Estimating the van der Waals and Redlich-Kwong Parameters from Critical Conditions

Estimating the van der Waals and Redlich-Kwong Parameters from Critical Conditions 

The a and b parameters in the RK and van der Waals class of equations are best estimated from a regression fit to an overall P-T-V data set for a gas, as described above. However, there is a much quicker way of estimating the same parameters based on the critical behavior of the gas. If these critical data are known with sufficient accuracy and precision, the estimates should be very good, and this approach is used quite frequently when the utmost accuracy is not required. Recall that the critical properties of a gas can also be used to estimate fugacities using the principle of corresponding states discussed in Chapter 11. 

Waals equation itself should also work at the critical point, so we can write the three following equations  

Solving these three equations for the critical constants gives 

We can apply exactly the same reasoning to the RK equation (16.7) and obtain 

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