# Kwong Equations

Improved Essays
Kwong equations are mainly used as they are simple and a temperature-dependent correction is used for EOS constant A. van der Waals Equation van der Waals proposed the first cubic EOS in 1873. The van der Waals EOS gives a simple, qualitatively accurate relation between pressure, temperature, and molar volume.
P=RT/(V-b)-a/V^2
where a is “attraction” parameter, b is “repulsion” parameter, and R is universal gas constant. Comparing this equation with the ideal gas law,P= zRT/v, we see that the van der Waals equation offers two important improvements. The prediction of liquid behavior is more accurate because volume approaches a limiting value 'b' at high pressures i.e, lim┬(p=∞)⁡〖V(p)=〗 b
The cubic Z-factor equation can readily be solved with an analytical or a trial-and-error approach. One or three real roots may exist, where the smallest root (assuming that it is greater than b) is typically chosen for liquids and the largest root is chosen for vapors. The middle root is always discarded as a nonphysical value. For mixtures, the choice of lower or upper root is not known a priori and the correct root is chosen as the one with the lowest normalized Gibbs energy, g*. where, gy=∑_(i=1)^n▒〖(ln⁡(〗 fi(y))*yi) gx=∑_(i=1)^n▒〖(ln⁡(〗 fi(x))*xi) where yi and xi = mole fractions of vapor and liquid, respectively, and fi = multicomponent fugacity
But in RK EOS all components have a critical compressibility factor of Zc=1/3, where, in fact, Zc ranges from 0.29 for methane to 0.2 for heavy C7fractions. The Redlich-Kwong value of Zc=1/3 is reasonable for lighter hydrocarbons but is unsatisfactory for heavier components. Even the vapour pressure calculated from it were
Here, alpha= (1+m(1-(Tr)0.5))2 and m= 0.480+ 1.574w-0.176w2
But there are some demerits of this equation too: BIP’s is recommended to be kij=0 for HC/HC pairs It grossly overestimates liquid volumes (and underestimates liquid densities) of petroleum mixtures
Even though it has some demerits it is still used as it offers an excellent predictive tool for systems requiring accurate predictions of VLE and vapor properties.
Peng and Robinson EOS
Peng robinson proposed a slightly different form of molecular attractive term so it eliminates the deficiency of liquid density prediction from SRK EOS.
For Peng and Robinson EOS: U=2, W=1 so PR EOS is P= RT/(V-b) - a/(V^2+2Vb-b^2 )
It can be written in terms of Z factor by putting (U=2, W=1) in equation 6
Z3 + Z2(B - 1)+ Z(A - 3B2 - 2B) -(AB -B3 -B2) =0 from equation 3, 4 and 5, we get

## Related Documents

• Superior Essays

The 1st limitation is that Beer’s law considers that the radiation reaching the sample is of a single wavelength i.e. that the radiation is purely monochromatic. however, even the best wavelength selector passes radiation with a small, but finite effective bandwidth. Polychromatic radiation always gives a negative deviation from Beer lambert’s law, but the effect is smaller if the value of ε is essentially constant over the wavelength range passed by the wavelength selector. For this reason, it is better to get absorbance measurements at the top of a broad absorption peak.…

• 1410 Words
• 6 Pages
Superior Essays
• Improved Essays

3.4.2.2. Mobile Phase Methanol, Acetonitrile, Water or any of their combination is generally reported to be compatible with Reverse Phase C-18 column, however other mobile phases can also be used [39]. Combination of Acetonitrile (ACN) and water is used in ration of 70:30 in this analysis. 3.4.3. Column length 25 cm column was selected because it gave better separation and delayed retention time for DPA, thus excluding the early peaks given with 10 cm column.…

• 715 Words
• 3 Pages
Improved Essays
• Improved Essays

However, there are three types of deviations between the results and the theoretical ones which can not be neglected. One of them is the “reversibility of the initial heterolysis” (O. T. Benfey, E. D. Hughes, and C. K. Ingold, J. Chem. Soc. 2489) which makes the reaction a pure first-order one at the beginning but slower than it should be in the later period. One sort of examples are the hydrolysis reactions of diarylmethyl halides.…

