Gas constant numerical value

In Section 2.1.1 we saw that, for an ideal gas, the numerical values of the pressure, p, and volume, v, are related according to/>°c 1/v, or p — c/v, where c — nrt (a constant). We can now explore how well the ideal gas law works for a real gas by considering experimental data1 for 1 mol of C02 at T=313 K. The ideal gas law suggests that pressure is inversely proportional to the volume and so in the first two rows of Table 2.3 we present the variation of p with 1/v for the experimental data (note that the working units for the pressure and volume in this case are atm and dm3, respectively). In the third row, we show values for l/vB, obtained using the ideal gas equation, where, in this case, the constant of... 

The term R in the ideal-gas equation is the gas constant. The value and units of R depend on the imits of P, V, n, and T. The value for T in the ideal-gas equation must always be the absolute temperature (in kelvins instead of degrees Celsius). The quantity of gas, , is normally expressed in moles. The units chosen for pressure and volume are most often atmospheres and liters, respectively. However, other units can be used. In most countries other than the United States, the pascal is most commonly used for pressure. M TABLE 10.2 shows the numerical value for R in various units. In working with the ideal-gas equation, you must choose the form of R in which the units agree with the units of P, V, n, and T given in the problem. In this chapter we will most often use R = 0.08206 L-atm/mol-K because pressure is most often given in atmospheres. 

The equilibrium constant in Eq. 2 is defined in terms of activities, and the activities are interpreted in terms of the partial pressures or concentrations. Gases always appear in K as the numerical values of their partial pressures and solutes always appear as the numerical values of their molarities. Often, however, we want to discuss gas-phase equilibria in terms of molar concentrations (the amount of gas molecules in moles divided by the volume of the container, [I] = j/V), not partial pressures. To do so, we introduce the equilibrium constant Kt., which for reaction E is defined as... 

It follows from these eqnations that in dilute ideal solutions, said effects depend only on the concentration, not on the nature of the solute. These relations hold highly accnrately in dilnte solntions of nonelectrolytes (up to about lO M). It is remarkable that Eq. (7.1) coincides, in both its form and the numerical value of constant R, with the eqnation of state for an ideal gas. It was because of this coincidence that the concept of ideality of a system was transferred from gases to solntions. As in an ideal gas, there are no chemical and other interactions between solnte particles in an ideal solution. 

The gas constant R is generally given the value 8.314 J K 1 mol 1, but in fact this numerical value only holds if each unit is the SI standard, i.e. pressure expressed in pascals, temperature in kelvin and volume in cubic metres. 

The value of R changes if we express the ideal-gas equation (Equation (1.13)) with different units. Table 2.3 gives values of R in various other units. We must note an important philosophical truth here the value of the gas constant is truly constant, but the actual numerical value we cite will depend on the units with which we express it. We met a similar argument before on p. 19, when we saw how a standard prefix (such as deca, milli or mega) will change the appearance of a number, so V = 1 dm3 = 103 cm3. In reality, the number remains unaltered. 

Although one can probably find exceptions, most equilibrium calculations involving flue gas slurries are performed with temperature as a known variable. With temperature known, the numerical values of the appropriate equilibrium constants can be immediately calculated. The remaining unknown variables to be determined are the activities, activity coefficients, molalities, and the gas phase partial pressures. The equations used to determine these variables are formulated from among the equilibrium expressions presented in Table 1, the expressions for the activity coefficients, ionic strength, material balance expressions, and the electroneutrality balance. Although there are occasionally exceptions, the solution sequence generally is an iterative or cyclic sequence. 

The procedure of Beutier and Renon as well as the later on described method of Edwards, Maurer, Newman and Prausnitz ( 3) is an extension of an earlier work by Edwards, Newman and Prausnitz ( ). Beutier and Renon restrict their procedure to ternary systems NH3-CO2-H2O, NH3-H2S-H2O and NH3-S02 H20 but it may be expected that it is also useful for the complete multisolute system built up with these substances. The concentration range should be limited to mole fractions of water xw 0.7 a temperature range from 0 to 100 °C is recommended. Equilibrium constants for chemical reactions 1 to 9 are taken from literature (cf. Appendix II). Henry s constants are assumed to be independent of pressure numerical values were determined from solubility data of pure gaseous electrolytes in water (cf. Appendix II). The vapor phase is considered to behave like an ideal gas. The fugacity of pure water is replaced by the vapor pressure. For any molecular or ionic species i, except for water, the activity is expressed on the scale of molality m ... 

Note 3 Numerical values of the molar entropy of transition should be given as the dimensionless quantity AxyS/R where R is the gas constant. 

Of course, the constant has a different numerical value in each of these equations.) For a monatomic ideal gas, these equations take the more specific form corresponding to (3.84b) ... 

Eq. (3.9) arises from the absolute rate theory and can be expressed in the following logarithmic form, using the numeric values of the Boltzmann constant k, the gas constant R, the Planck constant h, and loge [108]. 

The numerical value of the constant in formula (18), as experiments and calculations by Shchelkin and Shaulov in the combustion laboratory at the Institute of Chemical Physics show, is of order 100 (all quantities—flame velocity, thermal conductivity—are in the cold gas). 

The numerical value of the conductance of a component in a vacuum system depends on the type of flow in the system. Gas flow in simple, model systems (e.g. tubes of constant circular cross-section, orifices, apertures) was considered for viscous flow (Examples 2.6-2.8) and molecular flow (Examples 2.9-2.11). The chapter concluded with two illustrations (Examples 2.13, 2.14) of Knudsen (intermediate) flow through a tube. 

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