Redlich and Kwong equation

In 1972, Soave published a method of calculating fugacities based on a modification of the Redlich and Kwong equation of state which completely changed the customary habits and became the industry standard. In spite of numerous attempts to improve it, the original method is the most widespread. For hydrocarbon mixtures, its accuracy is remarkable. For a mixture, the equation of state is ... 

In Example 1 the ideal gas law was used. To test if this law can be used, another, more accurate law, must be available. The REDLICH and KWONG equation appears to be well adapted for this purpose, both by its simplicity and its ease of application. This analytical state equation relates the pressure p, to the temperature T and the molar volume V ... 

To illustrate how an empirical equation may be used to calculate fugacity coefficients, we use the equation of Redlich and Kwong (R2), which generally gives satisfactory results for nonpolar fluids. This equation is... 

To obtain an analytic function / in Eq. (55), Chueh uses the Redlich-Kwong equation however, since the application is intended for liquids, the two constants in that equation were not evaluated (as is usually done) from critical data alone, but rather from a fit of the pure-component saturated-liquid volumes. The constants a and b in the equation of Redlich and Kwong are calculated from the relations... 

The modification of the Van der Waals equation by Redlich and Kwong [29], who introduced a different temperature dependence and a slightly different volume dependency in the attractive term, is very important since it opened the way to a better description of the temperature dependent properties like virial coefficients. 

Redlich and Kwong proposed an equation of state which takes into account the temperature dependencies of the molecular attraction term in a manner similar to Clausius.14... 

The search for better equations of state continues apace, since computers make the computational part relatively easy. Stryjek and Vera [14], for example, have developed a complex equation of state based on that of Redlich and Kwong, but which is suitable for representing the P-V-T behavior of liquid and gas phases over a wide range of temperature and pressure for pure nonpolar compounds. 

In liquids and solids, particles are very close together and repulsive forces play a much more important role than they do in gases. It is not surprising, therefore, that equations of state, such as those of van der Waals, and Redlich and Kwong, do not do a good job of predicting liquid and solid phase data. Usually, data for liquids and solid are presented in the form of thermal expansion coefficients and isothermal compressibilities. Some data for a and k of selected liquids and solids are given in Table 3. 

The modern development of cubic equations of state started in 1949 with publication of the Redlich/Kwong equation (Redlich and Kwong, Chem. Rev., 44, pp. 233-244 [1949]) ... 

In thermodynamics, the pressure-volume temperature relationships of real gases are described by the equation of state. The compressibility factor from the reduced pressure and temperature can be rearranged from Redlich and Kwong [9] to two constant state equations in the form... 

Redlich and Kwong (16) go one step further they introduce a weak temperature dependence into the second term, and obtain the well-known Redlich-Kwong (RK) equation ... 

The calculated values obtained from Equation 30, together with those obtained from the equations of Redlich et al. (10), Edmister et al. (II), Redlich and Kwong (I), and Sugie et al. (12) are compared with the Z values of Pitzer s work in Table III. The proposed equation provides the smallest standard deviation. 

In addition, the calculated and the experimental Z values of hydrogen sulfide (16), in the regions including gas, vapor, and liquid, are compared in Table V. The calculated results obtained from the equations of Redlich and Kwong (1) and Sugie et al. (12) also are included in this table for comparison. Again, the proposed equation yields the best results. 

Rules are proposed by Redlich and Kwong (I) for combining the pure-component parameters so the equation of state can be applied to mixtures... 

The equations of state most commonly used at the present time to represent gas behavior at moderate to high pressures are based on a simple modification of the van der Waals equation published by Redlich and Kwong in 1949 ... 

Fugacity coefficients of species in liquid or vapor mixtures can be obtained from (4-52). If the R-K equation of state is applied, a rather tedious procedure, as given by Redlich and Kwong, leads to the following working equations. 

The five-constant equation of Beattie and Bridgeman, the eight-constant equation of Benedict, Webb, and Rubin (B-W-R), and the two-constant equation of Redlich and Kwong (R-K), are empirical relationships applicable over a wide range of pressure. The R-K equation is particularly attractive because it contains only two constants and these can be determined directly from the critical temperature and critical pressure Pc-Furthermore, the R-K equation has an accuracy that compares quite favorably with more complex equations of state and if has the ability to approximate the liquid region, as is illustrated in the following example. The two-constant van der Waals equation can fail badly in this respect. 

It is fascinating to follow the iterations that began in the seventeenth century and are still being refined. Over the years, numerous authors modified the VDW equation of state e.g., Redlich and Kwong [1949], Soave [1972], Peng and Robinson [1976], Patel and Teja [1982], or Schwartzentruber et al. [1989]. Their relations, written as P = P V, T) are known as cubic equations of state, which are algebraically simple and relatively accurate [Wei, 1998 Valderrama and Alfaro, 2000] ... 

In the descriptions of pxue-fluid phase behavior presented in this section, we rely on the simple yet qualitatively realistic equation of state developed by Redlich and Kwong (4.5.66). That equation is cubic in the volume and can be written in a pressure-explicit form. 

The approximation to ideality is not very satisfactory for equilibrium reactions which occur at high pressure, such as the synthesis of ammonia. It is however generally assumed in chemical kinetics. To check the validity of this approximation, the Redlich and Kwong state equation (cf Chap. Ill) will be used. These authors have also suggested correlations which permit the fugacity coefficients to be estimated. ... 

A very widely used modification of the van der Waals equation published by Redlich and Kwong in 1949 is... 

Derive an expression for Hildebrandt solubility parameter as given by Equation (4.7) for the Redlich and Kwong EOS summarized as... 

Early in the history of development of equations of state, it was realized that the parameter a in the van der Waals equation of state had to be temperature dependent in order to correlate accurately the PVT properties of gases. Out of tens of modifications proposed in the first half of the 20 century, the most notable one was the equation proposed by Redlich and Kwong in 1949. The Redhch-Kwong equation of state is written as ... 

Generalized Equations of State.— Redlich and Kwong proposed the following modified form of equation (2) ... 

This equation - Redlich and Kwong (RK) - is much improved with regards to the Van der Waals equation but it is still unable to accurately describe the hquid state and therefore gas-hquid equilibria. For one mole, it takes the following form ... 

---