• 1114 Words
• 5 Pages
Improved Essays
• Improved Essays

4.2 Resources CO2 Fig.1 depicts the principle of chemical energy transmission system. Fig.2 explain the Eva-Adam process. 5. Thermodynamics of CO2 reforming of methane It is essential to understand the thermodynamic of CDRM represents as follow: CH_4+CO_2 □(→) 2CO+〖2H〗_2 ∆H_298=247 KJ⁄(mol ) (1) ∆G^o=61770-67.32 T This reaction above is highly endothermic which is favored by low pressure but, requires a higher temperature. A reverse water-gas shift reaction occurs as a side reaction as below CO_2+H_2 □(→) CO+H_2 O ∆H_298=41 KJ⁄(mol ) (2) ∆G^o=-8545+7.84 T Under conditions of stoichiometric CO2 reforming, carbon deposition…

• 1143 Words
• 5 Pages
Improved Essays
• Superior Essays

Hence, this concentration of Xanthan and Chitosan was taken as the optimum value. The bead diameter decreases with increase in concentration and viscosity of encapsulation solution.25 Another important observation made here is that at concentration of Xanthan and Chitosan at 0.75%, a mixture of stable as well as unstable capsules were formed. This can be attributed to the fact that the concentration of both Xanthan and Chitosan is close to the limits of workability range. Similarly when Xanthan concentration was approaching to that of 2%, the capsules were a mixture of both amorphous and stable ones. All the size was average of 10 capsules each from 3…

• 1096 Words
• 5 Pages
Superior Essays
• Superior Essays

Crushed quart filler is mainly “inert”at room temperature, however, is able to improve workability considerably in M-S-H ternary system (MgO-SF-QF). Fillers content is effective from 10-40% of the binder without clear optimal…

• 1558 Words
• 7 Pages
Superior Essays
• Improved Essays

Acid base titrations: A titration is the addition of a measured volume of one solution, from a burette, to an unknown volume/concentration of another solution until the reaction between then is complete. An acid base titration is carried out to determine an unknown concentration by using a solution of known concentration. An indicator is used to show a dramatic and rapid colour change, at the end point of the titration. Preparing a standard solution: The substance used for the standard solution must have a high degree of purity, preferably solid, because this is easier to measure (using a scale) and the substance can’t absorb water or release water. Oxalic acid and anhydrous sodium carbonate are used to make the standard solutions.…

• 803 Words
• 4 Pages
Improved Essays
• Improved Essays

The Ideal Gas Law relates several variables of state of an ideal gas with the following equation: P V = n R T, where P is the pressure of the gas in atmospheres, V is the volume of the gas in liters, n is moles of the gas, and T is the temperature of the gas in Kelvin degrees. R is the ideal gas constant. The Ideal Gas Law is a combined summary of Boyle’s Law, Charles’s Law, and the Avogadro’s Law. This Law works best under low pressure, room temperature (298K) environments because these environments allow gases to behave ideally, namely to assume that these gas molecules are point masses with no significant volume, experience little interaction with each other, and that all collisions (whether with each other or with the walls of the container)…

• 752 Words
• 4 Pages
Improved Essays
• Improved Essays

The errors in these solutions must have canceled out which would explain why the last solution, 0.500M, did not have a large percent error. Figure 1 was created to prove the Beer-Lambert Law by showing the linear relationship between concentration and absorbance of colored solutions. Since the R2 value is so close to one, it can be concluded that the relationship is valid. The chart is essential to the lab because the concentration of the unknown and the made CuSO4 solutions cannot be found without the equation that was derived from the linear trend…

• 733 Words
• 3 Pages
Improved Essays
• Superior Essays

Therefore, for each mole of Mg used, the same amount of H2 will be produced. Avogadro’s Law states this information: (V1/N1 = V2/N2). In this case, N = the gas’s mole count. Finally, Dalton’s Law of Partial Pressures states that the total pressure exerted by something is equal to the sum of the partial pressures of the individual gases and other substances (Physical Science Department, 1), has an impact on the experimental calculations. Dalton’s Law was relevant in this experiment because it can be used to find the partial pressure exerted by the hydrogen by itself.…

• 1765 Words
• 8 Pages
Superior Essays