Standard value molar volume

At standard ambient temperature and pressure (SATP), which means exactly 25°C (298.15 K) and exactly 1 bar, the conditions commonly used to report data in chemistry, the molar volume of an ideal gas is 24.79 L-mol l, which is about the volume of a cube l ft on a side (Fig. 4.15). The expression standard temperature and pressure (STP) means 0°C and 1 atm (both exactly), the conditions formerly used to report data and still widely used in some calculations. At STP, the molar volume of an ideal gas is 22.41 I.-mol1. Note the slightly smaller value the temperature is lower and the pressure is slightly higher, and so the same amount of gas molecules occupies a smaller volume than at SATP. 

Determine the value of the gas constant R in units of ft3 atm/lb mol °R), starting with the value of the standard molar volume of a perfect gas. 

The four gas laws in the previous section are all special cases of the ideal gas law. We can use the ideal gas law to calculate the volume one mole of gas occupies at standard conditions. Standard conditions are 0°C (273 K) and 1 atm pressure. The volume at these conditions is known as a standard molar volume. Plugging the numbers into the ideal gas law equation gives a value of 22.4 liters for the standard molar volume. 

With most properties (enthalpies, volumes, heat capacities, etc.) the standard state is infinite dilution. It is sometimes possible to obtain directly the function near infinite dilution. For example, enthalpies of solution can be measured in solution where the final concentration is of the order of 10-3 molar. With properties such as volumes and heat capacities this is more difficult, and, to get standard values, it is usually necessary to measure apparent molal quantities 0y at various concentrations and extrapolate to infinite dilution (y° = Y°). Fortunately, it turns out that, at least with volumes and heat capacities, the transfer functions AYe (W — W + N) do not vary significantly with the electrolyte concentration as long as this concentration is relatively low (3). With most of the systems investigated, the transfer functions were calculated from apparent molal quantities at 0.1m and assumed to be equivalent to the standard values. 

In equations (18.91) and (18.92), C° 2 and V are the partial molar heat capacity and partial molar volume of the surfactant in the infinitely dilute solution (standard state values). 

Partial molar volumes and the isothermal compressibility can be calculated from an equation of state. Unfortunately, these equations require properties of the components, such as critical temperature, critical pressure and the acentric factor. These properties are not known for the benzophenone triplet and the transition state. However, they can be estimated very roughly using standard techniques such as Joback s modification of Lyderson s method for Tc and Pc and the standard method for the acentric factor (Reid et al., 1987). We calculated the values for the benzophenone triplet assuming a structure similar to ground state benzophenone. The transition state was considered to be a benzophenone/isopropanol complex. The values used are shown in Table 1. 

For a given set of values for H, V, and n, values of n, n", and n " can be calculated if the molar enthalpies and molar volumes of the three phases can be determined. The molar volumes can be obtained experimentally, but the absolute values of the molar enthalpies are not known. In order to solve this problem, we make use of the concept of standard states. We choose one of the three phases and define the standard state to be the state of the system when all of the component exists in that phase at the temperature and pressure of the triple point. If we choose the triple-primed phase as the standard phase, we subtract nH " from each side of Equation (8.50) and obtain... 

In Equations (10.43) and (10.44) Vf represents the partial molar volume of the component in the infinitely dilute solution, which is also the partial molar volume of the component in the standard state. The right-hand side of Equation (10.44) contains only quantities that can be determined experimentally, and thus A/j. [T, P, x] can be determined. However, just as in the previous case, the pressure is a function of the mole fraction. Therefore, if we require values of A/tf at some arbitrary constant pressure, the correction expressed in Equation (10.34) must be made with the substitution of Vf for... 

The value of R in SI units is 8.314 J/mol/K. We can calculate this from the standard molar volume in cubic meters and the standard pressure in pascals. 

With Tw a reference molar volume of gas, VG = RTJp0 = 24.782 dm3mol-1 is defined, which by chance is very close to the value of the standard volume V°G = RT°/p° = 24.79 dm3mol-. ... 

The best confirmations of the additivity of molar volume were obtained from the studies of homologous series. Studies of several series of compounds with increasing numbers of CH2 groups have led to rather accurate values for the contribution of this group to the molar volume. Values found by several investigators are summarised in Table 4.4. The mean value is 16.45 cm3/mol with a standard deviation of 0.2 cm3/mol. 

Since the value of the molar Van der Waals volume of a polymer is derived from universal values of atomic radii and atomic distances, it may be concluded that the method of calculation of the different standard molar volumes (1298 K) as given by Eq. (4.8) provides a sound basis for the estimation of polymer densities under standard conditions. 

Recommended values for group contributions to standard molar volume, 87 Recoverable shear, 531,551 Recoverable shear strain, 551 Recrystallisation, 703 Rectilinear flow, 527 Redox doping, 341 Reduced... 

You should also commit to memory the following values of the standard specific molar volume ... 

Remember from Chapter 11 that the most convenient unit for counting numbers of atoms or molecules is the mole. One mole contains 6.02 X 10 particles. The molar volume for a gas is the volume that one mole occupies at 0.00°C and 1.00 atm pressure. These conditions of temperature and pressure are known as standard temperature and pressure (STP). Avogadro showed experimentally that one mole of any gas will occupy a volume of 22.4 L at STP. The fact that this value is the same for all gases greatly simplifies many gas law calculations. Because the volume of one mole of a gas at STP is 22.4 L, you can use the following conversion factor to find the number of moles, the mass, and even the number of particles in a gas sample. 

The density of phosgene vapour under standard reference conditions was measured to be 4.526 [742] or 4.525 kg m 3 [1281]. Using the value of the standard molar volume, Vnj j, the density of the gas at 0 C and atmospheric pressure was calculated to be 4.413 kg m 3 Phosgene vapour is thus, unexpectedly, far removed from ideality. An attempt has been made to generalize the Benedict-Wee-Rubin equation of state using three polar parameters as part of a study of a large series of polar substances, which includes COClj as one of the examples [1518]. 

Negative values of standard reaction enthalpies indicate exothermic reactions, whereas positive values indicate endothermic reactions. Together with the molar volume, vaporization enthalpy is used in determining the —> Hildebrand solubility parameter. 

It is remarkable that no empirical mixture parameters and no experimental data are required to use the equation. The only parameters in the Flory-Huggins equation are the hard core volumes V, which are a pme-component property, and the atomic or group contribution values are found in standard compilations. Since the v/s are significant in the FH equation only in terms of their ratios, pure-liquid molar volumes are often used for V in place of hard core volumes. For solutions of polymers of the same chemical formula, molecular masses are legitimate substitutes for V , for the same reason. Thus the volume fractions ( ) can be substituted by mass fractions W . Either volume fraction or mass fraction is directly related to laboratory data. To avoid mole fractions, the activity tti from Equations (4.368) and (4.369) can be used to calculate by / = aj. ... 

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