 28 and 29, respectively. 

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