Molar volume temperature dependence

Molarity (M) mol solute L solution Useful in stoichiometry measure by volume Temperature-dependent must know density to find solvent mass... 

Molarity is temperature dependent simply because it is expressed as mole/volume. Volume is temperature dependent—most liquids expand measurably when heated and contract when cooled. Molality is moles/mass both moles and mass are temperature independent... 

Concentrations are independent of temperature if based solely on mass or temperature-independent properties related to mass, specifically, mass percent, molality, mole fraction, and mole percent. Concentrations based on volumes—volume percent and molarity—are temperature dependent. 14-3. HCl is undissociated in C6H6(1), and the concentration of HCl in C6H6(1) should closely follow PHCi(g) above the solution. On the other hand, HCl(g) reacts with H20(l) to produce H30 (aq) and Cl (aq). The relationship between PHCi(g) end the aqueous concentrations of ions is more complex. 14-4. Start with (Pa - Pa)/Pa = Note that ( A - Pa)/Pa = 1 - PJP )-According to Raoult s law, a = xaPai which means that Pa/Pa = Thus, we arrive... 

Since we make the simplifying assumption that the partial molar volumes are functions only of temperature, we assume that, for our purposes, pressure has no effect on liquid-liquid equilibria. Therefore, in Equation (23), pressure is not a variable. The activity coefficients depend only on temperature and composition. As for vapor-liquid equilibria, the activity coefficients used here are given by the UNIQUAC equation. Equation (15). ... 

Molality is used in thermodynamic calculations where a temperature independent unit of concentration is needed. Molarity, formality and normality are based on the volume of solution in which the solute is dissolved. Since density is a temperature dependent property a solution s volume, and thus its molar, formal and normal concentrations, will change as a function of its temperature. By using the solvent s mass in place of its volume, the resulting concentration becomes independent of temperature. 

The virial equations are unsuitable forhquids and dense gases. The simplest expressions appropriate (in principle) for such fluids are equations cubic in molar volume. These equations, inspired by the van der Waals equation of state, may be represented by the following general formula, where parameters b, 9 5, S, and Tj each can depend on temperature and composition ... 

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

The concept of equilibrium is central in thermodynamics, for associated with the condition of internal eqmlibrium is the concept of. state. A system has an identifiable, reproducible state when 1 its propei ties, such as temperature T, pressure P, and molar volume are fixed. The concepts oi state a.ndpropeity are again coupled. One can equally well say that the properties of a system are fixed by its state. Although the properties T, P, and V may be detected with measuring instruments, the existence of the primitive thermodynamic properties (see Postulates I and 3 following) is recognized much more indirectly. The number of properties for wdiich values must be specified in order to fix the state of a system depends on the nature of the system and is ultimately determined from experience. 

Temperature, pressure, and composition are thermodynamic coordinates representing conditions imposed upon or exhibited by the system, andtne functional dependence of the thermodynamic properties on these conditions is determined by experiment. This is quite direct for molar or specific volume which can be measured, and leads immediately to the conclusion that there exists an equation of. state relating molar volume to temperature, pressure, and composition for any particular homogeneous PVT system. The equation of state is a primaiy tool in apphcations of thermodyuamics. 

Solubility parameters are generally tabulated, together with the corresponding liquid molar volumes, only at 25°C. Although solubility parameters are themselves temperature-dependent, the combination of quantities in Eq. 70 is not. Differentiating Eq. 70 with respect to temperature gives — the excess entropy, a quantity which has been assumed to be zero in accord with the definition of a regular solution. Thus only data at 25°C are needed. Solubility parameters may be... 

Next we consider a molecular crystal composed of N2 molecules, (Vp = 0). Molecular N2 solids at low temperatures and low pressures are in the a structure (Pa3). Using PIMC simulations we studied the low temperature properties of N2 sohds [260] (B = 2.88 K, = 500). In Fig. 6 the temperature dependence of the molar volume is shown for our simulational as well as for experimental [289] data. We note that the classical simulations (corresponding to P = 1) lead to a nonzero slope of the volume at very low temperatures, which is in sharp contrast to the experimental behavior [289]. 

In this approach, connectivity indices were used as the principle descriptor of the topology of the repeat unit of a polymer. The connectivity indices of various polymers were first correlated directly with the experimental data for six different physical properties. The six properties were Van der Waals volume (Vw), molar volume (V), heat capacity (Cp), solubility parameter (5), glass transition temperature Tfj, and cohesive energies ( coh) for the 45 different polymers. Available data were used to establish the dependence of these properties on the topological indices. All the experimental data for these properties were trained simultaneously in the proposed neural network model in order to develop an overall cause-effect relationship for all six properties. 

From (5) we see that the molar volume of ammonia at 25°C and one atmosphere pressure is 24.5 liters, whereas it is 22.4 liters at 0°C. The molar volume of ammonia depends upon the temperature. This result is no surprise—a sample of gas expands when heated at constant pressure. So when we compare the molar volumes of different gases, they should be at the same temperature (and, by the same sort of argument, at the same pressure). 

In the past, it has been customary to assume that partial molar volumes depend only on temperature and are independent of composition and pressure (Cl, P13). This assumption is very poor in the critical region. Primarily... 

In their correlation, Chao and Seader use the original Redlich-Kwong equation of state for vapor-phase fugacities. For the liquid phase, they use the symmetric convention of normalization for y and partial molar volumes which are independent of composition, depending only on temperature. For the variation of y with temperature and composition, Chao and Seader use the equation of Scatchard and Hildebrand for a multicomponent solution ... 

We start by noting that any dependent thermodynamic variable Z is completely specified by two — and only two — independent variables X and Y (if n held constant). As an example, the molar volume of the ideal gas depends upon the pressure and temperature. Setting p and T fixes the value of Vm through the equation... 

There is an unfortunate consequence of replacing segment fraction by volume fraction. For given composition (weight or mole fraction), volume fraction is temperature dependent because molar volume is temperature dependent. 

Batsanov et al. 23) reacted sulfur with PtCU and PtBr2 by heating mixtures of the reactants in evacuated, sealed ampoules. At 100 -200°C after 12-24 h, sulfide chlorides PtCljS (1.70 < x < 2 0.6 s y < 3.35) and sulfide bromides PtBr S (1.87 < x 2.06 0.84 y s 1.80) were formed. The compositions depended on the initial PtX2 S ratio, and the temperature. At 320-350°C, loss of chlorine led to the compounds PtClS (1.7 y 1.9). According to their X-ray powder patterns, all of these products retained the main structural features of the original platinum halides. From considerations of molar volumes, the authors deduced the presence of polysulfide anions. 

A main objective of the work of Hardt et al. was to study the influence of heat transfer on the achievable molar flux per unit reactor volume of the product species. They compared unstructured channels to channels containing micro fins such as shown in Figure 2.31. Heat transfer enhancement due to micro fins resulted in a different axial temperature profile with a higher outlet temperature in the reaction gas channel. Owing to this effect and by virtue of the temperature dependence... 

M is the molar mass and Vm the molar volume expressed in litres, which, if compared with the vapour produced by a perfect gas, gives, depending on the temperature at which Cgq is measured ... 

Both molarity (Chap. 10) and normality (Chap. 15) are defined in terms of a volume. Since the volume is temperature-dependent, so are the molarity and normality of the solution. Two units of concentration that are independent of temperature are introduced in this chapter. Molality is defined as the number of moles of solute per kilogram of solvent in a solution. The symbol for molality is m. Note the differences between molality and molarity ... 

Before the raw data can be fitted to a thermodynamic model it must first be converted into mass or mole fractions. This operation can be accomplished quickly using a Microsoft Excel spreadsheet that is linked to the Aspen. aprbkp file in order to obtain the solvent molecular weights and temperature dependent densities. The molar volume of Form A Cimetidine is also required for this conversion, however, as is often the case it was not available so a density of 1 g/ml has been assumed. 

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

The so-called glass transition temperature, Tg, must be considered below this temperature the liquid configuration is frozen in a structure corresponding to equilibrium at Tg. Around Tg a rather abrupt change is observed of several properties as a function of temperature (viscosity, diffusion, molar volume). Above 7 , for instance, viscosity shows a strong temperature dependence below Tg only a rather weak temperature dependence is observed, approximately similar to that of crystal. Notice that 7 is not a thermodynamically defined temperature its value is determined by kinetic considerations it also depends on the quenching rate. 

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